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AN ABSTRACT OF THE THESIS OF Mary Lynn Roush for the degree of Doctor of Philosophy in Crop Science presented on April 29, 1988. Title: Models of a Four-species Annual Weed Community: Growth. CompetiO.on and Community Dynamics. Abstract approved:_ Redacted for privacy Steven R. Radosevich Models of weed communities aid in the development of weed management strategies and elucidate the processes and mechanisms that regulate plant populations and communities. A conceptual weed community model was developed to organize key regulatory life-history processes. Specific investigations focused on the processes of plant growth and competition, and relationships between growth ability and competitive ability. Plant competition was investigated from two perspectives: the intensity of competition and the importance of competition. Intensity is the response of a plant to competition; importance is the role of competition in regulating populations and communities. Recent applications of fundamental yield-density relationships have enhanced interpretations that can be made about the mechanisms and implications of competition. Plant growth and competition experiments were conducted for a community of four annual weed species to 1) quantify competition intensity using yielddensity relationships, 2) link processes of plant growth and competition, and 3) characterize the importance of competition in the community. The weed species were Amaranthus retroflexus L., Chenmodium album L., Echinochloa crus-galli L., and Lolium multiflorum Lam.. Experiments were conducted for two years in the field, using isolated, container-grown individuals for growth analysis, and an addition series design for competition. Results indicated strong relationships between plant growth traits and competitive abilities; however, these relationships were sensitive to variation in the environment. Yield-density models and population models suggested that the role of competition in population dynamics varied for the four species, and indicated that other key life-history processes may significantly influence the weed community. In particular, seed bank dynamics and interactions between the environment (temperature and light) and growth, competition and seed bank processes were emphasized for further development and implementation of the weed community model. Models of a Four-species Annual Weed Community: Growth, Competition, and Community Dynamics. by Mary Lynn Roush A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Completed April 29, 1988 Commencement June 1988 APPROVED: Redacted for privacy Professor of Crop Science in charge of major Redacted for privacy Head of Department of Crop Science Redacted for privacy Dean of Gradu e School Date thesis presented April 29, 1988 "To laugh often and much; to win the respect of intelligent people and the affection of children; to earn the respect of honest critics and endure the betrayal of false friends; to appreciate beauty; to find the best in others; to leave the world a little better place than we found it, whether by a healthy child, a garden patch or a redeemed social condition; to know even one life breathed easier because you lived. This is to have succeeded." Ralph Waldo Emerson ACKNOWLEDGEMENTS Encouragement, input, and constructive criticism from advisors and peers played a tremendous role in the success of this dissertation. I would like to take this opportunity to recognize some of the individuals that contributed to my research and to my growth as a scientist and individual. This research also was supported by the USDA Competitive Grants Program. Dr. Steven Radosevich is an artist in the advising and directing of graduate students. I came to a surprising revelation near the end of my Ph.D. degree. The research began to develop in 1981-1982, after I visited with Steve about potential avenues for investigating weed ecology. Steve suggested a few vague ideas about growth rates and competition. Several grant proposals, experi- ments, and papers later, I had developed 'my' research project. The revelation was that 'my' research project was exactly what Steve had been talking about all along. Through Steve's assistance, I focused those initial ideas, clarified them, and drew from them a strong experimental approach to understand plant-plant interactions. Steve's art rests on encouragement, inspiration, and subtle direction. However, his contributions transcend the research itself. As a mentor and friend, Steve has influenced, enhanced, and enriched my intellectual development and my personal growth. ii I also acknowledge the assistance, direction, and fellowship of the other advisors on my committe. I appreciate their time and attention, and I feel fortunate to consider all of them good friends. Dr. Mark Wilson taught me about the rigors of ecology and the scientific method. Mark inspired me to organize and define my research because I always expected from Mark careful scrutiny of the logic, structure, and relevance of my work. His thoughtful and careful review of this manuscript was extremely valuable. Mark also helped me bridge the gap between relating as studentprofessor and as peers and friends. Dr. Arnold Appleby taught me, by teaching and by example, about the 'heart and soul' of weed science. I am truly inspired by his conscientious commitment to stay current with advances in basic weed science and to serve the regional needs of weed managers. Dr. Paul Doescher was a source of enthusiasm and inspiration. Unlike the many 'ecofizzers' who seem to prefer the 'tools' to the questions, he has an insightful, problem-solving approach to study plantenvironment interactions in range systems. I was fortunate to have more than a grad-rep in Dr. David Hibbs. As an active member of our 'competition' group, he provided many insights about research on plant interactions and vegetation management. iii I also wish to acknowledge my fellow graduate students/co-workers/friends that enriched the research and my life. They offered their hands in the field, their ears and minds in the lab, and their hearts and smiles in many times and places. For their contributions of science, non-science, and nonsense, I would like to acknowledge 'the group': Pam Bold, Sam Chan, Julie Concannon, Jimmy Dukes, Abdul Hashem, Tim Harrington, Bruce Maxwell, Terry Peterson, Lauri Shainsky, Suzanne Simard, Bernal Valverde, and Bob Wagner. In particular, I would like to recognize Bruce Maxwell for his passionate approach to science. Bruce, a true twentieth century Darwinian, has an unbounded curiosity, coupled with amazing energy and tenacity. Although his activities in the field and on the computer often left me breathless, I look forward to following his whirlwind of research as he develops his career. I thank Julie Concannon for her effervescence, innocence, and trust and faith in me. As a coworker and friend, she was my extra eyes, ears, and shoulders in many times of need. I particularly enjoyed witnessing her amazing transition and development as a scientist. What began as pure unbridled energy was progressively harnessed and focused. But through it all she maintained her values and her enthusiasm. iv Lauri Shainsky and I have travelled many roads together since we first met in the Advanced Ecology course at U.C. Davis, Fall 1981. We have shared both scholarship and fellowship. Through many of our shared experiences, I have learned about the strength and the vulnerability of the human spirit, and the value of friendship. Last but not least I acknowledge my family. I appreciate both my parents, who supported and encouraged me from the start. They taught me to expect no less than excellence from myself, and I learned much from their examples: my mom's hunger for achievement and perfection, my dad's commitment, patience, and endurance (and his copies of American Scientist at a key point in my early education). Second, I thank my two wonderful sons that helped each new day begin with joy. Kyle arrived at the close of the first field season. Nickolas arrived during analysis and synthesis. They are an endless source of pride and happiness, two sparkling fountains of enchantment and of fulfillment. Most of all, I wish to acknowledge the patience and understanding of my husband, Bradley Dean Roush. He has waited, watched, and wondered through this long journey, a rock of calm in my tumultuous quest for the 'Golden Ring'. V TABLE OF CONTENTS page Part 1: Prologue. 1 Part 2: Literature Review. 5 Chapter I. MEASURING COMPETITION IN WEED-CROP ASSOCIATIONS: INTENSITY OF COMPETITION. ABSTRACT INTRODUCTION METHODS USED TO STUDY COMPETIITON RESULTS AND INTERPRETATION OF COMPETITION EXPERIMENTS CONCLUSIONS LITERATURE CITED Chapter II. MEASURING COMPETITION IN WEED-CROP ASSOCIATIONS: IMPORTANCE OF COMPETITION. ABSTRACT INTRODUCTION METHODS TO STUDY THE IMPORTANCE OF COMPETITION RESULTS AND INTERPRETATIONS LITERATURE CITED Part 3: Growth, competition, and community dynamics in a four-species annual weed community. Chapter III. MODELS OF A FOUR-SPECIES ANNUAL WEED COMMUNITY: GROWTH AND COMPETITION. ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS LITERATURE CITED APPENDIX 5 5 6 9 20 35 46 52 52 53 55 60 69 71 71 71 73 79 87 98 114 117 vi Chapter IV. MODELS OF A FOUR-SPECIES ANNUAL WEED COMMUNITY: COMPETITION AND COMMUNITY DYNAMICS. ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSIONS LITERATURE CITED APPENDIX 121 121 123 128 134 148 169 171 Part 4: Epilogue. 176 SYNOPSIS 177 SPECULATION Plant growth analysis Designing competition experiments Yield-density models: pearls or red herrings? The importance of competition Key processes and factors other than competition Population dynamics versus community dynamics 182 182 SYNTHESIS: MODELS OF WEED POPULATIONS AND COMMUNITIES. Part 5: Bibliography. 186 192 196 199 206 209 211 vii LIST OF FIGURES page Figure 1.1. Replacement series diagrams. 39 Figure 1.2. Models describe relationships between plant biomass and plant density (N). 41 Figure 1.3. A fan, Nelder-Bleasdale design for competition experiments. 43 Figure 1.4. Addition series designs for two and four plant species. 44 Figure 1.5. General models of crop yield loss due to the presence of weeds. 45 Figure 2.1. General form models developed by Sagar and Mortimer (1976) for simulating weed population dynamics. 66 Figure 2.2. Models for simulating leafy spurge (Eulphorbia esula) population dynamics. 67 Figure 2.3. A model developed by Roush, Radosevich and Wilson to understand and explain the regulation of an annual weed community. 68 Figure 3.1. A conceptual model of an annual weed community. 110 Figure 3.2. An addition series experimental design. 111 Figure 3.3. Growth analysis results from 1985 and 1986. 112 Figure 4.1. A conceptual model of an annual weed community. 165 Figure 4.2. Four-species addition series design. 166 Figure 4.3. Reciprocal-yield responses to intraspecific competition in 1985. 167 Figure 4.4. Monoculture responses (W) of A. retroflexus, C. album, E.crus-aalli, and L. multiflorum. 168 Figure A4.1. Recruitment patterns, Fall 1986 through July, 1986. 179 viii LIST OF TABLES page Table 1.1: Competition indices derived from substitutive and systematic designs for competition experiments. 38 Table 3.1. Meteorological data from Corvallis, OR and Davis,CA during competition and growth experiment growing seasons. 99 Table 3.2. Addition series types. 100 Table 3.3. Growth analysis parameters and formulae for calculations. 101 Table 3.4. Reciprocal-yield models for 1985 competition experiment. 102 Table 3.5. 1985 mean relative competitive abilities. 103 Table 3.6. Reciprocal-yield models for 1986 competition experiment. 104 Table 3.7. 1986 mean relative competitive abilities. 105 Table 3.8. 1985 Growth analysis results. 106 Table 3.9. 1986 Growth analysis results. 107 Table 3.10. Correlations between relative competitive ability (Rid) and growth analysis parameters for 1985 and 1986 growth and competition experiments. 108 Table 3.11. Growth and competition hierarchies in the two years of study at Corvallis, OR, and in comparison with data from Davis, CA (Roush and Radosevich 1985). 109 Table A3.1. Full Spitters' models for 1985 competition. 118 Table A3.2. Correlations among growth and competition parameters. 119 Table A3.2. Correlations between growth and competition parameters for 1986 growth and competition experiments. 120 ix page Table 4.1. Addition series types. 151 Table 4.2. 1985 Monoculture parameter estimates from reciprocal yield, nonlinear, and lntransformed nonlinear models. 152 Table 4.3. Multispecies reciprocal-yield competition models for 1985. 153 Table 4.4. Yield-density model parameters (Watkinson 1980, 1981) derived from reciprocalyield models for the 1985 experiment. 154 Table 4.5. 1986 Competition models from 1986 proximity factors. 155 Table 4.6. Comparison of 1986 competition models including only 1986 proximity factors with 1986 models that include both 1985 and 1986 proximity factors, and 1985 yield data. 156 Table 4.7. Coefficients of determination for 1985 and 1986 competition models. 157 Table 4.8. Population growth rates (PGR=dN/dt) of four annual weed species between 1985 and 1986. 158 Table 4.9. Relative population growth rates (days-1, RGR=1/N*dN/dt) of four annual species that comprise a weed community. 159 Table 4.10. Model summaries for explaining 1986 population densities of four annual weed species from their 1985 densities and yields. 160 Table 4.11. Partial, simple correlations between 1986 densities and 1985 densities and yields. 161 Table 4.12. Model summaries for explaining population growth rates (PGR) of four annual weed species from their 1985 densities and yields. 162 Table 4.13. Population model summaries for explaining relative (intrinsic) growth rates of four annual weed species from their 1985 densities and yields. 163 page Table 4.14. A compaKison of the coefficients of determination R for yield-density and population response competition models. 164 Table A4.1. Significance (p values) of pre-planned comparisons of plant frequencies at varying census dates and harvests, by species and series. 172 Table A4.2. 1986 yield-density models for a community of four annual weed species. 173 Table A4.3: Correlations among 1985 densities and yields of each species. 174 MODELS OF A FOUR-SPECIES ANNUAL WEED COMMUNITY: GROWTH, COMPETITION AND COMMUNITY DYNAMICS Part 1: Prologue My interest in weeds began as an awe of their incredible capacity for success in environments disturbed by humans. I was and still am curious about the ecological, physiological, and genetic mechanisms that contribute to the tenacity of weeds in disturbed habitats. Awe and curiosity have driven me to embark on this quest for knowledge about the ecology of weeds, to study the processes that regulate weed communities in agricultural systems, to boldly go where no agronomist has gone before. The development of my approach to studying weed ecology began with the question: "what physiological traits of weeds contribute to their success in agricultural systems?". This approach began by focusing on the processes of plant growth and competition. The primary objective of my M.S. thesis was to discover relationships between the growth ability of isolated individuals of four weed species and the competitive abilities of those species when grown in mixture. This approach assumed that 2 plant growth acts as an integrator of physiological processes; therefore, plant growth analysis would provide information about the physiological traits of the species that may contribute to competitive success. Relationships were established that linked key growth parameter with competitive ability for four summer-annual weed species, at Davis, CA (Roush and Radosevich 1985). The first phase of the research assumed that plant growth and competition were key processes in the lifehistories of the annual weed species, and that they were key regulatory processes in weed populations and communities. The next phase of the research demanded closer scrutiny of that assumption. A second set of questions then arose: 1) How are weed communities regulated? 2) What is the role of competition in annual weed communities? 3) Can the dynamics of weed communities be predicted? My approach to these questions forms the basis for this dissertation. How are weed communties regulated? I have taken a population modelling approach to answer this question. Dr. M.V. Wilson, Dr. S.R. Radosevich, and I have collaborated to devise a conceptual model of an annual weed community (Figures 2.3, 3.1, 4.1). The model assembles life-history stages of weed species, and the processes that regulate transitions among the life-history stages. The processes are the focus of the research because they 3 represent potential key regulators of weed communities. What is the role of competition in annual weed com- munities? The first phase of the research involved the processes of plant growth and competition; therefore, it seemed a logical step to build and expand from the relationships constructed around these processes. This focus on the process of competition embraced two distinct approaches to studying plant interactions: 1) the intensity of competition, and 2) the importance of competition. The intensity of competition concerns the physiological mechanisms and responses of competing plants. The importance of competition concerns the role of competition in regulating the evolution of populations and communities. The overall role of competition in annual weed communities must be studied by addressing both the intensity and importance of competition. The first section of this dissertation reviews methodology for measuring the intensity (Chapter I) and importance (Chapter II) of competition. The second section then investigates the physiological processes of plant growth that contribute to competition (Chapter III) and the influences of competition on community dynamics (Chapter IV) of a four-species summer-annual weed community. Can we predict the dynamics of weed communities? Predictive models may be built in two ways: 1) empirical models that describe how systems often work, and 2) 4 models built from theory that explain how systems ought to work. My approach is explanatory; therefore, I look for ecological theory that provides a framework to predict community dynamics in agricultural systems. Weed associations are a special type of plant community. Once key life-history processes are understood, the model that we have developed can be adapted to predict species shifts and population densities of weed species in response to management. The research has focused on the processes of plant growth and competition; other processes must now be investigated. The final section of this dissertation (Epilogue) outlines the next steps in bringing the model beyond the conceptual stages. In the final analysis, this dissertation is not intended to recommend weed-control strategies. Rather, it should be judged on its broader scientific contributions. The needs of weed managers in predicting species shifts and weed densities provide inspiration. The goal of this research is to provide a rational basis for addressing those needs. This rational basis is a research approach that elucidates processes and mechanisms to understand the dynamics of a system. The system of interest is a weed community, and the populations of the four annual weed species included in the community. By understanding how the system works, eventually we can hope to manipulate the system. 5 Part 2: Literature Review Chapter I. MEASURING COMPETITION IN WEED-CROP ASSOCIATIONS: INTENSITY OF COMPETITION. M. L. Roush and S.R. Radosevich ABSTRACT Competition experiments in agricultural systems have primarily addressed the intensity of competition. Aproaches to measure competition have broadened in scope to address the increasing complexity of questions that are raised concerning weed-crop competition. The appropriateness of individual approaches and designs of competition experiments depends upon the experimental objectives. Additive, substitutive and systematic designs each contribute to certain experimental objectives. Neighborhood and sphere of influence approaches expand the interpretations that can be made from these experimetnal designs. Systematic designs provide most accurate and informative approach to quantifying the intensity of weed-crop interactions in plant stands because they account for the proximity factors of total density and species proportion. 6 INTRODUCTION Competition is studied in agricultural systems for a variety of reasons: to determine yield responses of crops to weed presence, to understand mechanisms of competition between weeds and crops, to establish economically acceptable thresholds of weed populations, or to forecast weed population dynamics and shifts among weed species. There also are numerous experimental methods available for addressing these research objectives. The appropriate choice of experimental method depends on the objective of the research and the breadth of interpretations that is required. Competition in weed-crop systems is described by measurement of both intensity and importance of competition (Welden and Slauson 1986). Intensity describes the levels or severity of competition. It is primarily the physiological and morphological responses of plants to the presence of neighbors. Importance is the role of competition in the evolution of plant populations and communities. Studies in weed-crop systems have focused primarily on measuring the intensity of competition, because the greatest interest has been in the response of crop yields to weeds. Zimdahl (1980) documents numerous studies that 7 describe the responses of crops to various amounts of weeds. Recent investigations provide more detail about the intensity of competition by differentiating between the roles of intra- and interspecific interactions, and of density and proportion (Harper 1977, Joliffe et al 1984, Radosevich 1987). These more detailed studies examine the process of competition among species, as well as describe how crops respond to the presence of weeds. The intensity of competition is regulated by factors of proximity, biology, and environment (Radosevich 1987). Thus, experimental designs used to study weed-crop systems must address the key factors involved in plant-plant interactions. Proximity factors define in competitive neighborhoods by determining the nearness and influencing the competitiveness of neighbors. The proximity factors that influence plantplant interactions are total density, species proportion, and spatial arrangement (Harper 1977, Radosevich 1987). Total density describes the total number of individuals in a plant stand. Species proportions, or frequencies, are the relative densities of the component species of the stand. The geometrical relationships among the locations of individual plants is described by spatial arrangement. Biological factors are traits that determine the relative success of individuals and species in 8 competitive interactions. Life-history characteristics of weed and crop species, such as annuality, perenniality, and timing and allocation of reproduction contribute to competitive ability; however, many crop-weed systems consist of species with similar life history traits. Plant growth is a mechanism for exploiting and usurping resources during competition. Plants that emerge sooner or grow faster than other individuals utilize a disproportionate amount of available resources (Ross and Harper 1972, Harper 1977, Grime 1979, Roush and Radosevich 1985). Thus, key biological factors include the timing and rate of growth of an individual, as well as physiological and morphological traits that contribute to growth and resource use. This paper reviews various approaches and methods to describe the intensity of competition in agricultural plant communities. We also discuss the results and interpretations provided by the different approaches and methods. The purpose is to clarify relationships among research objectives, experimental methods, and interpretations of experiments that exist in studies of competition intensity. 9 METHODS USED TO STUDY COMPETITION Competition must be studied by methods that control, measure, or test the various factors of proximity and biology. The three experimental designs most used to study the intensity of competition are described as being additive, substitutive and systematic (Radosevich and Holt 1984, Radosevich 1987). The designs vary in how they address or control proximity factors. Biotic factors can be manipulated with each design, by manipulating or testing for emergence, growth rates, and physiological and morphological traits of the individuals. Additive experiments. Conventional stand-centered bioassays (Harper 1977, Radosevich 1987) and individual-centered neighborhood (Weiner 1982, Goldberg and Werner 1984) or sphere (or area) of influence (Oliver and Chandler 1985, Gunsolus and Coble 1986) approaches primarily utilize additive designs. Conventional additive experiments subject a stand of a crop at a "typical" planting density to a range of weed densities. Such experiments confound factors of proximity because total density, species proportion, and spatial arrangement vary simultaneously. Neighborhood and area of influence approaches are not limited to additive designs; however, they may make their greatest contribution in unravelling the influences 10 of proximity factors that are confounded by conventional additive experiments. Neighborhood approaches to additive experiments measure the influence of neighbors (measured as biomass, leaf area or some function of distance and biomass or leaf area) on the performance of a target individual (Goldberg and Werner 1984). Sphere of influence approaches measure the influence of an individual weed on the neighboring stand of plants (Oliver 1985, Gunsolus and Coble 1986). Statistical analysis of stand-centered additive experiments generally consists of an analysis of variance in which responses to weed density treatments are compared, or regressions of crop biomass responses to the influence of weed density are performed. Analysis of the neighborhood approach centers around regression techniques. The analysis models the response of a target individual as a dependent variable, and influence of neighbors as independent variables. Various combinations of neighbor distance, orientation, and size (biomass, leaf area etc.) often are included as independent variables (Mack and Harper 1977, Goldberg and Werner 1984). However, separating the competitive relationships among target plants and neighbor plants involves numerous statistical complexities (Firbank and Watkinson 1987) that must be considered when using either neighborhood or area of influence techniques. 11 Substitutive experiments. The most common type of substitutive experiment utilizes a replacement series. This experimental design controls the proximity factors of total density and (usually) spatial arrangement, while systematically varying species proportion (de Wit 1960, Harper 1977). Conventional analysis of replacement series experiments assumes that plants are at a total density large enough to invoke a 'constant final yield' (Holliday 1960, Harper 1977). The analysis is based on theoretical models of binary liquids (de Wit 1960) and enzyme kinetics (Bleasdale and Nelder 1960, Joliffe et al. 1984). The analysis tests a null hypothesis that plant yields in monoculture predict yields in mixture. Influences of species proportion on the yields in mixture then are interpreted depending on whether they conform to the null model (i.e. no competition or competitive equivalence), or one of several models which vary from it (Figure 1.1)(de Wit 1960, Harper 1977). Numerous approaches have been proposed to quantify the influences of proportion on plant mixture responses in replacement series experiments. The methods proposed by deWit (1960) involve fitting response data to the following model: Yi = (kid Pi) /(kid Pi + Pj) * Mi. Eq.l.l In this equation, yield of species i in mixture (Y1) is 12 predicted from the monoculture yield of species i (Mi), the relative frequencies (proportion) of species i (pi) and j (pj), and a relative crowding coefficient (kij). The relative crowding coefficient is an indicator of the relative competitive abilities of species i and j: kij = (xi/xj)/(mi/mj), Eq.1.2 when x is the mean weight per plant in mixture and m is mean weight per plant in monoculture. McGilchrist and Trenbath (1973) describe a different approach for calculating and testing relative competitive abilities, using a parameter called aggressivity (aij, Table 1): aij = 1/2 ( Mi/Yi - Mj/Yj). Eq.1.3 Relative yield total (RYT, Table 1) measures overall resource use in the system, and is calculated as: RYTij = 1/2 (Mi/Yi + Mj/Yj). Eq.1.4 Systematic experiments. While additive designs have been criticized because they confound proximity factors (Harper 1977, Radosevich and Holt 1984, Radosevich 1987), substitutive designs have been criticized because of their dependence on a single plant density (Inouye and Schaffer 1981, Joliffe et al. 1984, Firbank and Watkinson 1985, Connolly 1986). These critics of additive and substitutive designs have proposed several approaches that vary both density and 13 frequency (proportion). Systematic experimental designs vary more than one proximity factor at a time, and vary them systematically to account for each factor. Joliffe et al. (1984) have proposed an alternative to substitutive experiments to account for the influence of total plant density on competition. The data analysis in this approach (Joliffe et al. 1984) uses the density responses of each species to construct a synthetic null model derived from theoretical yield-density relationships. The synthetic null or no-interaction model predicts the response of biomass (projected yield, Yp) to density if there were no influences of either intra- or interspecific competition. The synthetic null model is calculated from parameters derived from a hyperbolic (constant final yield) model relating biomass to density (Figure 1.2a, De Wit 1960, Holliday 1960, Joliffe et al. 1984): Y = ("Ymax)/(Kn N) Eq.1.5 A convenient form for this hyperbolic model is the double-reciprocal model, similar to models for enzyme kinetics: 1/Y 1/Ymax (Kn/Ymax)(1/11) Eq.1.6 In these equations, Y is yield per unit area, Ymax is the maximum, asymptotic ("constant final") yield of a stand, and N is density. Kn describes the hyperbolic response of yield to plant density, and is the density where Y = 1/2 14 max The synthetic, null model is a function of Ymax, Kn, and density. The slope of the response of projected yield (Yp) to density is equivalent to the slope of the yield density model in Eq. 1.5 when N=1.0: Yp (Ymax/Kn)*N Eq.1.7 The influences of proportion and density then are determined by comparing mixture responses to the synthetic, null model. Experimental designs for this approach (Joliffe et al.,1984) include: (1) conducting several traditional replacement designs, each performed at a different total density, (2) a single replacement series experiment with a complete monoculture density study performed for each species used in the plant mixtures, or (3) a BleasdaleNelder mixture design (Bleasdale 1967a, Radosevich and Holt 1984) that varies density along a continuum of concentric circular arcs with density increasing toward the center (Figure 1.3, Bleasdale 1967a), and with plant mixtures superimposed upon the grid of plant density. Modified designs that include aspects of both additive and replacement series experiments are called addition series. Addition series designs systematically vary densities of all species in the experiment, resulting in a range of both total plant density and proportions (relative density, or frequency) of each of the species. Addition series designs were initially 15 proposed as a set of replacement series at varying total density (Spitters 1983). Addition series between two species also can be constructed as a two-way density gradient (Figure 1.4a), although treatments of density and proportion may be randomized in the field. More than two species may be studied simultaneously by constructing more complex designs which achieve a range of total and relative densities for each species (Roush and Radosevich 1987, Figure 1.4b). Analysis of addition series experiments depends on regression techniques and on theoretical yield-density relationships for plant-plant interactions, i.e. similar procedures to those proposed by de Wit (1960) and Joliffe et al. (1984). The responses of total yield and yield (or weight) per plant can be modelled as a rectangular hyperbolic response to density (Figures 1.2a and 1.2b) (Shinozaki and Kira 1956, Bleasdale and Nelder 1960, Watkinson 1980): = A + B N. Eq.1.8 This model expresses the weight of an individual plant, raised to the exponent -9, as a linear function of density. The exponent describes the curvilinear nature of the hyperbolic function. Historically, this exponent has been assumed to tend toward a value of -1 as resources in a system are used more completely. At 9 = 1.0, the yield-density response is asymptotic. The frequent and 16 continued use of the exponent -1.0 in such models has led to the 'Reciprocal Yield Law' for describing plant responses to density (Figure 1.2c): Eq.1.9 1/W = A + B N. Numerous recent investigations indicate that the exponent -9 does not universally approach a value of -1.0 (Watkinson 1980, Firbank and Watkinson 1985, Weller 1987), and that nonlinear regression should be employed to estimate the value of this exponent, as well as the values of the linear parameters (Watkinson 1980, Firbank and Watkinson 1985). The simplified reciprocal yield model (Eq.1.9) has been used by Spitters (1983) as the basis for analyzing systematic studies of competition in plant mixtures. Spitters extends the reciprocal yield model to include the influences of densities of more than one species, and assumes that these influences are additive: 1/W1 B10 4- B11 N1 4- B12 N2 Bin Nn. Eq.1.10 -I- In this model, W is the weight of an individual of species 1, Nn is the density of species n, B10 is the reciprocal of the theoretical maximum size an individual of species 1 would obtain with no competitors, B11 describes the influence of intraspecific competition, and Bin describes the influence on species 1 of interspecific competition between species 1 and n. From this model, relative competitive abilities (rid) of the species can 17 be calculated as the ratio of intra- to interspecific competition coefficients (Table 1.1): rij= Bii / Bij. Eq.l.11 Connolly (1987) has proposed a similar approach for measuring responses in mixture experiments, and suggested a number of additional parameters for describing plant responses. In an example of this approach, data first were fit to reciprocal yield models. Then, Connolly (1987) calculated substitution rates (sij) that are equivalent to the inverse of Spitters' (1983) relative competitive ratio (rij, Eq.l.11, Table 1.1). Connolly derived substitution rate (sij) as: sij = (dfi/dNj)/(dfj/dNi). Eq.1.12 where fi is the reciprocal yield-density model for species i (Connolly, 1987). Connolly (1987) also has proposed a parameter called relative resource total (RRT) to replace RYT from conventional replacement series analyses (Table 1), where: RRT = Ni/Nio + Nj/Njo. Eq.1.13 In this expression, Nio is the monoculture density of species i that would produce a mean weight per plant identical to the mixture response of species i, at density Ni and growing with species j. Finally, Connolly (1987) has proposed an efficiency index (REI) that is based on the differences between relative growth rates of species when in mixtures: 18 REI = Ri - Rj. Eq.1.14 Ri and Rj are the relative growth rates of species i and j. Connolly (1987) suggested that REI indicates the relative fitness of the species in mixture. Watkinson (1981) and Firbank and Watkinson (1985) utilize a more general form of the yield-density models to measure the intensity of competition in monocultures and mixtures: W = Wm (1 + aN)b Wi = Wm (1 + ai (Ni + eij a Nj ))b. Eq.1.15 Eq.1.16 In these models, b is equivalent to -ve (eq. 1.8). The exponent b defines the curvilinearity of the response of plant biomass (Wi) to density (Ni and Nj), and describes the efficiency of resource use in the system (Watkinson 1980, Firbank and Watkinson 1985). Wm is equal to A-1/6 (Watkinson 1980) and also defines the theoretical maximum size of a plant without competition. The parameter ai (Eq.s 1.15 and 1.16) is equivalent to B/A from Eq.1.8. It describes the minimum area necessary to achieve Wm, or the minimum area to avoid interactions with neighbors. The parameter eij is the equivalency ratio, or relative competitive abilities of two species (Table 1.1, Watkinson 1981, Firbank and Watkinson 1985). This model describing plant-plant interactions also has been extended to include more than two species at a time (Watkinson 1981, Firbank and Watkinson 1985, Roush and Radosevich 1987). 19 Biomass versus marketable yield. The hyperbolic yield-density relationships (eq. 8-10 and eq.15, Bleasdale and Nelder 1960, Watkinson 1980) were developed for the biomass responses of entire plants. Yield can be measured as total plant biomass, or it can be measured as marketable biomass, or yield of individual plant parts. Data for yields of plant parts indicate that yield-density relationships for marketable yield are described better by models other than the hyperbolic yield-density relationships (Bleasdale 1967b, Willey and Heath 1969). In particular, yields of vegetative and reproductive plant parts often follow a parabolic yield-density model (Bleasdale and Nelder 1960, Willey and Heath 1969). 20 RESULTS AND INTERPRETATIONS OF COMPETITION EXPERIMENTS The results of experiments that used differing methods to describe the intensity of competition will be discussed in two ways: (1) factors that are assessed by each design, including proximity and biology, (2) inferences that can be drawn from the experiments as they were conducted. The discussion will proceed by increasing the complexity of experimental objectives and thus the range of factors that must be addressed by the various experimental approaches. Assessing Proximity factors. Additive designs are generally least instructive in describing the influences of proximity factors, because they do not separate the influences of density and proportion in the outcome of competition experiments. Substitutive designs systematically vary species proportion while density is maintained constant. Therfore, substitutive designs address the influences of species proportion but cannot account for influences of total density (Inouye and Scheaffer 1981, Jolliffe et al. 1984, Roush et al. 1988). Proximity factors are described best by systematic designs that simultaneously address factors of density, proportion and spatial arrangement (Watkinson 1981, Connell 1983, Connolly 1986, Radosevich 1987). 21 The value of accounting for proximity factors depends upon the objective of the experiment. If the objective is a simple model (bioassay) of crop response to weed density, then both additive and systematic experiments are appropriate, because both approaches describe a response function relating crop yield to weed presence. However, systematic experiments also provide information about how the density of the crop influences the response function. Conventional substitutive approaches would be least suitable for this objective, since models are not as easily interpreted for typical cropping systems where total density (crop plus weed) varies. Zimdahl (1980) has reviewed numerous studies where the primary objective is to measure the extent of yield reduction of the crop due to competition with varying levels of weed density. The only generality that can be drawn from this body of evidence is that weed competition reduces crop yields. A general relationship between crop yield and weed density was proposed by Zimdahl (1980) for many of these studies, where crop yield was modelled as a decreasing, sigmoid function of weed density (Figure 1.5a, Zimdahl 1980, Aldrich 1987). Cousens (1985) reanalyzed many of the additive studies used to generate the sigmoid yield-loss model, and some substitutive experiments. He found that a hyperbolic response was more 22 was more appropriate than the sigmoid model for describing yield loss due to weed density (Figure 1.5b). Although models from additive studies successfully describe the general nature of the response of crops to weeds, they cannot accurately predict actual yield responses. Zimdahl (1980) indicated that two factors account for the lack of predictiveness in crop-weed competition models based on additive experiments. First, additive experimental designs vary, as do the results of additive experiments. Therefore, general, predictive models have not been developed. Second, results of individual competition studies were strongly influenced by sitespecific factors, including climate, irrigation, weather, fertility, and time of weed germination (Appleby 1977). The variability of additive experimental designs and the site specificity of competition results represent factors of both the intensity and importance (Radosevich and Roush 1988) of competition that are not addressed by conventional, additive experiments. Response models from additive studies are variable and diverse because they have no basic, theoretical model as a framework to account for proximity factors and to address questions about the intensity of competition. Such studies also lack a framework to account for environmental variables that influence the importance (Chapter II) of competition in weed-crop systems. Zimdahl (1980) and Radosevich 23 (1987) have argued that further use of conventional, additive competition studies will not advance our ability to predict crop responses to weeds, nor will they advance our understanding of weed-crop competition. Neighborhood and sphere of influence approaches to competition promise to clarify and simplify the interpretations and predictions that can be drawn from weed-crop studies using additive experimental designs (Goldberg and Werner 1983, Oliver 1985, Gunsolus and Coble 1986). Until recently, neighborhood measures of competition intensity have been used primarily by basic plant ecologists to describe plant interactions, using substitutive and systematic designs. For example, Mack and Harper (1977) used a design that included all possible pairwise and all-species combinations of four annual species, at two densities. By describing precise neighborhood relationships of individuals (i.e. weight, distance, and angular dispersion of neighbors), they accounted for up to 69 percent of the variance in weight and fecundity of individual plants. Neighborhood approaches have been used by theoretical ecologists to develop models of intra- and interspecific competition that describe population processes from the perspective of individual plants (Weiner 1982, Pacala and Silander 1985, Silander and Pacala 1985, Pacala 1986). Weiner (1982, 1984) tested neighborhood models for 24 describing intraspecific competition, using two species of knotweed (Polygonum minimum Wats. and P. cascadense Baker, Weiner 1982), and pine (Pinus rigida Mill., Weiner 1984) monocultures. Pacala and Silander (1987) calibrated their models by conducting simple systematic neighborhood experiments with a two-species stand of velvetleaf (Abutilon theo-phrasti) and redroot pigweed (Amaranthus retroflexus). Although these studies dealt with agriculturally important species, the experiments were motivated primarily for model validation and exploration of methodology. However, their results explained the responses of the species based on biological factors, and on possible mechanisms of resource exploitation. Applications of neighborhood approaches to study the intensity of competition in agriculture have been most widely adopted in forest systems. Competition indices, based on neighborhood measures of intraspecific competition, have been developed for numerous tree species [e.g. Douglas-fir (Pseudotsuga menzeisii), jack pine (Pinus banksiana ), red pine (P. resinosa), aspen (Populus tremuloides), and Eucalyptus spa., Bella 1971; red pine, Martin and Ek 1984; loblolly pine (P.ellioti), Daniels et al. 1986). Neighborhood indices for interspecific competition, for development of management strategies in forest systems, have been investigated by Wagner and Radosevich (1987). 25 Applications of neighborhood approaches in annual crop systems have primarily taken the area or sphere of influence perspective, where the influence of an individual weed on the crop stand is assessed (Oliver and Chandler 1985, Gunsolus and Coble 1986). Although the potential for using this approach in weed management has been well recognized (Oliver and Chandler 1985), few examples of this approach are yet in the literature. A study by Gunsolus and Coble (1988) investigated effects of weeds on soybeans and of soybeans on weeds, using both sphere of influence and neighborhood approaches. Low densities (3 m apart) of cocklebur (Xanthium strumarium L.) and sicklepod (Cassia obtusifolia L.) were planted with and without soybeans, and weed-free soybeans also were planted. Using regression techniques, responses of soybeans to the weed species were described as the distance along the crop row that was influenced by each individual weed over the course of the growing season. The neighborhood and sphere of influence approaches to quantify interactions promise to enhance the range of interpretations that are possible from additive experimental designs. However, these approaches only address the responses of individuals. When data are reconstructed to predict stand yields, proximity factors must be addressed or assumed to have no effect. For example, influences of the crop density or spatial 26 arrangement on weed-crop competition can not be assessed by neighborhood approaches if they were never varied in the experimental design. Neighborhood approaches only delay consideration of density and spatial arrangement (i.e. row spacing) in crop stands. Carlson and Hill (1985) performed a set of modified additive experiments to determine the intensity of competition between spring wheat and wild oat (Avena fatua L.). They measured the influence of the weed on crop yield, at two different crop densities. Because Carlson and Hill (1985) grew the crop at more than a single density, they were able to partially separate the influences of density and proportion. Yield of wheat was modelled in response to the ratio of wild oat density (WO) to total plant density (WO+W). This ratio (WO/WO+W) accounted for the influences of both density and proportion, and allowed predictions of wheat yield based on the abundance of both plant species. The presence of wild oat always decreased wheat yields; however, the influence of the weed on wheat yields diminished as total density (WO+W) increased. A systematic competition experiment performed by Concannon and Radosevich (1987) evaluated influences of both density and proportion on crop and weed responses. They studied competitive interactions between spring wheat and annual ryegrass (Lolium multiflorum L.), using 27 an addition series design. Data from the experiment were used to construct models of crop and weed response to the presence of both the crop and the weed. Similar to the results of Carlson and Hill, they found that wheat density strongly influenced the impact of ryegrass competition on wheat yields. As wheat density increased, the influence of ryegrass on a per-gram basis decreased, such that ryegrass was a severe competitor only at low wheat densities. Their data, and the data from Carlson and Hill, suggest that management of wheat density may be a better and more efficient approach to minimizing the weed-crop interference than direct control of the weed. The experiments of Carlson and Hill (1985) and Concannon and Radosevich (1987) provided useful, meaningful models describing wheat-weed interactions, partially because their objectives were broader than a simple bioassay of wheat yield response to weed presence. Their objectives also were to understand and quantify competitive relationships between the crop and weed. To achieve this objective, more information was needed about the influence of the crop density on the interaction. By modifying their studies to a more systematic approach, they were able to account for proximity factors, address the broader objectives, and ultimately to provide a more informative approach to modelling crop loss response to weed density. 28 Relative competitive ability. An important objective in addressing the intensity of competition has been to quantify relative competitive abilities of competing species, and to understand the nature of interactions between species. Weed scientists are concerned with measures of relative competitive ability because a goal of weed science is to maximize the relative competitive ability of crops relative to weed species. Because they do not control proximity factors, additive studies have contributed only limited information to these objectives. Substitutive and systematic approaches have been the primary avenue for addressing the above objectives, but have provided interpretations and predictions of variable accuracy and applicability. Applications of substitutive approaches to competition in agricultural systems come primarily from the intercropping literature (eg. Trenbath 1976, Willey 1979, Francis 1986). In these studies, researchers are primarily concerned with maximizing niche differentiation, or potential overyielding of the intercrop system. Niche differentiation has been described by indices of the overall use of resources in the system (Table 1). Niche differentiation occurs when species partition 29 resource use, temporally or spatially, to avoid interference (Harper 1977). When this occurs, a species mixture may yield more than monocultures of the species. In weed-crop systems, scientists are concerned with niche differentiation because it indicates whether competition for limited resources (i.e. RYT=1.0) or non-competitive forms of interference (i.e. mutual benefit, RYT > 1.0, or mutual antagonism, RYT < 1.0) occur in their study. Substitutive experiments in crop-weed systems for measuring niche differentiation and relative competitive abilities (Table 1.1) include competition between flax and Camellina species (Grummer 1955, 1958), wheat and ryegrass (Lolium multiflorum, Rerkasem 1978), barley and common lambsquarters (Chenopodium album, Elberse and Kruyb 1979), beans and barnyardgrass and nightshade (Echinochloa crus-galli and Solanum spp., Fennimore et al. 1984), and ponderosa pine and manzanita (P. ponderosa and Arctostaphyllos patula, Shainsky and Radosevich 1986) . Substitutive designs also have been used to investigate hierarchies of relative competitive ability among weed species. For example, Marshall and Jain (1969) investigated competitive differences between Avena fatua and A. barbata that contributed to variations in the distributions of the two species. Roush and Radosevich (1985) defined a consistent hierarchy of competitive 30 ability among four annual weed species, using the statistic aggressivity (aid), derived from replacement series of all possible pairwise combinations of the species. Patterson and associates (1986) demonstrated that competitive relationships between Texas panicum (Panicum texanum) and wild proso millet (Panicum miliaceum) shifted with changes in temperature and photoperiod. The responses of the two Panicum species were consistent with the different geographical distributions of the species, and were interpreted to limit potential spread of the species into new regions. Replacement series also have been used to measure the influence of environmental factors other than proximity on the intensity of competion in agricultural systems. For example, replacement series experiments have assessed the influence of nematodes (Sibma et al., 1964), and of pH and fertilizers (van Dobben 1955) on competition between barley and oats. De Wit (1966) studied influences and interactions between rhizobioum and fertilizers on competition in a grass-legume system. Often, measures of relative competitive ability shift with changes in the biotic or abiotic environment. Substitutive, or replacement designs have received considerable criticism in recent literature. Inouye and Schaffer (1970), Joliffe et al. (1984), and Connolly (1986) caution that when total density is constant, the 31 outcome of competition may depend entirely on the predetermined density of the experiment. Variations in density may lead to variations in how species proportions influence competitive outcomes (Joliffe et al. 1984). Roush et al. (1988) have demonstrated that traditional analytical approaches to modified substitutive experiments can provide different interpretations than a systematic, yield-density approach applied to the same set of data. Traditional replacement series analysis was less sensitive in detecting and interpreting influences of total density on interactions between wheat and annual ryegrass than was the systematic approach. Connolly (1986) has examined replacement series data from the literature and evaluated a number of the parameters that describe competitive interactions. Connolly utilized linear, multispecies reciprocal yield models (as in Spitters, 1983) to evaluate the performance of the indices kid, aid, and RYT for different (theoretical) pure stand densities. Thus, he produced differing null-model replacement lines for comparison with actual mixture data. He demonstrated that kid, aij, and RYT were "wildly unstable" as total density varied. Connolly (1986) also demonstrated that substitutive approaches produce indices that are biased, depending on the density at which data were obtained. 32 Connolly (1986) proposed that systematic approaches and regression analysis overcome the limitations of traditional substitutive experimenets in measuring the intensity of competition. Systematic competition experiments have been conducted using addition series designs and yield-density relationships to quantify intra- and interspecific competition, measure relative competitive ability, and indicate overall resource use for twospecies (Watkinson 1981, Spitters 1983ab, Firbank and Watkinson 1985, Concannon and Radosevich 1987, Shainsky and Radosevich 1987) and four-species (Miller and Werner 1987, Roush and Radosevich 1987, 1988) mixtures of agriculturally important plants. These studies provided definitive assessments of the influences of density and proportion on competition between crops and weeds, and among weed species. Biological factors. When biological factors are investigated in addition to proximity factors, they provide information about possible mechanisms of competition, competitive ability, and competition intensity. Studies that address biological factors of crop and weed competition measure the influences of key life-history traits of the species on competitive interactions. These life-history traits include timing of germination and growth, growth rates, 33 and physiological and morphological traits that contribute to the timing and rate of growth of individuals. Competition experiments in agricultural systems that address factors of weed and crop biology have focused primarily on critical periods of interaction (Nieto et al. 1968, Dawson 1970, Spitters and Van den Bergh 1982). These studies address the timing of competition. Although they suggest variation in phenology and timing of resource requirements that may contribute to variation in competitive outcomes and crop yield, these studies do not directly measure traits of phenology or resource use. Recent studies have incorporated growth analysis techniques (Hunt 1982) into competition experiments (eg. Patterson et al. 1984, 1986, Shainsky and Radosevich 1986, Gunsolus and Coble 1988, Concannon and Radosevich 1988). Growth analysis of plants that are grown in competition and harvested sequentially aids in interpreting how competition changes over the season, and when species begin to interact. Evidence for mechanisms of competition can be gathered more directly when growth analysis is combined with measurements of resource levels and/or physiological responses of plants to resources. For example, Shainsky and Radosevich (1986) linked measurements of plant-soil water relations with growth responses of ponderosa pine (Pinus ponderosa) and greenleaf manzanita (Arctostaphylos patula) to explain the outcome of 34 competition between the two species. Growth analysis also suggests biological traits of weed and crop species that contribute to relative competitive abilities. For example, Roush and Radosevich (1985) conducted growth analysis on individual plants of four weed species grown in isolation. They utilized aggressivity (aid), measured from a replacement series experiment, to define a competitive hierarchy among the four weed species. Physiological and morphological attributes of the species, which were measured by growth analysis of isolated individuals, were strongly related to the competitive abilities of the species in mixture. 35 CONCLUSIONS The appropriateness of an experimental approach or design to measure competition must be judged by how well it addresses the specific objectives of an experiment. The need to account for competition factors (proximity and biology) increases as experimental objectives become more complex. The range of experimental designs and approaches has increased to address the broadening scope of questions about weed-crop competition that are being posed by weed scientists and plant ecologists. Approaches that account for various combinations of proximity and biology factors have explained, with varying success, the responses of crops to competition with weeds and the mechanisms of competitive interactions. Additive experiments may be appropriate for studies to measure crop losses in response to weeds for a given field, location, and season. Substitutive experiments may be sufficient for simple descriptions of relative competitive abilities among species. Of the currently available approaches to measure competition, the recent derivations of yield-density relationships for modelling interspecific competition (Watkinson 1980, 1981, Connolly 1983, Spitters 1983) provide the most definitive and accurate assessment of the influences of proximity factors. Therefore, these models provide the most 36 definitive and accurate characterizations of the intensity of competition, and the most readily interpretable results. Studies of the mechanisms of competition require investigations of biological factors (e.g. time and rate of growth, physiology and morphology) in addition to proximity factors. Appropriate experiments for studying the mechanisms of competition require careful control over biology and proximity factors. Therefore, substitutive and systematic experiments, coupled with manipulations of biological traits of crops and weeds, will make the greatest contributions for these objectives. Objectives that address factors other than proximity and biology can not be adequately investigated within the framework of competition intensity alone. For example, numerous investigations described the influence of biotic and abiotic environmental factors on the intensity of competition (eg. van Dobben 1955, Sibma et al. 1964, De Wit 1966). These studies measured changes in relative competitive ability due to presence or absence of the environmental factor. The studies did not address the relative importance of competition and environmental factors in determining individual plant responses. They also did not address whether shifts in competitive ability will be important in regulating plant populations 37 will be important in regulating plant populations and communities. Objectives that focus on the forecasting of weed population dynamics and weed-species shifts, and the implementation of economic threshold models (Cousens 1985) must be addressed within the context of the importance of competition. Studies of importance will require different approaches and methods to measure competition (Chapter II). 38 Table 1.1: Competition indices derived from substitutive and systematic designs for competition experiments. competition index experimental design reference substitutive De Wit 1960 Harper 1977 relative competitive ability k13 a13 . r 13 sib relative crowding coefficient substitutive McGilchrist and Trenbath 1973 systematic Spitters 1983a substitution ratio systematic Connolly 1987 equivalency ratio systematic Firbank and Watkinson 1985 aggressivity index relative competitive ratio niche differentiation RYT relative yield total systematic De Wit 1960 McGilchrist and Trenbath 1973 Spitters 1983a substitutive LER land equivalent ratio systematic Spitters 1983b RRT relative resource total systematic Connolly 1987 39 Figure 1.1. Replacement series diagrams, representing a variety of models that describe exerimental results. The vertical axis indicates plant yield, the horizontal axis indicates the relative proportions of the two species in mixture. Model I describes situations where the two species (A and B) are equivalent competitors, or the species do not interact. Model IIa and IIb describe uneven partitioning of resources between the species, such that one species 'wins' and one species 'loses'. Models III and IV describe mutual antagonism and mutual benefit, respectively. (Modified from Harper, 1977). 40 Figure 1.1. Model a) 1.0 A 0 B 1.0 0 species proportion Model IIa b) c) Model IIb *15 rl G) -,4 Model III d) 0 B 1.0 e) 1.0 A 0 0 B1.0 Model IV 1.0 A 0 species proportion species proportion 41 Figure 1.2. Models describe relationships between plant biomass and plant density (N): a) Responses of total yield (Y) to density often are hyperbolic and are assumed to follow the 'Law of Constant Final Yield'. b) Biomass per individual plant (W) responds to density in a negative, rectangular hyperbolic form (W-w=A+BN). c) When 0 = 1.0, individual biomass can be modelled as the linear response of reciprocal weight to density (1/W=A+BN). 42 Figure 1.2 YIELD DENSITY RELATIONSHIPS CONSTANT FINAL YIELD N RECTANGULAR HYPERBOLA e W =A + B N N RECIPROCAL YIELD 43 Figure 1.3 Length w 1 t . 1 1 \ l i ii 1 \ 4° I \ / / ./ I 1 / t I .4, \ % 6 M 12 M11 Me etc I i ,i ,_ "'a,r ., I 4 ... _I_ ),04, If i 411 4 , 4 , 1 I el. __ 4. Base lino Figure 1.3. A fan design for competition experiments, referred to as a Nelder or Nelder-Bleasdale design, that was developed by Bleasdale (1967) for studying effects of intraspecific competition. Dots represent plant positions. The design decreases plant density outwards in concentric arcs. 44 a) 1O0 4 ScM 0 0 O SO C) O 10 >4 4.3 0 a 0 200 O 10 SO 100 Density species B (plants m-2) b) 11111111; aoe 0 715111 1; :"' 1111111 111 .... 41 0. " 100 0 0 SO 10 ---7.Tr.4'..11......aimmuiner:7 s gro led 4.1 0 ; II 0 MOM 10 SO 100 200 , Density species B (plants m-4) Figure 1.4. Addition series designs for a) two and b) four plant species. Both designs are established as a two-way density gradient, with densities of each of two species increasing along an X and a Y axis. One or two additional species then may be planted in strips that are superimposed on the two-species design, where density of the strip species increases in a counter-clockwise direction. These designs result in a range of relative and total densities of the species (Roush and Radosevich 1987, adapted from Miller and Werner 1987). 45 (a) Weeds/m2 (b) 0 Weeds /m2 Figure 1.5. 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PhD Thesis, Department University of Western Australia, of wheat and annual and yield components of Agronomy, 212 + 182 pp. Roush, M.L., and S.R. Radosevich. 1985. Relationships between growth and competitiveness of four annual weeds. Journal of Applied Ecology, 22, 895-905. Roush, M.L., S.R. Radosevich, R.G. Wagner, R.G. Maxwell, and T.D. Petersen. 1988. A comparison of methods for measuring effects of density and proportion in plant competition experiments. (Submitted to Weed Science.) Shainsky, L.J., and S.R. Radosevich. 1986. Growth and water relations of Pinus ponderosa seedlings in competitive regimes with Arctostaphylos patula seedlings. Journal of Applied Ecology, 23, 957-966. Shainsky, L.J., and S.R. Radosevich. 1987. Competitive interactions between Douglas-fir (Pseudotsuga menziesii Mirb. Franco) and Red Alder (Alnus rubra) seedlings: growth analysis, resource use, and physiology. WSSA abstracts, St.Louis. Shinozaki, K. and T.Kira. 1956. Intraspecific competition among higher plants. VII. Logistic theory of the C-D effect. Journal of the Institute of Poytechnics, Osaka City University 7:35-72. Sibma, L., J. Kort, and C.T. de Wit. 1964. Experiments on competition as a means of detecting possible damage by nematodes. Jaarb. I.B.S. 1964, 119-124. Silander, J.A., and S.W. Pacala. 1985. Neighborhood predictors of plant performance. Oecologia. 66, 256-263. Spitters, C.J.T. 1983b. An alternative approach to the analysis of mixed cropping experiments. 1. Estimation of competition effects. Netherlands Journal of Agricultural Science, 31, 1-11. 50 Spitters, C.J.T. 1983b. An alternative approach to the analysis of mixed cropping experiments. 2. Marketable yield. Netherlands Journal of Agricultural Science, 31, 1-11. Spitters, C.J.T., and J.P. Van den Bergh. 1982. Competition between crops and weeds: a system approach. In: W.Holzner and N. Numata (eds) Biology and Ecology of Weeds. Dr. W. Junk, The Hague, pp. 137-148. Trenbath, B.R. 1976. Plant interactions in mixed crop communities. in: Multiple Cropping. American Sociey of Agronomy special pub. #27, pp.129-169. Wagner, R.G., and S.R. Radosevich. 1987. Interspecific competition indices for vegetation management decisions in young Douglas-fir stands on the Siuslaw National Forest: Report No. 1. Department of Forest Science, College of Forestry, Oregon State Univ., Corvallis. 17pp. Watkinson, A.R. 1980. Density dependence in singlespecies populations of plants. Journal of Theoretical Biology. 83: 345-357. Watkinson, A.R. 1981. Interference in pure and mixed populations of Agrostemma githago. Journal of Applied Ecology, 18, 967-976. Weiner, J. 1982. A neighborhood model of annual-plant interference. Ecology, 63(5), 1237-1241. Weiner, J. 1984. Neighborhood interference amongst Pinus rigida individuals. Journal of Ecology, 72, 183-195. Welden,C.W. and W.L. Slauson. 1986. The intensity of competition versus its importance: an overlooked distinction and some implications. Quarterly Review of Biology 61, 23-44. Weller, D.E. 1987. A reevaluation of the -3/2 power rule of plant self-thinning. Ecological Monographs, 57(1). 23-43. Willey, R.W. 1979. Intercropping - its importance and research needs 2. Agronomy and research approaches. Field Crop Abstracts, 32(2), 73-81. Willey, R.W. and S.B. Heath. 1969. The quantitative relationships between plant population and crop yield. Advances in Agronomy, 21, 281-321. 51 Wit, C.T. de. 1960. On Competition. Verslagen van Landbouwkundige Onderzoekingen. PUDOC, Wageningen, Netherlands. 66.8, 82 pp. Zimdahl, R.L. 1980. Weed Crop Competition: A review. International Plant Protection Center, Corvallis, Or. 52 Chapter II. MEASURING COMPETITION IN WEED-CROP ASSOCIATIONS: IMPORTANCE OF COMPETITION. M. L. Roush and S.R. Radosevich ABSTRACT Competition experiments in agricultural systems have primarily addressed the intensity of competition. However, measurements of the importance of competition, and weed populations models, are important for devising long-term weed management strategies (Cousens 1986). Models of weed populations help identify critical lifehistory stages and processes of weeds that are most vulnerable to regulation and manipulation (Firbank and Watkinson 1986, Maxwell et al. 1988). Models of weed population and community dynamics also provide a basis for forecasting weed infestations and for formulating economic weed control models (Cousens 1986). The better interactions among crops and weeds are understood and quantified, the better efficient and effective weed management strategies can be planned. 53 INTRODUCTION The importance of competiton in weed-crop associations is its role relative to all other biological processes that regulate agricultural systems (Welden and Slauson 1986, Radosevich and Roush 1988). Assessment of importance is necessary to develop models that describe weed population and community dynamics. An understanding of the processes that regulate weed abundance can improve strategies for manipulating weed populations in agricultural communities. Welden and Slauson (1986) identify a key distinction between the importance and intensity of competition. Intensity describes levels of competition and their influence on crop yield. Importance is the role of competition in the evolution of populations and communities. For example, if disturbance, herbivory, or seed bank processes dramatically influence the dynamics of weed communities, competition may be of relatively little importance to the long-term structure or species composition of the weed community. A knowledge of importance enhances weed control strategies because it allows predictions about weed population densities and species composition in response to management. Shifts in weed species composition or the development of herbicide resistance can by avoided or 54 anticipated by adequate knowledge about weed population and community dynamics in relation to competition and management. Weed population and economic threshold models (eg. Sagar and Mortimer 1976, Cousens 1985, 1987, Cussans et al. 1986, Coble 1987) integrate measurements of both the intensity and importance of competition to predict weed-crop community dynamics and the resulting influences of weed communities on crop yield. The prevalence and importance of competition as a regulatory process in nature have been debated (Schoener 1983, Connell 1983, Strong 1983, Welden and Slauson 1986). However, few studies have directly addressed the role of competition in plant community development in natural systems and none have evaluated the importance of competition in agricultural community dynamics. The objective of this paper is to review methods and data concerning the importance of competition and to propose an approach to understand the roles of competition and management in weed-crop community development. 55 METHODS TO STUDY THE IMPORTANCE OF COMPETITION Key factors and processes in plant communities. Although Welden and Slauson (1986) theoretically uncouple competition intensity and importance in plant communities, measurement of the two processes is strongly linked. Measurement of the importance of competition in agricultural plant communities is enhanced by accurate assessment of intensity. Thus, measurement of importance should consider factors of proximity and biology that contribute to the intensity of competition (Chapter I) as well as other factors and processes that regulate plant populations and communities. Proximity factors include total plant density, species proportion, and spatial arrangement (Radosevich 1987 and Chapter I). The phenology and rate of growth of individual plants are factors of biology that influence competition (Chapter I). However, other biotic and abiotic factors also regulate plant populations and communities and influence the relative importance of competitive interactions in determining species composition. While competition depends on proximity, noncompetitive factors and processes often are densityindependent. These generally non-competitive factors include plant and soil disturbance, seedbank processes, herbivory, and non-competitive plant-plant interactions 56 (eg. allelopathy or mutualism). Agricultural systems are influenced strongly by disturbance, which varies in intensity, frequency, and scale (Grime 1977, Sousa 1980). Disturbance processes in agriculture include a wide range of management tactics, such as tillage, herbicide use, and herbivory (from intentional grazing or pests). Seed banks are influenced by both biotic and abiotic factors. For example, seeds move vertically and horizontally in the soil due to disturbance. Seed banks also are influenced by biological factors such as dormancy, germination, senescence and decay, and predation. Noncompetitive antagonistic or mutualistic interactions among plants also may contribute to community dynamics, and decrease the relative importance of competition in weed-crop systems. Although density-independent factors usually are defined as being non-competitive, they may interact with competition to regulate plant communities. For example, seed bank processes that influence the emergence time and spatial arrangement of new germinants also determine proximity and biological factors that influence competition. Competition may concomitantly influence seed-bank dynamics by determining reproductive success of plants and, thus, seed inputs into the seed bank. 57 Measurement of importance. The importance of competition in weed-crop systems is determined by comparing the influence of competition with all processes that influence the densities and species composition of weed and crop populations. To measure the importance of competition, the influences of competition must be separated from the influences of other processes. Welden and Slauson (1986) propose a method to determine importance using the coefficient of determination (R2) from regression models that describe the intensity of competition. Coefficients of determination (R2) estimate the proportion of variation in a dependent variable that is described by a regression model. In experiments proposed by Welden and Slauson (1986), plant performance would be described by a neighborhood approach (Chapter I) where the response of an individual plant is described as a function of the presence of individuals of similar and different species. The slope coefficients generated by the models will describe the intensity of competition between the target plant and its neighbors. Coefficients of determination indicate the variation in performance of the target plant that was accounted for by the competition model. Welden and Slauson (1986) propose that R2 values from such regression models also estimate how much 58 of the target plant's response was due to competition. Regression models for sphere-of-influence approaches and for stand-centered data (Chapter I) can be used in a similar fashion to generate R2 values that estimate the importance of competition in weed-crop systems. Plant population and community models coupled with sensitivity analysis of life history processes provide an alternative approach to assess the importance of competition in agricultural communities. Models and sensitivity analysis provide a means to compare directly the influences of competition to the influences of other plant community processes. Population- and communitylevel models (eg. Figures 2.1, 2.2, 2.3; Sagar and Mortimer 1976, Werner and Caswell 1977, Watson 1985, Maxwell 1987, Roush and Radosevich 1987) integrate key processes in the life histories of weeds and crops. The relative influences of these processes on population and community dynamics then can be evaluated and compared. Useful tool for the modelling of plant populations are transition matrix models that predict plant population growth (Leslie 1945, Caswell and Werner 1977, Caswell 1978, Werner and Caswell 1978, Watson 1985, Cousens 1986, Maxwell et al. 1988). These models define a set of age, size, or life-history stages of a plant population. Transition rates, the probabilities of moving from one life-history stage to another, drive the model and deter- 59 mine growth rates of the entire population. The transition matrix organizes and summarizes transition probabilities (Maxwell et al. 1988), which are estimated from experiments on key biotic and abiotic factors influencing life-history stages. Sensitivity analysis is a tool for determining the relative sensitivity of a model to its component processes, and may suggest the relative importance of the processes in regulating the overall system (Caswell and Werner 1977, Caswell 1978, Maxwell et al. 1988). Sensitivity analysis can be used to identify the component processes in a model that must be investigated with the greatest precision. Sensitivity analysis also can identify the susceptible points in the life-history of a pest population that may be useful for developing pest management strategies. Selection and definition of key life-history stages and transitions is the first step in developing models for understnding the regulation of weed populations. Once the key processes are defined and mathematically described, such models predict population and community level dynamics in response to variation in system inputs and driving variables. These inputs and driving variables may include the environmental factors, biological traits, and management tactics that influence plant life history processes, and thus population and community dynamics. 60 RESULTS AND INTERPRETATIONS OF EXPERIMENTS Coefficients of determination. Values of R2 from regression models have been used to indicate the relative importance of competition in plant-plant interactions in natural systems (Yeaton and Cody 1976, Yeaton et al. 1977, Welden and Slauson 1986). In Chapter IV, we use R2 values to characterize the importance of competition in a community of four annual weeds. We conducted addition series experiments for a community of four annual weed species, over two growing seasons. Specific densities and proportions of the four species in the community were planted in the first year, and plants were allowed to recruit naturally in the second year. Yield-density models were constructed for each year and the R2 values of the two years were compared. In the first year, up to 76 percent of the variation in individual plant size was described by the competition model. However, only 39% of the variation observed in the second year was attributed to the competition model. This reduction in R2 suggested that factors other than competition may have been more influential in the second year (natural recruitment) than in the first year (planted, controlled densities). 61 Coefficients of determination may underestimate the importance of competition if the model from which they are derived does not adequately describe the influence of various competition factors on plant performance. For example, stand-centered data can be inappropriately fit to simple, linear reciprocal yield models when more general, non-linear forms of the yield density relationships provide greater accuracy. Individualcentered (neighborhood) data also may fit poorly to regression models if independent variables are inappropriately included or excluded. In these cases, the R 2 values generated may be significantly smaller than the R 2 values of more appropriate models, and the role of competition in the interactions may be underestimated. In addition, the models must include the key competition factors that contribute to plant interactions. If appropriate proximity and biological factors are not considered in the models, coefficients of determination may be reduced significantly and the importance of competition underestimated. Importance may be either over- or underestimated by R 2 values if the factors believed to be associated with competition actually influence other processes (Radosevich and Roush 1988). For example, influences of competition and herbivory have been found to interact in plant communities (Fowler and Rausher 1985, Louda and 62 Keeler 1988). If the influences of herbivory and competition on plant responses covary in response to environmental factors, or if herbivory alters the of influences of competition on plant responses, models that describe only proximity factors (competition) may over- or underestimate the importance of competition in plant response. It appears that characterizations of importance cannot be accomplished accurately by only coefficients of determintion. Rather, supporting investigations are required, to examine both competition and non-competitive factors (Firbank and Watkinson 1986). Such investigations would measure the influences on weed populations and communities of competition and of other factors and processes (e.g. disturbance patterns, seed-bank dynamics, and environment). Population and Community Model Approach. Models of agricultural populations and communities can contribute to assessments of importance, and to forming integrated management strategies. Maxwell et al. (1988) point out that models aid in organizing existing knowledge, identifying information gaps, and forming hypotheses about how weed populations are regulated. Models help indicate the potentially important factors and processes in weed populations and communities. 63 Sagar and Mortimer (1976) devised a generalized life-table of weed populations that serves as a working scheme for studying processes that regulate weed populations (Figure 2.1). They applied their model to populations of Alopecurus myosuroides, Avena fatua, Poa annua, Senecio acobea, Daucus carota, and Ouercus petrae, by assembling data from numerous studies on specific life history processes of each species. The resulting models suggested critical phases in the species' life-histories for regulation and potential manipulation of population levels. Although these models concentrated heavily on seed and seed bank processes, and virtually ignored processes of competition among weeds and crops, they provide an important framework for studying the mechanisms of population regulation. Watson (1977) and Maxwell et al. (1988) investigated population dynamics of leafy spurge (Euphorbia esula L.) using transition matrix models. Sensitivity analysis of the initial model (Watson 1977, figure 2.2a) indicated that a key transition in the life history of the spurge population was from basal buds to vegetative shoots. Maxwell et al. (1988) then developed a second generation model to investigate possible mechanisms that influenced this transition, including intraspecific competition. The effects of leafy spurge density then were included in the model, using a submodel that described how transition 64 model, using a submodel that described how transition probabilities responded to shoot density of the weed (Figure 2.2b). Simulations of the model indicated that intraspecific competition was important in regulating the entire leafy spurge population. The weed population model also was used to identify potentially vulnerable stages in the life history of the weed, and to assess the influence of various management tactics on the weed population (Maxwell et al. 1988). Firbank and Watkinson (1986) developed a population model for Agrostemma githago and its influence on yields of spring wheat. The model was driven by mathematical expressions that describe density-independent and density-dependent mortality, individual biomass-density responses, and seed production. Firbank and Watkinson (1986) simulated the influences of seed cleaning and other control practices on the abundance of A. githago. The model demonstrated how the intensity of competition between the weed and spring wheat influenced crop yield. It also indicated that the important factor for regulating the weed population was dispersal, and that seed cleaning was a critical aspect for effective weed control. A conceptual model of weed-crop communities has been developed by Roush, Radosevich, and Wilson (Figure 2.3, Roush and Radosevich 1987, 1988, and Chapter IV). This 65 model is a framework for investigating the importance of intra- and interspecific competition in weed-crop associations. It also identifies key processes that we think regulate these communities. The model, similar to the population models of Sagar and Mortimer(1976), Watson (1977), and Maxwell et al. (1988), is based on life- history traits of plant species. The key processes are described as responses of each life-history trait to competition (density-dependent) and density-independent factors. When the processes that are indicated in Figure 2.3 are expressed as mathematical relationships, the model can be evaluated using simulation and sensitivity analysis. The model, or others like it, then can be used to predict changes in weed species composition resulting from variation in the environment or management tactics. 66 Mature Individuals Generation Gy A1 Seeds produced B Invading seeds Seed rain G C Route I on soil Surface Burled seed seed d bank bank VRoute II 01 D2 Seedlings Established plants F Mature individuals Generation G1+1 A2 Figure 2.1. General form models developed by Sagar and Mortimer (1976) for simulating weed population dynamics. Boxes represent life-history stages that occur between generations (First generation, G1; second generation, G1+1). Arrows indicate the proportion of individuals that continue from one stage to the next. 67 Leafy Spurge Muphorble esula) Diagrammatic Model BASAL BUDS SEEDS 14 1E1311 I 1 ISE DLINGS 02 VEGETATIVE SHOOTS F FLOWERING SHOOTS SS I BASAL BUDS TOTAL G2 SHOOTS "" Hypothesized it relationship _IVEGETATIVE SHOOTS 0 shoot density 1 HFLDAERING I SHOOTS Figure 2.2. Models for simulating leafy spurge (Euphorbia esula) population dynamics: a) the original model developed by Watson (1985) and b) a submodel developed by Maxwell et al. (1988) to include influences of intraspecific competition. 68 REPRODUCTIVE BIOMASS VEGETATIVE BIOMASS NiFIFIEPRODUCTIVE ALLOCATION MATURE ADULTS GROWTH AND INTERFERENCE JUVENILES PREDATION SENESCENCE AND DECAY tESTABLISHMENT SEEDS SEEDLINGS DEAD \DISPERSAL EMERGENCE GERMINATION BREAKING DORMANCY DORMANT conditional DORMANT INDUCING DORMANCY V SOIL SEED BANK NON DORMANT PREDATION SENESCENCE' AND DECAY Figure 2.3. A model developed by Roush, Radosevich and Wilson (Roush and Radosevich 1987, 1988) to understand and explain the regulation of an annual weed community. Boxes represent life-history stages, arrows represent key processes that regulate transitions among those stages. 69 LITERATURE CITED Aldrich, R.J. 1987. Predicting crop yield reductions from weeds. Weed Technology, 1(3), 199-206. Caswell, H. 1978. A general formula for the sensitivity of population growth rate to changes in life history parameters. Theoretical Population Biology, 14, 215-230. Caswell, H., and P.A.Werner. 1978. Transient behavior and life history analysis of teasel (Dipsacus sylvestris Huds.). Ecology, 59 (1) 53-66. Coble, H.D. 1987. Using economic thresholds for weeds in soybeans. Weed Science Society of America, abstracts, St. Louis, MO. Cousens, R.D. 1986. The use of population models in the study of the economics of weed control. European Weed Research Society Symposium Proceedings. 1986, Economic Weed Control, 269-276. Cousens, R.D. 1987. Theory and reality of weed control thresholds. Plant Protection Quarterly, 2(1), 13-20. Cussans, G.W., R.D. Cousens, and B.J. Wilson. 1986. Thresholds for weed control-the concepts and their interpretation. Proceedings gf the European Weed Research Society Symposium, Economic Weed Control. pp. 253-260. Firbank, L.G. and A.R. Watkinson. 1985. On the analysis of competition within two-species mixtures of plants. Journal of Applied Ecology, 22, 503-517. Firbank, L.G. and A.R. Watkinson. 1986. Modelling the population dynamics of an arable weed and its effects upon crop yield. Journal of Applied Ecology, 23, 147159. Fowler,N.L., and M.D.Rausher. 1985. Joint effects of competitors and herbivores on growth and reproduction in Aristolochia reticulata. Ecology 66 (5), 15801587. Harper, J.L. 1977. Population Biology of Plants. Academic Press. New York. 892 pp. Leslie, P.H. 1945. On the use of matrices in certain population mathematics. Biometrika, 33, 183-213. 70 Louda, S.M., and K.H. Keeler. 1988. A genreal role for herbivory in plant dynamics and competitive interactions. in: Perspectives in Plant Competition, D. Tilman and J. Grace (eds). Academic Press. (in press) Maxwell,B.D., M.V.Wilson, and S.R.Radosevich. 1987. A population modeling approach for studying leafy spurge (Euphorbia esula). Weed Technology (in press). Radosevich, S.R., and M.L. Roush. 1988. The role of competition in agriculture. in: Perspectives in Plant Competition, D. Tilman and J. Grace (eds). Academic Press. (in press) Roush, M.L., and S.R. Radosevich. 1987. A weed community model of germination, growth and competition of annual weed species. WSSA abstracts, St.Louis. Roush, M.L., and S.R. Radosevich. 1988.Competition and community dynamic in a summer-annual weed community. WSSA abstracts, Las Vegas. Sagar, G.R., and A.M. Mortimer. 1976. An approach to the study of the population dynamics of plants with special reference to weeds. Annals of Applied Biology. 1, 1-47. Sousa, W.P. 1980. The role of disturbance in natural communities. Annual Review of Ecology and Systematics, 353-391. Watson, A.K. 1985. Integrated management of leafy spurge. in: A.K. Watson (ed.) Leafy Spurge. Weed Science Society of America, Champaign, IL. Welden,C.W. and W.L. Slauson. 1986. The intensity of competition versus its importance: an overlooked distinction and some implications.Ouarterly Review of Biology 61, 23-44. Werner, P.A., and H. Caswell. 1977. Population growth rates and age versus stage-distribution models for teasel (Dipsacus sylvestris Huds.). Ecology, 58, 1103-1111. Yeaton, R.I., and M.L. Cody. 1976. Competition and spacing in plant communities: the Northern Mohave Desert. Journal of Ecology, 64, 689-696. Yeaton, R.I., J. Travis, and E. Gilinsky. 1977. Competition and spacing in plant communities: the Arizona upland association. Journal of Ecology, 65, 587-595. 71 Part 3: Growth, competition, and community dynamics in a four-species annual weed community. Chapter III. MODELS OF A FOUR-SPECIES ANNUAL WEED COMMUNITY: GROWTH AND COMPETITION M.L. Roush and S.R. Radosevich ABSTRACT Growth and competitive ability were measured for a community of four annual weeds over two years. The community consisted of redroot pigweed (Amaranthus retroflexus L.), common lambsquarters (Chenopodium album L.), barnyardgrass (Echinochloa crus-galli L.) and Italian ryegrass (Lolium multiflorum Lam.). Competition was measured using an addition series design planted in 1985 to systematically establish a range of densities and proportions. The second-year populations recruited naturally from 1985 seed production. Analysis of the responses of biomass to density for both years using yield-density relationships quantified relative competitive abilities, and described responses of each species to intra- and interspecific competition. Growth analysis, performed on isolated plants, examined absolute 72 and relative growth rates, net assimilation rate, leaf area ratio, dry weight, root/shoot ratio, canopy area index, leaf area, and leaf area growth rates for each species. Relationships between growth and competition were measured and compared for the 1985 and 1986 seasons, and were compared with a similar experiment conducted at Davis, CA. Results indicated that hierarchies of growth parameters were consistent with competitive outcomes in all cases, with similar relationships established for the 1985 and 1986 communities. Significant changes in the nature of the predictions were observed between the Davis,CA and Corvallis, OR data, indicating that environment significantly influenced the relationships between growth and competitive ability. 73 INTRODUCTION Agricultural systems present a unique opportunity to study processes that regulate plant populations and communities. An understanding of those processes will, in turn, form the basis for planning efficient, economical management strategies. The species composition of weed communities varies in response to all forms of management that are imposed on crop systems (Salisbury 1961, Radosevich and Holt 1984). A population modelling approach to studying agricultural communities organizes and directs research to understand key processes that influence changes in population densities and species composition (Maxwell et al 1988). Models for predicting weed population densities and species shifts also will enhance the development of threshold and management models for weed control (Coussens 1986, 1987). Plant-plant interactions involve complex factors of plant proximity (e.g., density, species proportion, and spatial arrangement) (Radosevich 1987, Roush and Radosevich 1988) and biology (i.e. morphology, physiology, life history, genetics etc.). Agricultural systems simplify many of the interactions of biological and proximity factors, primarily because the overwhelming influences of management and disturbance restrict and 74 homogenize environmental and biotic factors (Radosevich and Roush 1988). For example, summer-annual weed communities consist of species that are very similar in life-history; therefore, key processes that regulate those communities may encompass a simplified suite of factors (Roush and Radosevich 1985, Radosevich and Roush 1988). Previous studies of weed demography using population models have focused primarily on seed production and dispersal processes (i.e. Sagar and Mortimer 1976) as key regulatory processes. Although considerable research has been conducted to measure the influence of weed competition on crop yield (competition intensity, Roush and Radosevich 1988), no studies have directly addressed the roles of plant growth and competition in weed population or community dynamics. A conceptual model (Figure 3.1) serves as the framework to organize the potential regulatory processes in a summer-annual system of weed species (Radosevich and Roush 1988). This model focuses on the major life-history stages of the species, and the processes that regulate transitions among those stages. The processes of plant growth and competition are the focus of this study. In a previous investigation (Roush and Radosevich 1985), relationships were discovered between the growth abilities and competitive 75 abilities of four summer-annual weed species. The premise for that investigation was that plant growth is a mechanism for successful competition in weed -crop systems (Harper 1977, Grime 1979, Roush and Radosevich 1985). Because of the premium on rapid growth in agricultural communities, traits of individuals that contribute to rapid growth ability should contribute to competitive ability in species mixtures. Before the processes of growth and competition can be integrated into a community model, they must be adequately quantified. Growth analysis techniques (Hunt 1982) performed on frequently harvested individuals quantify rates of growth and patterns of biomass allocation. Key growth parameters may include plant size (e.g. biomass, leaf area, height), growth rates (i.e. absolute growth rate and relative growth rate), physiological and morphological components of growth rates (i.e. net assimilation rate and leaf area ratio), root/shoot ratios, plant architecture indices, leaf morphology and leaf area duration. Techniques for measuring the intensity of competition among and within species vary in approach and interpretations (Connolly 1986, Radosevich 1987, and Chapter I). An important motivation for this study was to evaluate recent derivations and expansions of yielddensity models originally developed by Shinozaki and Kira 76 (1956) and others (Bleasdale and Nelder 1960, Holliday 1960, Willey and Heath 1969, Watkinson 1980, 1981, Connolly 1983, Spitters 1983, Firbank and Watkinson 1985). Watkinson (1980, 1981) proposes a general form for plant competition models: W1 = Wm.1 (1 + a. N + (Ni ..N.) 13 3 -b Eq.3.1 where the mean weight per individual of species i (Wi) is described by a nonlinear function of the densities of species i (Ni) and j (Nj). The functions are defined by four parameters: 1) Wmi is the theoretical maximum size of an individual of species i, with no competition, 2) ai is the area necessary for an individual of species i to obtain Wmi, 3) eij is an index of the competitive equivalency (relative competitive ability) of species i and j, and 4) b describes the efficiency of resource use, and defines the curvilinear nature of the response (Watkinson 1981, Firbank and Watkinson 1985). A monoculture model is obtained by setting Nj=0. A similar competition model assumes that the value of the parameter b is 1.0, and is an expanded form of the reciprocal yield law (Spitters 1983): W-1 = B10 B11 N1 + B13 N3 + + Bi nN n Eq.3.2 where the reciprocal of mean weight per individual of species i is described as a linear function of the additive influences of species i, j, n in mixture. In this equation, Bio is the reciprocal of the theoretical 77 maximum size of an individual, and is equivalent to Wm-1/b . The coefficients B.. and B.. 13 describe the influences of intra- and interspecific competition, respectively. Relative competitive abilities are calculated from the expanded reciprocal yield model as the ratio of intra- to interspecific competition (Spitters 1983): Rid = Bii/Bij. Eq. 3.3 The relative competitive ability indices eij and Rid are mathematically related by: R1 .. = e..-1/13 13 Eq. 3.4 When the general form model (Eq. 3.1) is forced to a reciprocal yield model (b=1.0), Rif is mathematically equivalent to 1/eij. We used an addition series design (Roush and Radosevich 1987, 1988, and Chapter I) and the multispecies yield-density relationships (Eqs. 3.1-3.3) to quantify the intensity of competition and competitive abilities among the four summer-annual weed species. Previous competition designs for manipulating proximity factors were limited to investigating two-species mixtures, and did not adequately assess interactions of the proximity factors (density, proportion, spatial arrangement) (Inouye and Schaffer 1981, Connolly 1986, Joliffe et al. 1984, Roush and Radosevich 1988). The design and analysis used in this investigation are unique 78 because they allow manipulation of multiple proximity factors as well as investigation of all-possible species combinations. The overall goal of the research was to develop models for describing interactions and dynamics of weed communities. There were three specific objectives for this study. The first objective was to quantify the intensity of competition and the competitive relationships among four annual weed species, using an addition series design and yield-density relationships. The second objective was to evaluate relationships between growth ability of isolated individuals of the four species and competitive abilities of those species in mixtures. The third objective was to determine whether the relationships between growth and competitive ability for the four species at Corvallis, Oregon, differed from relationships established previously (Roush and Radosevich 1985) for a similar set of species at Davis, California. 79 MATERIALS AND METHODS Growth and competition experiments were conducted in 1985 and 1986 on a 0.2 ha field at the Hyslop Agronomy Farm near Corvallis, OR. The soil was a Woodburn silt loam with approximately 3% organic matter. Before this study, the field had been an established alfalfa stand for five years. Because of the competitive nature of alfalfa, the weed flora was relatively depauperate. The field was treated fall 1984 with dicamba (3,6-dichloro-2methoxybenzoic acid) and glyphosate (N-(phosphonomethyl)glycine) to kill the alfalfa and any weeds present in the field. In May 1985, the field was treated with the soil insecticide chlopyrifos [o,o-diethyl o-(3,5,6-trichloro2-pyridyl)phosphorothioate] and a 10-20-20 (NPK) fertilizer was applied. Meteorological data were collected at Hyslop Farm by the Oregon State University Climatic Research Institute. Mean air temperatures (daily maxima and minima) and daily solar radiation during the experimental periods are presented in Table 3.1. The field was irrigated regularly (approximately every 1.5 to 2 weeks) during the growing season. The weed species included in the study were Amaranthus retroflexus L.(AMRE), Chenonodium album L. (CHAL), Echinocloa crus-galli L. (ECCR) , and Lolium Multiflorum Lam.(LOMU). Seeds were collected from local 80 populations during summer and fall 1984, and stored at 20C. Competition experiments. Monocultures and mixtures of each species were planted in 1985 using an addition series design (Figure 3.2). Each addition series consisted of a two-way density gradient (0 to 200 plants m-2) of two of the weed species. The two other species then were superimposed on the design as a set of strips in a plaid design (Figure 3.2). Plant densities in the strips increased in a counterclockwise direction. Each addition series consisted of 81 units. Each unit was 1 m2 in size and contained some complement of the four weed species. Treatments thus consisted of monocultures of each species, and mixtures of two, three, and four species, at varying total density. All possible two-species combinations were used for the background density gradients, resulting in six addition series types (Table 3.2). Each series type was repeated three times, and arranged in blocks. The eighteen addition series were randomly located in the field, and rotated to vary orientation. Seeds of each species were broadcast planted by hand over a one-week period in June 1985. Soil then was raked over seeds. The field was irrigated after planting, and as 81 needed throughout the growing period. Plants of each species emerged four to six days after irrigation. Emerging weeds that were not species included in the study were removed from the field, and densities of the study species were thinned as needed during the growing season. Plants were harvested 60 days after planting in 1985. All plants within a 0.1 m2 circular quadrat in the center of each 1 m 2 unit were harvested. Plants were separated by species and counted. The aboveground biomass was separated into reproductive and vegetative portions, then dried to constant weight (approximately 2 days at 60C) and weighed. Roots were not harvested. Plants that were not harvested from each experimental unit (90 percent of the original populations) continued to grow and set seed until October 1985, when plants were mechanically flattened to the soil surface. Plants and seeds then were left undisturbed until Spring 1986. Seedlings of the study species began to emerge in mid-March 1986. In April 1986, the field was sprayed with glyphosate (2 lbs/A) to kill Lolium multiflorum and other annual plants that had overwintered or emerged. The field was carefully rototilled (one inch depth) to avoid displacing seed in the soil. The 1985 addition series plots then were relocated and reconstructed in the field. 82 Recruitment of individuals of the four annual weed species was measured 6 March, 22 March, 14 May, 3 June, and 10 July 1986. Individuals within 0.1 m2 circular quadrats in each unit of the addition series of one block were counted. Densities were not manipulated (i.e. thinned) during the growing season in 1986. Final densities were recorded and biomass was harvested in all blocks 26-28 July 1986, 80 days after the beginning of seedling emergence. The harvest proceeded as in 1985. Data from both years were fit to yield-density models (Eqs. 3.1-3.3, Watkinson 1981, Spitters 1983, Connolly 1983, Firbank and Watkinson 1985), using linear regression (SAS Institute Inc. 1985). Both the general model form (Watkinson 1981, Firbank and Watkinson 1985) and the simplified reciprocal-yield model were evaluated. Relative competitive abilities of the species were estimated from coefficients derived for the reciprocal yield models. Separate models were developed for each of the three blocks of addition series. Two forms of mixture models were developed: 1) models using densities of all four species as independent variables, and 2) models for all possible two-species combinations from the experimental design. Relative competitive abilities (Rij) were calculated from Spitters' (1983) form of the multispecies reciprocal-yield models (Eq. 3.3). Values of Rij were calculated 83 for each species from models including all possible species combinations and from models of pairwise species interactions (three replicates each). When the influence of intra- or interspecific did not contribute significantly in a regression model, the value of Bii or Bij was defined as 0.00001 (Appendix). Analyses of variance were conducted to test for variation among the species in Rij, using a general linear models program (SAS Institute Inc. 1985). The analyses estimated and compared overall, mean values of relative competitive ability for the four species. Analyses of variance also were conducted to determine whether results in the pairwise combinations differed from the results for all possible species combinations. Growth analysis. Individuals of each species were grown in isolated pots adjacent to competition experiments, in 1985 and 1986. Pots were filled with soil directly from the field, after tillage and fertilization. Seedlings were exhumed from the margins of the competition experiment and transplanted into the pots in raised beds. Six replicate plants were planted of each species for each of twelve destructive harvest dates. In 1985, individuals of each species were harvested at emergence, and at 5-day intervals until 50 days after emergence. The 84 twelfth harvest was conducted 120 days after emergence. In 1986, individuals were harvested at 5-day intervals until 40 days after emergence, and at 10-day intervals from 40 to 80 days after emergence. At time of harvest, 1985 and 1986, the area of the ground covered by the plant canopy (GA) and plant height (HT) were measured for each individual of the four species. The number of leaves (LVS) on the main axis of each plant was counted, and leaf lengths were measured. Plants then were removed from the soil, separated at the soil line into root (WR) and shoot (Ws) portions, and shoot biomass was separated into stem (WST), leaf (WLF), and reproductive (WRp) components. Leaf areas (LA) were measured using a Licor LI-3100 leaf area meter. Plant parts were dried to constant weight (2 days, 60C), and weighed. From these data, we calculated total biomass (W), root/shoot ratio (R/S), canopy area index (CAI), absolute growth rate (AGR), relative growth rate (RGR), net assimilation rate (NAR), leaf area ratio (LAR), specific leaf area (SLA), leaf weight ratio (LWR), leaf area duration (LAD), relative leaf area growth rate (RGRLA), and rela- tive rates of growth of leaf (RGRLF), shoot (RGRSH), and root (RGRRT) biomass (Table 3.3). Relative growth rates were derived by fitting data to polynomial models that described the response of natural log transformations of 85 the data to time (Hunt 1982). Relative growth rates were calculated as first derivative of each polynomial model. Leaf area duration was derived by integrating the leaf area function, using a linear model for the response of ln-transformed leaf area data to time (Hunt 1982). Analyses of variance were performed as a homogeneity of regression analysis (SAS Institute Inc. 1985). This statistical approach tested for variation among the four species for means of each parameter, accounting for variation in response to time as a covariate. The analysis tested three null hypotheses: 1. the species did not vary in overall mean for the parameter, 2. the parameters did not vary over time, 3. the trends over time did not vary among species. Least square means for each species and each parameter were calculated and separated in the analysis, similar to pairwise t-tests. Homogeneity of regression analysis also was used to test for changes in growth traits between years, and changes in species hierarchies of those traits between years. Correlations between parameters that described growth ability and relative competitive ability, and correlations among growth parameters, were derived using correlation and regression procedures (SAS Inst. 1985). A general regression model was derived that related the mean relative competitive ability of each species (Ri*) with the means of each growth parameter measured for the 86 species. Because only means were evaluated, the sample size was limited to the four species. The correlation matrix of all dependent and independent variables then was evaluated to indicate potential relationships between growth and competition, and among growth parameters. 87 RESULTS AND DISCUSSION Competition. 1985 Multi-species reciprocal-yield models for each of the four species in the addition series experiment for 1985 are presented in Table 3.4. These models described 41 to 76 percent of the variation in reciprocal mean weight per plant as an additive, linear function of the densities of the four species in the system. For example, the response of A. retroflexus was described by a linear multiple regression equation that included as independent variables the densities of all species but L. multiflorum. The greatest influence on A. retroflexus was exerted by C. album, as judged by the magnitudes of the coefficients. The set of coefficients Bic, which describe the influence of C. album on each of the four species, were always greater than the coefficients for the influences of the other species; therefore, C. album had the greatest influence on the biomass responses of all four species. E. crus-galli and L. multiflorum contributed least to the models for the four species; therefore, they had the least influence on the responses of the species. Relative competitive abilities (Rip that were calculated directly from the reciprocal-yield models 88 (Table 3.4) are presented in Table 3.5. Least-squares mean values of relative competitive ability, averaged over all competitors (ri*, Table 3.5), indicate that the superior competitors were A. retroflexus and C. album. The grass species (E. crus-galli and L. multiflorum) were significantly less competitive than the two broadleaf species (p=.0001). 1986. Results of the second-year competition experiment were described less precisely by the competition models than were the 1985 data (adjusted R2, Table 3.6). The experiment populations, naturally recruited from 1985 seed production, were highly unbalanced with respect to species. The range of densities was similar in 1986 and 1985 for A.retroflexus and E.crus-aalli. The maximum density of C.album increased from 77 plants m -2 in 1986 to over 160 plants m-2 in 1986. The maximum density of L. multiflorum decreased from 40 plants m-2 in 1985 to 2 plants m-2 in 1986. Samplesizes for each species (n, Table 3.6) indicated that C. album was present in 1217 of the 1458 1 m 2 subunits in the field. L. multiflorum was only present in 27 of these subunits. This species was considered to have been eliminated from the weed community. Therefore, the 1986 models were for three species only, and the relative competitive abilities of A. retroflexus, C. album, and E. crus-galli were assessed. 89 Competition models for 1986 data that included only the 1986 densities of each species as independent variables indicated that C. album was the only species to consistently and significantly influence the responses of the four species (Table 3.6). Mean relative competitive abilities, calculated from the three-species models and from pairwise interactions (Table 3.7), indicated a distinct competitive hierarchy among the three species (p=.0009 for natural logarithmic transformations of Rid) as follows: C. album > A. retroflexus > E. crus-galli. Data from both years indicated that there were no significant differences between the Rid values and species hierarchies defined by the models that included all species and those defined by the models that included only pairwise interactions. Thus there was no evidence that the data violated the assumption that species interacted in an additive fashion, or that interactions were transitive (i.e. the interactions in the four-species system were a function of the additive influences of the two-species interactions. Salt (1979) defines an "emergent property" of an ecological system as a property that is "wholly unpredictable from observation of the components of that unit". Thus, there was no evidence for emergent properties of competition in the four-species community. The competitive interactions appeared to be 90 transitive because the hierarchies were consistent, regardless of the number and identity of species being considered. 91 Growth Analysis. Mean values of the measured and derived growth parameters for each species in 1985 and 1986 are presented in Tables 3.8 and 3.9. Overall, plants of all species were larger, leafier, and grew faster in 1985 than in 1986 (W, LA, HT, AGR, RGR, NAR, LAR, SLA, and LAD p=.0001). Root/shoot ratios (R/S) also were greater in 1985 than 1986 (p=.03). The two parameters that did not differ between 1985 and 1986 were CAI (an indicator of the openness of the canopy architecture) and LWR (an indicator of leaf morphology). The superior plant growth in the first of the two years may be due to two factors. First, mean daily maximum and minimum temperatures and daily radiation levels were greater in the experimental period for 1985 than in 1986 (Table 3.1). Tillage and subsequent initiation of plant growth occurred earlier in the second year; therefore, temperatures were cooler and light intensity was lower in 1986. Second, the field was not fertilized prior to tillage in the second year and nutrients may have been more limiting in 1986 than in 1985. Patterns in growth parameters for describing plant size (W, LA, HT) differed between 1985 and 1986 (p=.0001), indicating shifts in size hierarchies among 92 the species between the years (Tables 3.8, 3.9, and 3.11). Hierarchies among the species in the growth rates AGR and RGR also shifted from 1985 to 1986 (p=.0001); however, patterns in NAR and LAR (components of RGR) among the species were similar in the two years (p=0.11 and 0.78). There were no differences in species heirar- chies of the allocation (R/S, p=0.16) and architecture (CAI, p=0.075) parameters between years. Although total leaf area (LA) and leaf area duration (LAD) hierarchies shifted between 1985 to 1986 (p=.0002 and .0001), hierarchies of leaf morphology parameters did not differ between the years (SLA p=0.69, and LWR p=0.86). These results indicate that although hierarchies in overall growth response (W, LA, HT, AGR, RGR, LAD) differed between years, species hierarchies of specific morphological, physiological, and architectural traits (NAR, LAR, R/S, CAI, SLA, LWR) remained relatively constant over the environmental changes from 1985 to 1986. All of the observed hierarchies in growth parameters differed strongly from the hierarchies observed for the similar four-species association that we investigated in 1983 at Davis, CA (Roush and Radosevich 1985). Thus, differences in growth ability in response to year to year environmental variation in a single location were more subtle than the responses to environmental differences between the Central Valley of California and the Willa- 93 mette Valley of Oregon (Table 3.1). In the previous study at Davis, CA, equivalent and high RGR's were acheived by four species by compensation between physiological efficiency (NAR) and morphology (leafiness, LAR) (Roush and Radosevich 1985). In this study, RGR was not equivalent among the species (Tables 3.8 and 3.9). Physiological and morphological mechanisms for the hierarchy in RGR that was observed in 1985 and 1986 at Corvallis, OR, may be inferred by investigating how the component parameters, NAR and LAR, contributed to RGR (Figure 3.3). The broadleaf species maintained a balance between efficiency (NAR) and leafiness (LAR), compared to the grass species. E. crus-galli and L. multiflorum maintained very high NAR values; however, there was insufficient leaf area to maintain RGR values as high as those of the broadleaf species. A. retroflexus, C. album, and E. crus-galli exhibited similarly reduced NAR values at Corvallis, OR, compared to values from Davis, CA (Roush and Radosevich 1985); however, the grass (E. crus-galli) also maintained a significantly smaller LAR in OR than the broadleafs. The broadleaf species better compensated for the decrease in physiological efficiency in the cooler, lower light intensity environment, by maintaining a leafier morphology than the grass species. Overall, in both 1985 and 1986, growth ability of the two broadleaf species (A. retroflexus and C. album) 94 was superior to the growth ability of the two grass species (E. crus-galli and L. multiflorum). This trend is in sharp contrast to the distinct hierarchy established at Davis, CA, where the superior species for most growth traits was E. crus-galli, followed by A. retroflexus, C. album, and S. nodiflorum (Roush and Radosevich, 1985). At Davis, CA, superior growth ability was associated with the species possessing the C4 photosynthetic pathway, inferior growth ability was associated with the C3 species. At Corvallis, OR, superior growth ability was associated with leafiness and the broadleaf morphology. Relationships between growth and competition. Most of the growth parameters measured on isolated plants were strongly correlated with competitive ability of the species in mixture in 1985 (Table 3.10, appendix table A3.1). Correlations between growth ability and competitive ability in 1986 were somewhat weaker than in 1985 (Table 3.10, appendix Table A3.2). The weaker relationships may be due to the unbalanced nature of the experiment and the generally poorer fit of competition models in the second year, as C. album occurred in a disproportionate number of competition treatments. Of greater importance may be staggered emergence of the four species in 1986, whereas species emerged nearly simultaneously in 1985. Thus interactions were influenced 95 and only by growth rate in 1985. In addition, we caution that correlations among growth and competition parameters were generated from only a sample of four data points (i.e. the mean values for each species). The strongest correlations with relative competitive ability were found in 1985 for NAR, LAR, LWR, and R/S (Table 3.10). NAR was negatively correlated with relative competitive ability in both years; therefore, the more efficient species (the grasses) were the least competitive. The growth parameters LAR, LWR, and R/S all describe allocation patterns. Allocation to root material, at the expense of shoots, was negatively correlated with relative competitive ability in both years. LAR indicates the relative leafiness of the plant, and LWR describes the allocation of biomass to leaf material. Both of these parameters were positively correlated with competitive ability. Overall, the correlations indicate that leafiness was the key growth trait regulating competitive ability in this environment. Traits that reduced or compromised the amount of leaf area produced by an individual plant reduced the competitiveness of that species in the species mixtures. Hierarchies of nearly all growth parameters generally mirrored competition hierarchies in both years at Corvallis, OR and in the previous study conducted at Davis, CA (Table 3.11). At Davis, CA, the poorest 96 predictor of competitive ability was RGR. In this study, RGR was an excellent predictor of competitive ability in 1985, a mediocre predictor of relative competitive ability in 1986. In all three years, the physiological and morphological components of RGR (NAR and LAR) were better predictors of competitive ability than RGR alone. The nature of the predictions generated by NAR and LAR varied dramatically between the hot, high-light intensity environment of Davis, CA, and the cooler, lower-light intensity environment of the Willamette Valley, OR. In the Central Valley of California, the photosynthetically efficient (high NAR) species were the superior competitors (E. crus-galli and A. retroflexus) and leafiness was negatively correlated with competitiveness. In Oregon, high NAR was negatively correlated with competitiveness and the leafier species were the superior competitors (C. album and A.retroflexus). In California, there was a definite competitive advantage conferred on the efficient, C4 species. In Oregon, that advantage was reduced, competitveness was determined primarily by leaf production, and the broadleaf species were the superior competitors. The relative success of A. retroflexus in both environments may be attributed to its responsiveness in allocation patterns across the two environments of 97 California and Oregon. In California, leafiness was negatively correlated with competitiveness primarily because leafiness and efficiency were negatively correlated. NAR values for all three of the species common to both environments were reduced from Davis, CA, to Corvallis, OR. The dominant species at Davis, CA., E. crus-galli, maintained relatively similar LAR values in the two environments. A. retroflexus had a greater LAR in Oregon than in California; therefore, it was able to compete successfully both in an environment where efficiency was advantageous (Davis, CA) and in an environment where leafiness was advantageous (Corvallis, OR). 98 CONCLUSIONS Strong and consistent relationships between growth ability and competitive ability were observed in both years at Corvallis, OR, and in the previous study at Davis, CA. The nature of the relationships changed with gross changes of environment. A decrease in daily maximum and minimum temperatures of approximately 5C (Table 1), and concomitant reduction in light intensity, resulted in an important shift in key traits for competitive success. In the hot, bright environment, the photosynthetically efficient C4 species were competitively superior to the C3 species; in the cooler, lower-light intensity environment, no advantage was conferred based on photosynthetic pathway. This shift agrees with predictions made by Pearcy et al. (1981) based on growth-chamber experiments for A. retroflexus and C.album. Year-to-year variation in environment influenced relationships between growth and competitive ability in a complex manner. Variations that were observed were not necessarily due to responses of growth rate to variation in environment (i.e. temperature), but were more likely due to variation in timing of emergence, or to difficulties in modelling and measuring relative competitive abilities in the second year (see Chapter IV). 99 Table 3.1. Meteorological data from Corvallis,OR and Davis,CA during competition and growth experiment growing seasons. Davis, CA Corvallis, OR parameter (mean values) 1985 June-July-Aug Temperature (deg.c) (daily maximum) (daily minimum) Radiation (Langleys day-1) 1986 May-June-July 1983 June-July 27.3 22.8 33 10.1 9.3 14 626 535 100 Table 3.2. Addition series types used in a four-species competition experimenta. Series Type AC AE AL CE CL EL Background Species AMRE AMRE AMRE CHAL CHAL ECCR and and and and and and CHAL ECCR LOMU ECCR LOMU LOMU Strip Species ECCR CHAL CHAL AMRE AMRE AMRE and and and and and and LOMU LOMU ECCR LOMU ECCR CHAL a Series types refer to the identity of the two species that were planted in the background, two-way density gradient (Figure 3.2). The species were A. retroflexus (A, AMRE), C. album (C, CHAL), E. crus-galli (E, ECCR), and L. multiflorum (L, LOMU). 101 Table 3.3. Growth analysis parameters and formulae. growth parameter abbreviated symbol operational formula W Dry Weight (g) Leaf Area (cm 2 theoretical formula ) \Root/shoot ratio LA R/S WR/Ws Canopy Area Index CAI LA/GA Absolute Growth AGR dW/dt RGR 1/W * dW/dt Rate (g day-J-) Relative Growth d(lnW)/dt Rate (day-) RGR/LAR Net Assimilation NAR Rate (g cm-' day-1) dW/dt * 1nLA /LA Leaf Are LAR LA/W SLA LA/WL Leaf Weight Ratio LWR WL/W Leaf Area Duration LAD LAdt RGRLA 1/LA * dLA/dt d(1nLA) /dt Leaf Weight RGR (days-) RGRLF 1/WSL * dWsL/dt d(lnWsL)/dt Shoot Wight RGR RGRSH 1/Ws * dWs/dt d(lnWs)/dt RGRRT 1/WR * dWR/dt d(1nWR) /dt Ratio (cm2 g--) Spec fic Leaf Area (cm4 g-1) elnLAdt= e(a+bt)dt (cm2 days) Leaf Arva RGR (days-J) (days-J-) Root Weight RGR (days-J-) 102 Table 3.4. 1/Wi = Reciprocal-yield models for 1985 competition experimenta. Bio + Bia Na + Bic Nc + Bie Ne + Bil N1 R2 N1 .54 i /Wa = .086 +.016 Na +.034 Nc +.014 Ne + 0 1/Wc = .068 +.011 Na +.019 Nc + 0 Ne +.002 N1 .76 1/We = .327 +.087 Na +.144 Nc + 0 Ne + 0 N1 .55 1/W1 =2.043 +.106 Na +.200 Nc + 0 Ne + 0 N1 .41 a In these models, Wi is the mean weight per individual of species i, Bio describes the reciprocal of the theoretical maximum potential size of an individual of species i, Bii describes the influence of species j on species i, N1 is the density of species i. The species are: a, A. retroflexus; c, C. album; e, E. crus-galli; 1, L. multiflorum. Adjusted coefficients of determination (R2) are indicated for each model. 103 Table 3.5. Mean relative competitive abilities in 1985a. species R1* R.la Ric Rie Ril AMRE 1.000 0.475 1.107 - CHAL 1.805 1.000 - ECCR 0 0 1.000 - 0.000145 b LOMU 0 0 - 1.000 0.000757 b 10.370 417.0 a 448.9a Relative competitive abilities were calculated from the coefficients in multispecies reciprocal yield models: a R.. 13 = 13 Ri* represents the least squares mean of relative competitive ability, over all competitor species (see appendix). Missing values indicate that Rii was not estimable because one or both of the speclAs had a coefficient=0. Values of Ri* that are followed by different small letters are significantly different (p=.0001). 104 Table 3.6. Reciprocal-yield models for 1986 competition experiment. lnW.1 = B10 + Bia Na + B Bic N c + B.i e N e + B. l N1 R2 971 lnWa = .16 -.013 Na -.027 Nc + 0 Ne + 0 N1 .38 lnWc = .31 + 0 Na -.013 Nc + 0 Ne + 0 N1 .18 1217 lnWe = .22 + 0 Na -.022 Nc + 0 Ne + 0 N1 .13 366 = .16 + 0 Na + Nc + 0 Ne - .41 Ni .32 27 a 0 In these models, Wi is the mean weight per individual of species i, Bio describes the reciprocal of the theoretical maximum potential size of an individual of species i, B describes the influence of species j on species i, NiJis the density of species i. The species 1, are:a, A. reEroflexus; c, C. album; e, E. crus-galli; L. multiflorum. Adjusted coefficients of determination (R2), and the number of observations for each regression (n), are indicated for each model. 105 Table 3.7. Mean relative competitive abilities in 1986a. species AMRE Ric 1.000 0.464 0.6657 b 1.000 91.3287 a CHAL ECCR Ri* Ria (1.00) 0.000 Rie 1.000 0.0482 c a Relative competitive abilities were calculated from the coefficients in multispecies reciprocal yield models: Rij Bii/Bij Ri* represents the least squares mean of relative competitive ability, over all competitor species. Missing values indicate that R. was not estimable because one or both of the species haaJa coefficient=0. Values of Ri . * that are followed by different small letters are significantly different (p=.0001). 106 Table 3.8. Growth analysis results for 1985a. parameter mean values b (Pi)a (P2) (P3) A W * .0001 .142a .123a .124a .066b .0001 .0001 LA * (cm2) .0001 22.9a 19.2a 12.7b 5.4c .0001 .0001 HT * (cm) .0001 4.4b 4.6b 10.3a 9.7a .0001 .0001 R/S (g g -1) .0001 .22b .14b 1.57a 1.31a .0001 .0001 CAI (cm2 cm-2) .0001 *63ab -78a 005 .0001 AGR (g d-1) .0001 .036 a .031a .025b .009 c .0001 .0001 RGR (d-1) .0001 .255 a .255a .205b .139c .0001 .0001 .0001 1.76b 1.73b 2.33a 2.10ab .04 (g) NAR (10-3g cm 2 d -1 ) -59b -72ab .0001 LAR (cm 2 g -1 ) .0001 200a 182a 120b 99b .0001 .0001 SLA (cm 2 g -1 .033 258a 223a 265a 190b .0001 .65 787 a ) LWR (g g-1) .0001 .725 b 486 d 547 c .0001 .0001 LAD* (cm2 d) .0001 21.9a 18.3b 12.0c 4.8d .0001 .0001 RGRLA (d-1) .0001 .225a .231a .204b .135c RGRLF (d-1) .0001 .243a .246a .218b .153c RGRSH (d-1) .0001 .255a .255a .229b .162c RGRRT (d-1) .0001 .243a .246a .218b .154c * parameters followed by this symbol were In transformed to homogenize variance prior to analysis. a p values are alpha probabilities for the three hypotheses tested by homogeneity of regression analysis (SAS inst. 1985): pi, parameter means did not vary among species; p2, parameters did not vary over time (slopes of parameters versus time = 0); p3, trends in parameter values over time did not vary among species (slopes do not vary among species). b values for species followed by different letters vary significantly (p<.05), according to pairwise t tests performed by homogeneity of regression analysis (SAS Inst. 1985). 107 Table 3.9. 1986 Growth analysis results. parameter (131)a mean values b .0001 .0001 3.4c .0001 .0001 8.8b 10.8a .0001 .0001 .0001 .257c .170c .716a .436b .0233 .0026 .0001 .623a .747a .438b .677a .0189 .0001 6.7c .0001 .0001 .0001 LA* .0001 7.7b 10.9a HT* (cm) .0001 2.5d R/S (g g-1) CAI (cm2 cm 2) (P3) .073b .109a .107a .079b W* (g) (cm2) (P2) A 4.6c 8.0b 8.8a 12.7b 12.8b AGR* (g d-1) .0001 RGR (d-1) .0001 .124a .121b .119b .085c .0001 .0001 NAR (10 -3 gcm-2 d -1 ).0001 1.30c 1.33c 1.88b 3.37a .0001 .0001 60c .0001 .0001 169ab 119c .0001 .71 LAR (cm 2 g -1 ) .0001 124a 116a SLA (cm 2 g- 1 ) .0001 180a 156b 84b LWR (g g-1) .0001 .660b .711a .493c .488d .0001 .0001 LAD* .0001 6.69b 9.24a 6.93b 2.53c .0001 .0001 (cm2 d) * parameters followed by this symbol were In transformed to homogenize variance prior to analysis. a p values represent alpha probabilities for rejecting three hypotheses tested by homogeneity of regression analysis (SAS inst. 1985): pl, parameter means do not vary among species; p2, parameters do not vary over time (slopes of parameters versus time = 0); p3, trends in parameter values over time do not vary among species (slopes do not vary among species). " b The parameters include dry weight (W), leaf area (LA), plant height (HT), root/shoot ratio (R/S), canopy ara index (CAI), absolute growth rate (AGR), relative growth rate (RGR), net assimilation rate (NAR), leaf area ratio (LAR), specific leaf area (SLA), leaf weight ratio (LWR), and leaf area duration (LAD). The growth parameters were calculated as instantaneous values (Hunt 1984). Small letters along a row indicate variation among the species for a particulat growth parameter (p<.05), according to pairwise t tests performed by homogeneity of regression analysis (SAS Inst. 1985). 108 Table 3.10. Correlationsa between relative competitive ability (R11) and growth analysis parameters for 1985 and 1986 gri6wth and competition experiments. growth parameter W* LA* R/S CAI AGR RGR NAR LAR SLA LWR LAD year 1985 1986 0.63 0.83 -0.99 0.37 0.80 0.87 -0.95 0.96 0.20 0.98 0.82 -0.51 0.39 -0.64 0.24 -0.27 0.58 -0.66 0.85 0.64 0.72 0.42 correlation coefficients (r) were generated from analysis of mean values of each growth parameter in relation to relative competitive abilities of each species. Critical significant values of r for three degrees of freedom (n=4) include: .959, p=.01; .878, p=.05; .805, p=.10. 109 Table 3.11. Growth and competition hierarchiesa in the two years of study at Corvallis, OR, and in comparison with data from Davis, CA (Roush and Radosevich 1985). parameter location and year Corvallis, OR Davis, CA 1986 1985 1983 Growth W E>A>C>S C=A=E>L C=E>A NAR E>A>C>S C=A<E=L C=A<E LAR E<A<C<S C=A>E=L C=A>E LWR C>A>L>E C>A>E LAD C>A>E>L C>A=E CAI E<A<C<S C=A>E=L C=A>E R/S E>A>C=S C=A<E=L C=A<E C=A>E=L C=A>E E=A=C=S C=A>E=L A>C=E E>A>C>S C=A>E=L C>A>E AGR RGR Competition R* a The parameters measured were: W, dry weight; NAR, net assimilation rate; LAR, leaf area ratio; LWR, leaf weight ratio; LAD, leaf area duration; CAI, canopy area index; R/S, root/shoot ratio; AGR, absolute growth rate; RGR, relative growth rate; and R*, overall relative competitive ability. 110 REPRODUCTIVE BIOMASS VEGETATIVE BIOMASS REPRODUCTIVE ALLOCATION MATURE ADULTS £ GROWTH AND INTERFERENCE JUVENILES PREDATION SENESCENCE AND DECAY ----ESTABLISHMENT SEEDS SEEDLINGS DEAD \DISPERSAL \EMERGENCE GERMINATION BREAKING DORMANCY DORMANT conditional DORMANT INDUCING DORMANCY NON DORMANT PREDATION SENESCENCE AND SOIL SEED BANK DECAY /O. Figure 3.1. A conceptual model of an annual weed community. Boxes represent life-history stages of each species in the community, arrows represent processes that regulate transitions among the life-history stages. 00 4-11i e 111111 MI I MMIVAIMM II 111I'M IIII I II 11.81111 11111111 MEM al 10011A.111002 Mali 0 brill= M / IIM IMINII111111=111111.1 I. Clor surasammi ImINIFIIII11111111111.111 113113504311 1111141,6111 4 1040"+1044 I 11 ' 111111111111ill a- a, I IT ril._. .,... 111 1151111P11110,0 7 aro 111111111 iii,ifiiiiiiti tiJninisiii Illuicirsium ma in ro s sir ni mil ft V. j ii oo . 4111.101= MIS _&1.4 3 On!! trial 11E1 - 11111. 1E'l . 11E11 lin III 1.1 ..1. am . , 1. `'`'JL 'w- 1111 - '1111111 111.111111 I lit ifs ajIiiiiii.11111111111111111,11 1111111111111zilrfirlfpiiiiiilai 7-Ag. .1111111.3111. la el: 416 i to- Nib EL! 4 pilir . rC1 s. H* cirommoi . a Ito *40. 0 2110111, um mow co t1 0 4,1,1 op 1 .11.111111. . ' II . . - I - II . . . " - - I- - - - - - - . - S I . II . . - iLsiialusi 112 Figure 3.3. Growth analysis results from 1985 and 1986, Corvallis, OR, for four annual weed species: AMRE, A. retroflexus; CHAL, C. album; ECCR, E. crus-galli; and LOMU, L. Multiflorum. The growth parameters RGR, NAR, and LAR were calculated as instantaneous values from the following formulae: RGR=1/W*dW/dt; NAR=1/LA*dW/dt; LAR=LA/W (Hunt 1984). In these equations, W refers to plant dry weight, LA refers to leaf area. 0 .1 v4 0 .1 .05 el LSD .05 LSD .05 LSD II I GROWTH RESULTS - 200 114 LITERATURE CITED Bleasdale, J.K.A., and J.A. Nelder. 1960. Plant population and crop yield. Nature, 188, 342. Connolly, J. 1986. On difficulties with replacementseries methodology in mixture experiments. Journal of Applied Ecology, 23, 125-137. Connolly, J. 1987. On the use of response models in mixture experiments. Oecologia, 72, 95-103. Cousens, R.D. 1986. The use of population models in the study of the economics of weed control. European Weed Research Society Symposium Proceedings. 1986, Economic Weed Control, 269-276. Cousens, R.D. 1987. Theory and reality of weed control thresholds. Plant Protection Quarterly, 2(1), 13-20. Cussans, G.W., R.D. Cousens, and B.J. Wilson. 1986. Thresholds for weed control-the concepts and their interpretation. Proceedings of the European Weed Research Society Symposium, Economic Weed Control. pp. 253-260. Firbank, L.G. and A.R. Watkinson. 1985. On the analysis of competition within two-species mixtures of plants. Journal of Applied Ecology, 22, 503-517. Grime, J.P. 1979. Plant Strategies and Vegetation Processes. John Wiley and Sons. 222 pp. Harper, J.L. 1977. Population Biology of Plants. Academic Press. New York. 892 pp. Holliday, R. 1960. Plant population and crop yield. Nature, 186, 22-24. Hunt,R. 1982. Plant growth curves. University Park Press, Baltimore. Inouye, R., and W.M. Scheaffer. 1981. On the ecological meaning of ratio (De Wit) diagrams in plant ecology. Ecology, 62 (6), 1679-1681. Joliffe, P.A., A.N. Minjas and V.C. Runeckles. 1984. A reinterpretation of yield relationships in replacement series experiments. Journal of Applied Ecology 21, 227-243. 115 Maxwell, B.D., M.V. Wilson, and S.R. Radosevich. 1987. A population modeling approach for studying leafy spurge (Euphorbia esula). Weed Technology (in press). Miller, T.E., and P.A. Werner. 1987. Competitive effects and responses in plants. Ecology. Pearcy, R.W., N. Tumosa, and K. Williams. 1981. Relationships between growth, photosynthesis and competitive interactions for a C 3 and a C 4 plant. Oecologia,(Berlin), 48, 371-376. Radosevich, S.R. 1987. Methods to study interactions among crops and weeds. Weed Technology 1(3), 190-198. Radosevich, S.R., and J.S. Holt. 1984. Weed Ecology, implications for vegetation management. John Wiley and Sons, NY. Radosevich, S.R., and M.L. Roush. 1988. The role of competition in agriculture. in: Perspectives in Plant Competition, D. Tilman and J. Grace (eds). Academic Press. (in press) Roush, M.L., and S.R. Radosevich. 1985. Relationships between growth and competitiveness of four annual weeds. Journal of Applied Ecology, 22, 895-905. Roush, M.L., and S.R. Radosevich. 1987. A weed community model of germination, growth and competition of annual weed species. WSSA abstracts, St.Louis. Roush, M.L., S.R. Radosevich, R.G. Wagner, R.G. Maxwell, and T.D. Petersen. 1988. A comparison of methods for measuring effects of density and proportion in plant competition experiments. (in preparation for Weed Science). Salt, G.W. 1979. A comment on the use of the term emergent propoerties. American Naturalist, 113(1), 145-161. Shinozaki, K. and T.Kira. 1956. Intraspecific competition among higher plants. VII. Logistic theory of the C-D effect. Journal of the Institute of Poytechnics. Osaka City University 7:35-72. Spitters, C.J.T. 1983a. An alternative approach to the analysis of mixed cropping experiments. 1. Estimation of competition effects. Netherlands Journal of Agricultural Science, 31, 1-11. 116 Spitters, C.J.T. 1983b. An alternative approach to the analysis of mixed cropping experiments. 2.Marketable yield. Netherlands Journal of Agricultural Science, 31, 143-155. Watkinson, A.R. 1980. Density dependence in singlespecies populations of plants. Journal of Theoretical Biology. 83: 345-357. Watkinson, A.R. 1981. Interference in pure and mixed populations of Agrostemma githago. Journal of Applied Ecology, 18, 967-976. Willey, R.W. and S.B. Heath. 1969. The quantitative relationships between plant population and crop yield. Advances in Agronomy, 21, 281-321. Wit, C.T. de. 1960. On Competition. Verslagen Landbouwk Onderz. The Hague. 66, 8. 117 APPENDIX THE R.* DILEMMA The statistics Bii and Bij were estimated through multiple linear regression of the mean reciprocal weight per plant of each species against the densities of the four species. However, full models (Table A3.1, all species forced into the model) contained parameters that were probably not significant (based on p values) and should not have been included. In addition, some of the parameters had negative coefficients! The biological interpretation of negative coefficients was unreasonable; moreover, negative values of Bii or Bij resulted in impossible calculations and interpretations of Rid. Stepwise regression was then performed for estimating the statistics Bii and Bij. These regressions generated models with no negative coefficients, but a number of 'missing' coefficients. Missing coefficients prohibited calculations of Rij. Theoretically, missing coefficients represented influences of intra- or interspecific competition that were not statistically distinguishable from zero. However, Bii and Bij values of zero also led to calculation errors in deriving Rij and Ri*. Therefore, all 'missing' values of Bii and Bij were defined as 0.00001. 118 Table A3.1. Full Spitters' (1983) models of 1985 competition (all proximity factors forced into model)a. Species: AMRE model p=.0001, adj.R2=.542, total df=751 var. param.est. Na Nc Ne N1 .0160 .0338 .0149 .0028 s e .0013 .0013 .0037 .0017 p value .0001 .0001 .0001 .0909 Species: CHAL model p=.0001, adj.R2=.760, total df=750 var. param.est. Na Nc Ne N1 .0105 .0190 .0006 .0019 s.e. .0006 .0004 .0016 .0007 p value .0001 .0001 .7144 .0054 Species: ECCR model p=.0001, adj.R2=.552, total df=630 var. param.est. Na Nc Ne N1 .0884 .1435 -.0225 .0035 s.e. .0071 .0057 .0169 .0074 p value .0001 .0001 .1829 .6361 Species: LOMU model p=.0001, adj.R2=.411, total df=719 var. param.est. Na Nc Ne N1 a .1050 .1983 -.0258 -.0103 s.e. .0113 .0097 .0332 .0130 p value .0001 .0001 .4363 .4298 The models were 1/Wi=BieBiaNa+BicNc+BieNe+BilN1, where W is the mean biomass per plant of species i and Ni is the density of species i. The species were: A. reEroflexus (AMRE, a), C. album (CHAL, c), E. crus-galli (ECCR, e), and L, multifloKum (LOMU, 1). Model significance values, adjusted 114, degrees of freedom, parameter estimates, standard errors, and parameter significance values are indicated. 119 Table A3.2. Correlations (r) among growth and competition parameters for 1985 growth and competition experimentsa. Correlation W* W* LA* RS CAI AGR RGR NAR LAR SLA LWR LAD* RCA 1.00 0.96 -0.51 -0.37 0.97 0.92 -0.35 0.78 0.87 0.46 0.96 0.63 1.00 -0.74 -0.13 0.99 0.99 -0.60 0.92 0.71 0.69 0.99 0.83 NAR NAR LAR SLA LWR LAD* RCA LA* 1.00 -0.85 0.10 -0.98 -0.60 -0.95 1.00 -0.45 -0.71 -0.79 0.98 -0.93 -0.06 -0.99 -0.73 -0.99 LAR 1.00 0.43 0.88 0.92 0.96 AGR CAI RS RGR 1.00 -0.19 -0.01 -0.55 0.11 -0.77 0.56 -0.14 0.37 1.00 0.98 -0.58 0.91 0.74 0.66 0.99 0.80 1.00 -0.66 0.93 0.62 0.76 0.99 0.87 SLA LWR LAD* 1.00 -0.02 0.71 0.20 1.00 0.69 0.98 1.00 0.82 d Critical significant values of r for three degrees of freedom (n=4) include: .959, p=.01; .878, p=.05; .805, p=.10. Values followed by this symbol were transformed using natural logarithms prior to analysis. 120 Table A3.3. Correlations between growth and competition parameters for 1986 growth and competition experimentsa. Correlation CORR W* LA* RS CAI AGR RGR NAR LAR SLA LWR LAD* RCA LA* 1.00 0.59 0.24 -0.17 0.96 0.35 -0.30 0.03 0.12 0.07 0.56 -0.51 1.00 -0.28 -0.05 0.78 0.94 -0.95 0.81 0.78 0.71 0.99 0.39 NAR NAR LAR SLA LWR LAD RCA 1.00 -0.94 -0.89 -0.77 -0.96 -0.66 1.00 -0.88 0.19 -0.19 0.38 -0.64 -0.05 -0.87 -0.25 -0.64 LAR 1.00 0.78 0.91 0.82 0.85 CAI RS SLA 1.00 0.46 0.81 0.64 1.00 -0.26 -0.24 0.04 0.22 -0.43 0.59 -0.10 0.24 LWR 1.00 0.69 0.72 AGR RGR 1.00 0.60 1.00 -0.54 -0.98 0.27 0.87 0.40 0.95 0.22 0.64 0.76 0.96 -0.27 0.58 LAD 1.00 0.42 a Critical significant values of r for three degrees of freedom (n=4) include: .959, p=.01; .878, p=.05; .805, p=.10. Values followed by this symbol were transformed using natural logarithms prior to analysis. 121 Chapter IV. MODELS OF A FOUR-SPECIES ANNUAL WEED COMMUNITY: COMPETITION AND COMMUNITY DYNAMICS. M.L. Roush and S.R. Radosevich ABSTRACT Competitive ability and community dynamics were measured for a community of four annual weeds over two years. The community consisted of redroot pigweed (Amaranthus retroflexus L.), common lambsquarters (Chenopodium album L.), barnyardgrass (Echinochloa crus- qalli L.) and Italian ryegrass (Lolium multiflorum Lam.). Competition was measured using an addition series design planted in the first year (1985) that systematically established a range of densities and proportions. Analysis of the responses of biomass to density for both years using yield-density relationships quantified relative competitive abilities and provided models describing responses of each species to intra- and interspecific competition. Yield-density models describing the intensity of competition in the second year included as independent variables the densities and yields from the first year, in addition to second-year 122 proximity factors. The first-year competition models described up to 70% of the observed variation in biomass. Second-year data represent natural recruitment from 1985 seed production. Models for the naturally recruited community described only 15 to 40% of observed variation. Variation in R2 among the models may indicate the relative importance of competition in the community. Recruitment of each species was measured at intervals during the second year. Population densities in the second year, and changes in density between years, were influenced by the identity and proximity of neighbors in the first year. Population models described the responses of second-year densities and population growth rates to first-year proximity factors. 123 INTRODUCTION Associations of weeds and crops are a special, simplified type of plant community. The strong influences of disturbance and resource manipulation that are imposed on crop, and weed systems often create communities that are less complex than more natural systems. These simplified communities provide an ideal opportunity to investigate the regulation of plant communities (Levins 1973, Radosevich and Roush 1988). Investigations of community dynamics in weed and weed-crop systems require an approach to understanding the roles of key lifehistory processes in the regulation of agricultural communities. The integration of basic ecological studies of those key processes into models of weed populations and communities ultimately will suggest strategies for manipulating weed communities and weed-crop systems (Cousens 1985, Radosevich 1987). The influences of competition in plant communities can be described through two distinct approaches: 1) the intensity of competition, and 2) the importance of competition (Welden and Slauson 1986, Radosevich and Roush 1988, Roush and Radosevich 1987, and Chapter II). While intensity is the physiological and morphological response of plants to competition, importance is the role 124 of competition in the evolution of populations and communities. Most investigations of agricultural communities have focused on the response of crop yield to the presence of weeds, ie. the intensity of weed-crop competition (eg. Zimdahl 1980). Investigations of community dynamics in agricultural systems should focus also on the importance of competition, and on other life-history processes that regulate plant populations (Radosevich and Roush 1988, Chapter II). Assessment of the role of competition in the development of weed communities requires accurate measurement of both the intensity and importance of competition. Yield-density relationships can be used to describe both the intensity and importance of competition in weed communities. Plant competition models based on these yield-density relationships were developed originally by Shinozaki and Kira (1956) and others (Bleasdale and Nelder 1960, Holliday 1960, de Wit 1960) to describe intra-specific competition. Recent renovations and expansions of the models describe the influences of both intra- and interspecific competition on plant yield (Watkinson 1981, Connolly 1983, Spitters 1983, and Firbank and Watkinson 1985) and on plant population densities (Firbank and Watkinson 1985). A useful form of the models, derived by Watkinson (1981) and Firbank and 125 Watkinson (1985) is: Wi = Wmi (1 + a(Ni + eijNj)-b. Eq. 4.1 This model is useful primarily because of the biological interpretations that can be assigned to the parameters (Watkinson 1980, 1981). In the model, Wi is the mean weight per individual plant of species i, Wmi is the theoretical maximum size of an individual of species i with no intra- or interspecific competition, a is the area necessary to obtain Wm, eij indicates the equivalency, or relative competitive ability, of species j relative to species i, b describes the efficiency of resource use, and Ni and Nj are the plant densities of species i and j, respectively. A similar, more restricted form of Eq. 1 is an expanded, multispecies form of the reciprocal-yield law (Spitters 1983): 1/Wi = Bio + Bii Ni + Bij Nj +... ...+ Bin Nn. Eq. 4.2 This model represents the special case in Eq. 1 when b=1.0. When Eq. 1 is forced into a reciprocal-yield model (b=1.0), the coefficients in the multispecies reciprocalyield model are related to the parameters in Eq. 1 as follows: B10 = 1/Wmi; Bii = ai/Wmi; Bij = (ai*eij)/Wmi. Eq. 4.3 In addition to assuming a single form of the nonlinear response of plant biomass to density (reciprocal yield, b=1.), the regression coefficients in 126 Spitters' (1983) model are interpreted differently than the parameters in Watkinson's model (1981). Bii and Bij indicate relative contributions of intra- and interspecific competition to the biomass response of species i. Relative competitive abilities must be derived from the regression coefficients as a ratio of intra- to interspecific effects: Rid = Bij/Bii. Eq. 4.4 This index of relative competitive ability is equal to the reciprocal of the efficiency index from Eq. 1 (Rij = 1/eij when b=1.0). The reciprocal-yield model is useful because it is easier to evaluate than the general yielddensity model (Watkinson 1981), primarily because it uses simple multiple regression techniques. Yield-density models can be used to measure indirectly the importance of competition in plant communities. Welden and Slauson (1986) indicate that the coefficients of determination that are generated when fitting such models indicate the importance of competition. Possible limitations to this approach were discussed by Radosevich and Roush (1988) and in Chapter II. R 2 values may both under- and overestimate the importance of competition; however, R2 values may indicate the relative importance of the influences of competition on the dynamics of plant populations in a community. 127 The influence of competition on weed community dynamics can be addressed by measuring the influence of competition on population densities and on changes in population density over time. This approach requires that investigations of weed communities continue over more than a single growing season. To understand the importance of competition in agricultural communities, the influences of competition on community dynamics must ultimately be integrated with the influences of other life-history processes that regulate populations and communities. Thus the development of conceptual and mathematical models that integrate the key processes in agricultural communities (eg. Figure 4.1) will more directly assess the importance of competition in weedcrop communities. The overall goal of the research is to develop models for describing interactions and dynamics of weed communities. The specific objectives of this investigation are: (1) develop yield-density models to quantify responses of a weed community to varying levels of competition, ie. the intensity of competition, (2) to characterize indirectly the importance of competition in the community, using yield-density relationships, (3) to characterize the importance of competition in the community using the responses of population densities and population growth rates to competition. .pa 128 MATERIALS AND METHODS Competition experiments were conducted in 1985 and 1986 on a 0.2 ha field at Hyslop Agronomy Farm near Corvallis, OR. The soil was a Woodburn silt loam with approximately 3% organic matter. Before this study, the field had been an established alfalfa stand for five years. Because of the competitive nature of alfalfa, the weed flora was relatively depauperate. The field was treated in fall 1984 with dicamba (3,6-dichloro-2-methoxybenzoic acid) and glyphosate (N-(phosphonomethyl)glycine) to kill the alfalfa and any weeds present in the field. In May 1985, the soil insecticide chlorpyrifos [o,o-diethyl 0-(3,5,6-trichloro-2-pyridyl)phosphorothioate] and a 10-20-20 (NPK) fertilizer were applied. Meteorological data were collected by the Oregon State University Climatic Research Institute located at the research farm. Mean daily maximum temperatures for the experimental periods in 1985 and 1986 were 27.3 C and 22.8 C, respectively. Mean daily minimum temperatures were 10.1 C and 9.3 C in 1985 and 1986, respectively. The weed species included in the study were Amaranthus retroflexus L.(AMRE), Chenopodium album L.(CHAL), Echinocloa crus-galli L.(ECCR), and Lolium Multiflorum Lam.(LOMU). Seeds were collected from local populations during summer and fall 1984, and stored at 20C. 129 Monocultures and mixtures of each species were planted June 1985, using an addition series design (Figure 4.2). The addition series consisted of a two-way density gradient (0 to 200 plants m-2) of two of the weed species. The two other species were then superimposed on the design as a set of strips in a plaid design (Figure 2). Plant densities in the strips increased in a counterclockwise direction. Each addition series consisted of 81 1 m2 units, where each unit contained a different complement of the four weed species. Treatments thus consisted of monocultures of each species, and mixtures of two, three, and four species, at varying total density. All possible two-species combinations were used for the background density gradients, resulting in six addition series types (Table 1). Each series type was repeated three times. The resulting eighteen addition series were located in a randomized complete block design in the field, and were rotated to vary orientation. Seeds of each species were broadcast planted by hand over a one-week period. Soil then was raked over seeds. The field was irrigated after planting, and as needed throughout the growing period. Plants of each species emerged four to six days after irrigation in June 1985. Emerging weeds that were not species included in the study were removed from the field, and densities of the 130 study species were thinned as needed during the growing season. Plants were harvested 60 days after planting in 1985. The plants within a circular 0.1 m2 quadrat in the center of each 1 m2 unit were harvested. Plants were separated by species and counted. In one block, biomass was separated into reproductive and vegetative portions, and heights of five individuals of each species were measured. All harvested material was then dried to constant weight (approximately 2 days at 60 c) and weighed. Biomass remaining in the addition series after the harvest continued to grow and set seed until October 1985, when plants were mechanically flattened to the soil surface. Plants and seeds remained undisturbed in the field until Spring 1986. Some seedlings of the study species began to emerge in mid-March 1986; however, the field was sprayed in April 1986 with glyphosate to kill plants of Lolium multiflorum and other annual species that had overwintered or emerged in the field. The field was carefully rototilled to a one inch depth to avoid displacing seeds in the soil. The 1985 addition series plots were relocated and restaked in the field. Recruitment of individuals of the four annual weed species was determined on 6 March, 22 March, 14 May, 3 June, and 10 July 1986. Individuals within 0.1 m2 131 circular quadrats in each unit of the addition series in one block were counted. Final densities were recorded and biomass was harvested 25-28 July 1986, 80 days after emergence of the species began. The harvest proceeded as in 1985. Biomass data from both years were fit to yielddensity models (Eqs. 4.1 and 4.2, Watkinson 1981, Spitters 1983, Firbank and Watkinson 1985), using linear and nonlinear regression (SAS Institute Inc. 1985, Statistical Graphics Corp. 1987). The nonlinear yielddensity model (Eq.4.1) was rearranged in two ways to facilitate estimation of the competition parameters. First, monoculture models were ln-transformed to linearize the equation with respect to the parameters Wm and b: In Wi = in Wmi - b In (1 + ai Ni) Eq. 4.5 The In transformation often improves homogeneity of variance in Wi over the range of densities for yielddensity models similar to Eq. 4.1 (Ratkowsky 1983). Data were fit to the model using linear regression to estimate Wm and b, by mechanically iterating values of a. Second, the monoculture models were simplified to the reciprocalyield model (Eq. 4.2) by setting b=1.0. This model assumed that reciprocal transformations of Wi have a constant variance over the range of density (Ratkowsky 1983). 132 Mixture models were evaluated as reciprocal and lntransformed multiple regression relationships, similar to the expanded reciprocal-yield models described by Spitters (1983) (Eq. 4.2). Multispecies reciprocal-yield regression coefficients from 1985 models were used to derive Wmi, ai, and eij for each species. Because the 1986 multispecies models were better described by the in, rather than reciprocal, transformation of Wi, strict analogies to Wmi, ai, and eij were intractable. Models for each species were developed using data from the three blocks of addition series that represent all possible combinations of the species. Models also were developed for all possible two-species combinations. Analyses of variance were conducted to determine whether results in the pairwise combinations differed from the results for all possible species combinations. Recruitment data were used to characterize emergence patterns for the four species in 1986, and to calculate changes in the population densities. Discrete, population growth rates (PGR) of the species were calculated as the difference in final, harvested densities between 1986 and 1985 (PGR=N 86-N85). Discrete, relative population growth rates, or intrinsic rates of growth (RGR), were calculated as the difference of the natural logs of the densities of the two years. One individual was added to each observed density in both years to permit 133 calculations of natural logs for all data points (avoiding N =O, RGR=ln(N86+1)-1n(N85+1)). General linear models procedures (SAS Inst. 1985) were used to determine whether densities (N) and population growth rates (PGR and RGR) varied among species, among years and census dates, or according to the identity of the predominant species in the addition series (background species in series, table 4.1). Interactions among these variables also were investigated. Second-year densities and population growth rates (PRG and RGR) were fit to multiple regression models (SAS Inst. 1985) that described the influence of 1985 densities and yields on 1986 populations. 134 RESULTS AND DISCUSSION Yield-density models. The responses of each species to intraspecific competition are presented in Figure 4.3. In 1985, L. multiflorum always had a significantly greater reciprocal yield, hence a smaller mean weight per plant, than the other three species (p<.001). The slopes of the yield density relationships of the four species were equivalent (Figure 3, p=.9722); therefore, the species responded similarly to increasing intraspecific competition. In 1986, a significant reciprocal-yield monoculture model was derived only for C. album; moreover, the 1986 model for C. album was a poor predictor of mean reciprocal-weight per plant (Table 4.2). Biomass responses of each species in monocultures were described better by reciprocal-yield models than by the nonlinear models (Table 4.2). The best least-squares solutions for the untransformed nonlinear models indicated that b, the coefficient that determines the curvilinear nature of the yield-density response, deviated from reciprocal-yield responses (b=1.0) (Table 4.2). However, when the nonlinear models were transformed to the In -form linear model (Eq. 4.5), and the parameter 'a' was set equal to the least squares solution from nonlinear regression, linear regression provided 135 estimates of 'b' nearly equal to 1.0 for A. retroflexus and C. album. Although these estimates of b may be biased, the ln-transformed models suggested that the reciprocal yield model was appropriate for these species. Variation in parameter estimates and coefficients of determination among linear and nonlinear regressions reflects inherent properties of the error structures of the models and of the different regression procedures. A component of this variation can be seen in graphical representations of the models (Figures 4.3 and 4.4a-d). Reciprocal-yield models were relatively simple to evaluate because of their linearity, and because the reciprocal transformation generally homogenized variances. The nonlinear yield-density models were especially difficult to evaluate because of 1) the nature of the curve and 2) the data at low values of density. The response was most sensitive (greatest changes in biomass per unit change in density) in the density range that was least represented and least precise (i.e. low densities, particularly densities less than 10 plants m2 ). Behavior of the residuals indicated that variation was greatest at low densities and decreased with increasing density for all species. Therefore, the untransformed nonlinear models violated the assumption that variance in W was constant, and the ln-transformed form of the general yield-denstiy model was more 136 appropriate for evaluating these data. Because the lntransformed model indicated that the assumption of reciprocal-yield (b=1.0) was appropriate for monocultures, models to describe species mixtures were developed primarily as linear, reciprocal-yield models. Multispecies reciprocal-yield models for 1985 data are presented in Table 4.3. The regression coefficients that described the influence of C. album on each of the species (Bic) always were greater than the coefficients that described the influences of the other species. Therefore, C. album exerted the greatest influence on the biomass responses of the species in 1985. Estimates of Wmi, ai, and eij from the reparameterized 1985 reciprocal-yield models (Eq. 4.3) are presented in Table 4.4. Values of Wmi predict that, if there were no intra- or interspecific competition, A. retroflexus and C. album would have the greatest potential biomass. The two broadleaf species also would require the greatest amount of unrestricted area (ai) to acheive that potential biomass. The equivalency indices reveal that A. retroflexus and C. album were the most competitive species (p=.0001) because the mean influence of an individual of a competitor species was less than the influence of an idividual of its own species (eij < 1.0). Thus the efficiency indices (eij) indicate that the dominant species in 1985 were A. retroflexus and C. album. 137 Second-year (1986) data were described better by models of in- transformed Wi than by reciprocal-yield models (based on R2 values and homogeneity of residuals). These models (Table 4.5) included only proximity factors (densities of each species) from the current year (1986). In 1986, only C. album consistently influenced the biomass responses of the four species (Table 4.5); thus, C. album appeared to be the dominant species in the mixture in both years. The coefficients of determination for the 1986 multispecies competition models indicate that the models were relatively poor predictors of biomass responses. Therefore a second set of multispecies models was constructed to include information (densities and yields of each species) from the previous year (1985). These models are summarized in Table 4.6. All of the models were improved, on the basis of adjusted R2, when 1985 densities and yields were included as potential variables. The independent variable from the 1985 data that contributed consistently to the 1986 models was the 1985 density of L. multiflorum. In the fall of 1985, after plants in the field were mechanically flattened to the soil, L. multiflorum individuals continued to grow. By spring 1986, overwintering L. multiflorum had established dense populations in the field. Although the L. multiflorum populations were killed prior to tillage, we 138 observed that recruitment and growth of all species was reduced in the experimental units that had dense stands of L. multiflorum. Thus, data that described the presence of L. multiflorum over the winter (ie. densities and yields in 1985) contributed to the 1986 models describing biomass responses of each species. Although explanatory power of the 1986 models was improved by including data from 1985, the models still were less able to make precise predictions in 1986 than in 1985. Table 4.7 compares the coefficients of determination of the yield-density models established for each species in 1985 with models for 1986. The expanded reciprocal yield models for 1985 described 41 to 76 percent of the variation in mean biomass per plant on the basis of plant density. In 1986, only 19 to 39 percent of the observed variation was described by the models. These models included both 1986 and 1985 densities, and 1985 yields, as independent variables. The differences in R2 between the 1985 competition models and the 1986 models suggest that competition was less important in describing plant responses in 1986 than in 1985. The competition experiment in 1985 was more controlled than in 1986. Plant densities were carefully established and maintained in 1985. In addition, the timing of planting and tillage in 1985 resulted in nearly simultaneous emergence of the four species. Plant densi- 139 ties recruited naturally in 1986, plants were not thinned to enforce density levels, and earlier tillage (late April versus late May) resulted in more variable and staggered emergence patterns of the four species (Appendix Figure A4.1 and Table A4.1). Topography in the field in 1986 also was more variable, due to differences in tillage and field preparation between years. Therefore, microsites and microenvironments may have been more variable in 1986 than in 1985. Thus, the 1986 community may have been influenced by a greater range of processes and factors (other than competition) compared to the 1985 community. The experiment in 1986 was highly unbalanced with respect to sample size (frequency, or number of experimental units in which each species was found). For example, in 1986 L. multiforum was only present in 27 of the 1458 1 m2 units in the experiment (Table 4.5). In 1985, each species was present in approximately 50 percent of the experimental units. Although the 1985 L. multiflorum population had a significant influence on the recruitment and growth of all the species in 1986, L. multiflorum was, for all practical purposes, eliminated from the community by the second year. The range of E. crus-galli also was reduced in 1986 (Table 4.5). The ranges of the two broadleaf species, A. retroflexus and C. album, were expanded (Table 4.5). C. album was found 140 with the greatest frequency in 1986, and was present in over 83 percent of the experimental units. Variation in sample sizes for the four species in 1986 is important for two reasons. First, the unbalanced nature of the experiment may be a factor in the loss of explanatory power of the 1986 models. Because C. album was present in a disproportionate number of experimental units, the influence of C. album may have overwhelmed potentially significant influences of the other species. These influences may have been more evident if more units had been free of C. album. Second, the sample sizes emphasize that density was not strictly an independent variable in 1986. Because the species recruited naturally in the second year, plant densities became additional dependent variables, and were subject to processes occurring both in vegetative and seed phases (Figure 4.1) of the plant life-histories. Population densities and dynamics. Absolute and relative rates of population growth indicated that mean population sizes of A. retroflexus and C. album within the experimental units increased, while E. crus-galli and L. multiflorum populations decreased (Tables 4.8 and 4.9). Series type (Table 4.1) significantly influenced the absolute and relative growth rates of the populations of A. retroflexus, C. album, and L. multiflorum (p=.0001). The background species in each 141 series (Table 4.1) were the most abundant species in the series. Thus the identity of the predominant species in a series influenced the growth rates of the plant populations in the experimental units of that series. Although absolute population growth rates (PGR) of E. crus-galli did not vary among series type (p=.32), relative growth rates of E, crus-galli populations did vary among series type (p=.0069). A. retroflexus and C. album performed best (greatest population growth rate) when the two grasses were the background, predominant species in 1985 (Tables 4.8 and 4.9). In these series, there was a greater proportion of units in which the broadleaf species were not present in 1985. Recruitment into these units always resulted in positive population growth. In contrast, units in which the species were present in 1985 could experience either positive or negative growth rates over the two years. A. retroflexus populations declined when C. album was a component of the series background, and C. album populations grew least in series where A. retroflexus was a component of the background (Tables 4.8 and 4.9). Populations of both grass species (E. crus-galli and L. multiflorum) decreased (negative growth rates) in all series types. Populations of L. multiflorum declined most sharply in series where it was a component of the background. Populations of L. multiflorum declined to 142 near zero in all experimental units. Therefore, the series with more experimental units that contained L. multiflorum in 1985 experienced more negative population growth between 1985 and 1986. This trend also occurred for RGR (Table 9), which describes population growth relative to the population size. Multiple regression models were constructed to describe more precisely the influence of 1985 proximity factors (total density and species proportion) on 1986 densities (Table 4.10 and Appendix Table A4.3) and on population growth rates of each species (PGR and RGR, Tables 4.12 and 4.13, and Appendix Tables A4.4 and A4.5). Table 4.11 presents a partial correlation matrix that indicates simple relationships between 1986 densities of each species and the 1985 densities and yields of each species. Yields in 1985 (Yi85) were included as independent variables because total biomass produced by each population in 1985 should be related to the seed production that contributed to the 1986 seed bank. Densities in 1985 (N185) also were included because they may explain influences of factors other than seed production on 1986 populations. Correlations between 1986 densities and 1985 densities and yields (Table 4.11 and Appendix Table A4.3) indicate that the 1986 densities of the four species were most strongly correlated with their own total yields in 143 1985. Thus seed production in the previous year may have been the most important factor influencing densities in the second year. However, yield per individual of each species in 1985, and thus total yield and seed production, were influenced by density and species proportion in 1985. The second strongest, positively correlated variable for each species was its own density in 1985. The 1985 densities and 1985 yields of each species were strongly correlated (Appendix Table A4.3). However, variance inflation factors in the multiple regression analysis indicated that multicollinearity was not a significant problem in the resulting regression models (maximum VIF=3.2, most values of VIF < 2.0). In all cases where significant regression models were obtained, the greatest proportion of the overall R2 for the population response (density, PGR, and RGR) of a species was accounted for the presence (density and/or yield) of that species in 1985 (Tables 4.10, 4.11, 4.12). In addition to the influence of its own 1985 density and yield, A. retroflexus population densities in 1986 (Table 4.10) were significantly influenced by the presence (density) of C. album in 1985. PGR of A. retroflexus (Table 4.12) was most strongly related to the presence in 1985 of A. retroflexus and C. album, while all four species contributed significantly to models that describe the response of RGR for A. retroflexus (Table 4.13). 144 Therefore, there is evidence that both intra- and interspecific competition were important influences on the population dynamics of A. retroflexus. However, the negative influences of intra- and interspecific competition may have been less important than the positive influences of the 1985 seed production. Multiple regression models indicated that the 1986 populations of C. album were most strongly influenced by the yield of C. album in 1985 (Table 4.10). The presence of the grass species in 1985 contributed significantly, but to a lesser degree, to the density model. Partial correlations (Table 4.11) also indicated that 1985 densities and/or yields of A. retroflexus may have had a significant, negative influence on the 1986 populations of C. album. Population growth rate models for C. album (PGR and RGR, Tables 4.12 and 4.13, respectively) identified the density of C. album as the most important factor, and described less variation in the population response than models for actual density (Table 4.14). However, interpretations of these models (Tables 4.10, 4.12, and 4.14) are similar to the interpretations of the population density model: population dynamics of C. album between 1985 and 1986 were most strongly influenced by the presence of C. album in 1985. The 1986 density models for E. crus-galli indicate that 1985 yields of E. crus-galli had the strongest 145 influence on 1986 densities (Table 4.10). However, simple correlations (Table 4.11) indicate that C. album and A. retroflexus may have played a role in influencing 1986 populations of E. crus-galli. Although all correlations were weak, the negative correlations between densities of E. crus-cialli and densities and yields of C. album and A. retroflexus were relatively strong, compared to all other correlations between 1986 densities of the four species and the 1985 densities or yields of other species. Interpretations from coefficients of determination about the importance of competition in regulating population densities and population growth rates must be approached with caution. For example, the extremely large coefficients of determination (R2) for models that describe the relationships between 1985 densities and population growth rates of L. multiflorum do not necessarily reflect the importance of competition in regulating populations of L. multiflorum. In nearly all cases, L. multiflorum populations declined to zero from 1985 to 1986. The rate of decline was related most strongly to 1985 densities of L. multiflorum; i.e. to experimental units in which there were individuals of L. multiflorum to lose. The importance of intra- and interspecific competition was probably negligible. The most important factor influencing the loss of L. multiflorum was probably the winter-annual life-history 146 of the species, and associated timing of germination and growth. The coefficients of determination (R2) from the yield-density and population models for each species are compared in Table 4.14. According to coefficients of determination, 1985 proximity factors described rates of population growth (Tables 4.12 and 4.13) better than they described actual 1986 population densities for A. retroflexus, E. crus-galli, and L. multiflorum (Table 4.14). The reverse was true for C. album: R2 values were greater for the model describing 1986 population density than the models for PGR and RGR (Table 4.14). In addition, R2 values for the population growth rates of the four species (Table 4.14) were negatively correlated with the actual PGR and RGR values of the species (Tables 4.8 and 4.9). Thus, the species with the most positive population growth rates (C. album and A. retroflexus) had the smallest R2 values for models of PGR and RGR, while the species with declining growth rates (E. crus-galli and L. multiflorum) had the greater R2 values. There also was a weak negative correlation between R 2 values from yield-density models (first column, Table 4.14) and R2 values from population growth rate models of the four species (second and third columns, Table 4.14). The species with the biomass responses to competition that were the least predictable (the two grasses) were 147 the species whose population dynamics were the most predictable. The negative correlation between R2 and population growth rate and between biomass R2 and population growth rate R 2 may indicate that the 'losers' from 1985 were more strongly regulated by competition in the community than were the 'winners'. The least competitive species, based on eij values in both years, were the two grasses. These species were strongly and predictably reduced in population size over the two years. The population dynamics of the more competitive, broadleaf species were weakly related to 1985 proximity factors. Thus, competition may have played a greater role in regulating populations of the grass species than of the broadleaf species, while factors other than competition may be relatively more important in determining the population dynamics of A. retroflexus and C. album. 148 CONCLUSIONS Yield-density relationships were used to describe the intensity and importance of competition in the fourspecies weed community. C. album and A. retroflexus were the competitive dominants and the two grass species (E. crus-galli and L. multiflorum) were the inferior species in the community during the first year (1985). In the second year (1986), C. album was the dominant species, A. retroflexus was intermediate, and E, crus-galli was the inferior competitor. L. multiflorum was eliminated from the community in 1986. R2 values suggested that competition was relatively more important in the first year for determining biomass responses of the species than in the second year. Thus, the relative importance of competition may have been reduced in the more variable, naturally-recruited second-year community. Influences of competition on the dynamics of the four-species community were measured as the influences of proximity factors on second-year population densities (N) and on population growth rates (PGR and RGR). There was strong agreement between the influences of competition on plant biomass in 1985 and the influences of competition on the population dynamics of the species. Similar to the biomass models, C. album and A. retroflexus were the superior species in population growth, while E. crus- 149 gain and L. multiflorum both decreased in population size. Although the strongest influence on population growth of each species was the density of that species in 1985, proximity factors that described interspecific interactions also significantly influenced population dynamics of the species. The identity of the predominant, background species significantly influenced 1986 population densities and population growth rates in each series. Densities and yields of competitor species contributed significantly to multiple regression models, or were at least relatively strong correlates of 1986 population densities and population growth rates. Thus, interspecific competition appeared to play a role in the dynamics of the weed community. The importance of competition, relative to all other processes that potentially regulated the community, could not be determined directly from the models. However, coefficients of determination suggested that competition was relatively more important in regulating the populations of the inferior competitors (E. crus-galli and L. multiflorum) than the superior competitors in the system. Population dynamics of the more competitive species (C. album and A. retroflexus) may have been more strongly influenced by processes other than competition, as suggested by the relatively small R 2 values for the 150 population models. These 'other' processes could include seedling emergence and responses of plant growth and development to microenvironmental heterogeneity. To directly assess the importance of competition in the development of weed communities it will be necessary to investigate the role of additional processes in the community dynamics. A conceptual model of a weed community (Figure 4.1) frames an approach for addressing and integrating these processes. The model organizes the life-history stages of the plant species and identifies the key processes that regulate transitions among those stages. Basic ecological investigations of such processes as seed-bank dynamics, seed germination and emergence, and interactions between growth, competition, and environment, then can be integrated into the model. Predictions of weed population densities and species shifts can then be incorporated into economic management models, and can direct and suggest strategies for manipulating the weed community. 151 Table 4.1. Addition series types used in a four-species competition experimenta. Series Type AC AE AL CE CL EL Background Species AMRE AMRE AMRE CHAL CHAL ECCR and and and and and and CHAL ECCR LOMU ECCR LOMU LOMU Strip Species ECCR CHAL CHAL AMRE AMRE AMRE and and and and and and LOMU LOMU ECCR LOMU ECCR CHAL Series type refers to the identity of the two species that were planted in the background, two-way density gradient (Figure 4.2). The species were: A. and CHAL; retroflexus, A and AMRE; C. album, E. crus-galli, E and ECCR; and L. multiflorum, L and LOMU 152 Table 4.2. 1985 Monoculture parameter estimates from reciprocal yield, nonlinear, and ln-transformed nonlinear models a . model: Bio species mean se B11 .. mean se R2 b mean se Wmi mean se mean se 23.8 20.0 12.3 1.5 0.38 0.40 0.27 0.03 (1.0) (1.0) (1.0) (1.0) .90 .87 .44 .17 23.8 9.6 13.5 12.9 13.5 16.9 1.6 0.2 0.96 1.24 0.66 1.95 2.40 12.94 0.01 0.07 0.69 0.22 0.64 0.13 0.43 0.37 3.08 21.63 .64 .65 .35 .16 46.1 31.2 25.0 (0.957) (0.659) (2.396) (0.009) 0.97 0.99 0.61 2.67 .85 .85 .36 .10 a 1/W: AMRE CHAL ECCR LOMU .042 .008 .050 .016 .081 .015 .679 .076 .016 .020 .022 .021 .001 .001 .003 .005 W: AMRE CHAL ECCR LOMU lnW: AMRE CHAL ECCR LOMU 1.4 1.1 1.1 1.2 1.1 0.41 0.04 0.09 0.85 a The parameters were estimated from the yield-density models (Watkinson 1980, Spitters 1983): 1/Wi = Bio+BiiNi; Wi = Wm.(1+a41.) -b ; 1nWi = lnWmi -b[ln(l+a.N.). Means are underlined and standard errors are indicated, values in parentheses were preset and were not evaluated by regression analysis, and non-underlined means of Wm and a were derived from: Wm=1/Bi0, a=Bii/Bio. R 2 values are the adjusted coefficients of determination. 153 Table 4.3. Multispecies reciprocal-yield competition models for 1985a. 1/Wi = Bio + Bia Na + Bic Nc + Bie Ne + Bil N1 1/Wa = .086 +.016 Na +.034 Nc +.014 Ne + 0 R2 N1 .54 1/Wc = .068 +.011 Na +.019 Nc + 0 Ne +.002 N1 .76 1/We = .327 +.087 Na +.144 Nc + 0 Ne + 0 Ni .55 1/W1 =2.043 +.106 Na +.200 Nc + 0 Ne + 0 N1 .41 a The species were A. retroflexus, a; C. album, c; E. crus-galli, e; and L. multiflorum,l. Multispecies reciprocal-yield models (Spitters 1983) describe the response reciprocal transformations of mean weight per plant of each species (Wi) to densities (Ni) of each species in the mixture. Bio is the reciprocal of the theoretical maximum size that an individual plant may obtain. The coefficients B. describe the influence of species j on speqies Adjufted coefficients of determination (114) are indicated for each species' model. 154 Table 4.4. Yield-density model parameters (Watkinson 1980, 1981) derived from reciprocal-yield models for the 1985 experimenta model parameters speciesi Wmi ai eiA eic eiE eiL e.* AMRE 17.13a 0.28a 1.00 1.58 0.33 0.11 0.76a CHAL 12.84a 0.23a 0.47 1.00 0.00 0.05 0.28a ECCR 5.88b 2.3E-6 7.2E6 12.6E6 1.00 0.83 5.9E6b LOMU 0.71c 1.0E -7 15.0E6 22.2E 6 3.4E 6 1.00 8.8E6c a Parameters were estimated through linear regression analysis of multispecies reciprocal yield models (Spitters 1983): 1/W=Bio+BiiNi+BijNj+....+BinNn. The parameters were derived according to the relationships: Wmi=1/B.l0r ai=Bii/Bio, eij=Bij/Bii Wmi (g) is the maximum potential size of qn indivfdual of species i, with no competition; ai (cm plant-i) is the area necessary to acheive Wmi; eii is an equivalency index that compares the influence of tpecies j on species i with the influence of species i on itself (Watkinson 1981); is the least squares mean of the equivalency index ffor species i, over all competitor species. Values in a column that are followed by different lette;'s are sj1gnificantly different (p=.05). E-I iclicates that values are The notation E multiplied by 10-° and 10-7, respectively. 155 Table 4.5. Competition models that describe biomass responses in 1986 from 1986 proximity factorsa. lnWi=Bio + Bia Na + Bic Nc + Bie Ne + Bil N1 R2 n lnWa=0.16 -.013 Na -.027 Nc + 0 Ne + 0 N1 .38 971 lnWc=0.31 + 0 Na -.013 Nc + 0 Ne + 0 Ni .18 1217 lnWe=0.22 + 0 Na -.022 Nc + 0 Ne + 0 N1 .13 366 lnW1 =0.16 + 0 Na + 0 Ne -0.41 N1 .32 27 0 Nc + a The models are related to expanded reciprocal-yield models (Spitters 1983) except that mean biomass per plant was ln-transformed (ln B. is the theoretical maximum size that a plan would attain, Bii describes the Ni iethe density of influence of species j on spcies species i (plants per 0.1 m4), R2 is Elie adjusted coefficient of determination, n is the number of observations included in each regression (number of units in which the species observed, where the total number of units=1458). 156 Table 4.6. Comparison of 1986 competition models that include only 1986 proximity factors with models that include both 1985 and 1986 proximity factors, and 1985 yield dataa. lnW.=f(1985 vars)R 2 lnW.=f(1985 & 1986 vars) R2 lnWa=f(Na,Nc) .38 lnWi=f(Na,Nc,Ne85,N185) .39 lnWc =f(N c ) .18 lnWi=f(Nc,N1,N185 rYc85) .22 lnWe=f(Nc) .13 lnWi=f(Nc,Ne85,N185 IYa851Yc85) .19 lnWl=f(Nc,N1) .32 lnWi=f(Nc,N1,N185 lYe851Y185) .53 a The models are related to expanded reciprocal-yield models (Spitters 1983) except that mean biomass per plant was log-transformed (1nWi). Models in the left half of the table were constructed using stepwisR regression of the 1986 densities (Ni, plants per 0.1 m4) of the four species as independent variables. Models in the right half of the table were from 1986 densities (Ni, slants per 0.1 m4) and 1985 densities (Ni854 plants per m4) and yields (Y185, g plant-J-). Adjusted R values for each set of models are indicated. Complete models are in the Appendix, Table A4.2, and Chapter III. 157 Table 4.7. Coefficients of determination for 1985 and 1986 competition modelsa. R2 species 1985 1986 AMRE CHAL ECCR LOMU .54 .76 .55 .41 .39 .22 .19 * a The models were two forms of multispecies yielddensity model (Spitters 1983): 1985: 1/Wi=Bio+BiiNi+BijNj+....+BinNn. 1986: lnWi=Bio+BiiNi+BiiNj+....+BinNn. L. multiflorum was excluded from the 1986 models because it was not a significant component of the 1986 community. Table 4.8. Population growth rates (PGR=N86-N85) of four annual weed species between 1985 and 1986a. species mean PGR series AC AE -0.95c +1.12b AL CE -0.26bc -1.65c CL EL -1.46c +4.40a AMRE +0.21b CHAL +13.67a ECCR -0.93c -0.95 -1.15 -1.11 -1.13 -0.61 -0.66 LOMU -5.20d -3.59a -3.41a -6.33b -3.64a -6.99b -7.24b a +8.36cd +9'55c +4.57d +17.15b +14.15b +27.96a Population growth rates were calculated as the change in density between harvest dates in 1985 and 1986. Mean growth rates vary significantly among the species (first column) followed by different letters (p<.012). Growth rates for any one species vary significantly among series types (along a row) that are followed by different letters (p<.03). The species were A. retroflexus, AMRE; C. album, CHAL; E. crus-galli, ECCR; and L. multiflorum, LOMU. Table 4.9. Relative population growth rates (days-1, RGR=logN86-logN85) of four annual species that comprise a weed communitya. species mean RGR AC AE series AL CE CL EL 0.00bc +0.01bc +0.85a AMRE +0.15b -0.21c +0.18b +0.08b CHAL +1.10a +0.65d +1.41b +0.76cd +0.99c ECCR -0.33c -°34abc-°'39bc -°'33abc- 0.48c -0.18 a -0.27 ab LOMU -1.13d -0.83a -0.81a -1.48b -1.47b a -0.77a -1.43b +0.79cd +1.95a Population relative growth rates (RGR) were calculated as the change in natural log of density (N+1) between harvest dates in 1985 and 1986. Mean growth rates vary significantly, among the species (first column) followed by different letters (p=.0001). Growth rates for any one species vary significantly among series types (along a row) that are followed by different letters (p<.05). The species were A. retroflexus, AMRE; C. album, CHAL; E. crus-galli, ECCR; and L. multiflorum, LOMU. 1 160 Table 4.10.. Models that explain 1986 population densities of four annual weed species from their 1985 densities and yieldsa. R2 1nN. = f( 1985 densities and yields) 1nN a =1 23 +.016 Ya85 -.020 Nc85 + 013Na85 part. R2 p-value .216 .0001 .019 .0001 .24 .006 .0080 1nNc=1.85 +.031 Yc85 +.028 Ne85 -.028 Y185 +.010 N185 .32 part. R2 p-value .314 .0001 .004 .0057 .003 .0190 .001 .1144 1nNe=0.84 +.024 Ye85 -.041 Ne85 -.007 Ya85 -.006 Yc85 .22 part. R2 p-value 1nN 1 = .166 .0001 .022 .0018 no significant model .018 .0040 .019 .0026 (p=.079, R2=.07) Models were generated using stepwise regression (SAS Inst. 1985), where the In transformed 1986 densities of each species were evaluated as dependent variables and independent variables included the 1985 densities (N) and yields (Y) of ech species. Adjusted coefficient of determination (124) for each model, and partial R values and p-values for each significant independent variable entered are indicated. The species were: A. retroflexus, a; C. album, c; E. crus-galli, e; and L. multiflorum, 1. 161 Table 4.11. Partial, simple correlations between 1986 densities and 1985 densities and yieldsa. Na Na Nc Ne N1 Na85 N c85 N e85 N 185 Y a85 Y c85 Y e85 Y 185 a 1.0000 -0.0920 -0.0260 -0.0084 0.2891 -0.2461 -0.0020 -0.0140 0.4324 -0.2910 -0.0245 -0.0521 correlation (r) Ne Nc -0.0920 1.0000 -0.0686 -0.0496 -0.1297 0.3743 -0.0592 -0.0986 -0.2329 0.5246 -0.1277 -0.1890 -0.0260 -0.0686 1.0000 0.0281 -0.1405 -0.1686 0.1396 0.0207 -0.1177 -0.1779 0.3992 0.1141 -0.0084 -0.0496 0.0281 1.0000 -0.0513 -0.0720 -0.0475 0.0821 -0.0154 -0.0867 -0.0243 0.1998 Partial correlations were derived from multiple regression analysis (SAS Inst. 1985) where the independent variables included 1986 densities (Ni), 1985 densities (Ni85), and 1985 yields (Yi85) of A. retroflexus (a), C. album (c), E. crus-gani (e), and L. multiflorum (1). 162 Table 4.12. Models that explain population growth rates (PGR) of four annual weed species from their 1985 densities and yieldsa. PGR1 = R2 f( 1985 densities and yields) PGRa=3.65 -.980 N a85 + 139 Y a85 part. R2 p-value .341 .0001 -. .074 .0001 063 Nc85 -.020 Yc85 .008 .0001 .42 .001 .0001 PGR c =6.40 -1.05 Nc85 +.674 Yc85 +.168 Ye85 +.052 Ya85 .16 part. R2 p-value .091 .0001 .067 .0001 .001 .0696 .002 .1255 PGRe =0.35 -1.11 N e85 +.137 Y e85 -.059 Y185 part. R2 p-value .490 .0001 PGR1 =0.03 -1.00 N185 part. R 2 p-value .998 .0000 .079 .0001 .006 .0001 .005 Ne85 +.020 Y 185 .000 .1255 .58 .99 .000 .0001 a Models were generated using stepwise regression (SAS Inst. 1985), where the population growth rates of each species (PGR=1986 density-1985 density) were evaluated as dependent variables, and independent variables included the 1985 densities (N) and yields (Y) of each species. Adjusted coefficient of determination (R4) for each model, and partial R.' values and p-values for each significant independent variable are indicated. The species were: A. retroflexus, a; C. album, c; E. crusgalli, e; and L. multiflorum, 1. 163 Table 4.13. Population models that explain relative (intrinsic) growth rates of four annual weed species from their 1985 densities and yields. RGR1 f(1985 densities and yields) R2 RGRa=0.64 -.086 Na85 -.021 Nc85 +.008 Ye85 -.014 Y185 part. R2 p value .318 .0001 .043 .0001 .002 .0201 .36 .003 .0175 RGRc=0.98-.064Nc85-.016Na85+.014Yc+.014Ya85+.024Ye85+.012Y185 part. R2 p value .203 .0001 .008 .0001 .009 .0001 .013 .0001 .005 .0034 .002 .0956 RGRe=0.10 -.284Ne85 -.011N185 -.0031c85 +.029Ye85 -.059Y185 part. R2 p value .514 .0001 .069 .0001 .011 .0001 .005 .0001 RGR1=-.30 -.168 N185 +.009 Ne85 +.002 Nc85 +.008 Y185 part. R2 p value .858 .0000 .0004 .0568 .0002 .1178 24 .60 .003 .0006 .86 .0003 .1111 a Models were generated using stepwise regression (SAS Inst. 1985), where the relative growth rates of each species (calculated as RGR=1986 density-1985 density) were evaluated as dependent variables, and independent variables included the 1985 densities (N) and yields (Y) of each species. Adjusted coefficients of determination (R 2 for each model, and partial 11values and p-values for each significant independent variable are indicated. The species were: A. retroflexus, a; C. album, c; E. e; and L. multiflorum, 1. ) 164 Table 4.14 A compariRon of the coefficients of determination (R4) for yield-denstiy and population response competition modelsa. W.1 model R2 PGR N. Ni 86 RGR AMRE .39 .24 .42 .36 CHAL .22 .32 .16 .24 ECCR .19 .22 .57 .60 LOMU ns ns .99 .86 species a Coefficients of determination (R 2 ) were generated from models developed using stepwise regression (SAS Inst. 1985). Biomass (Wi86), densities (Ni"), population growth rate (PGR), and relative growth rate (RGR) of each species in 1986 were evaluated as dependent variables in the models. The potential independent variables included in all of the models were the 1985 densities and yields of each species. Adjusted coefficients of determination (R 2 for each model are indicated. The species were: A. retroflexus (AMRE), C. album (CHAL), E. crus-galli (ECCR), and L. multiflorum (LOMU). ) 165 REPRODUCTIVE BIOMASS VEGETATIVE BIOMASS REPRODUCTIVE ALLOCATION MATURE ADULTS 1 GROWTH AND INTERFERENCE JUVENILES PREDATION SENESCENCE AND DECAY tESTABLISHMENT SEEDS SEEDLINGS DEAD \DISPERSAL EMERGENCE BREAKING DORMANCY DORMANT conditional DORMANT INDUCING DORMANCY GERMINATION NON DORMANT PREDATION SENESCENCE AND SOIL SEED BANK DECAY Figure 4.1. A conceptual model developed by Roush, Radosevich and Wilson (Roush and Radosevich 1987) to understand and explain the regulation of an annual weed community. Boxes represent life-history stages, arrows represent key processes that regulate transitions among those stages. -11111111 'lilts i I Sim i o 11 11. 1.1 OM MI easagsioar.iaticA g MOEN a oo War, o 074'9'0 111111BI, IIIN ti&noingsi I 111. MN ME Di /Ili EN i ... .. i micron!!! 6121111. . ' '.."-, 11 ammil V 2 WW1 III 111Q.-;11 I A Ig.1IM 166:1-:1171 - a - - OWN ,- 4 '''.. :111111NII Ill li . III --2- =------r----- . . . II IIIII II II II lik!AL 'IL!. 11111 mom MI -I 111= I 'MI . moo ow IFNI All . 11111111 IaI .-. rIZT47,111111111.111111mnimisamemouraliiiiiiiiesimi IN ciiiirsimuto II *Mel* 7,1. rill iFiLi 171.7 111111111. . IIIIMBEItZugitanualIuma ' ilk! 1611 pun lows. ion amir.l. I loilisiaNslimonsi '471 re I Ii::: lq ...... in . 0000000 c -.....;-..7.-. no . 1.11110 ale , NOW 1111 I I* .0.414 moo o 211111111 rani . . . - - . - - . - . - II . - - I - II. I - I - 167 1.2 1 = A + BN 1.0 AMRE 0 CHAL ECCR LOMU 12 24 48 36 DENSITY (plants 60 m2 ) Figure 4.3. Reciprocal-yield (1/W, where W is mean biomass per plant, g-i) responses of A. retroflexus, C. album, E.crus-galli, and L. multiflorum to intraspecific competition (density, N) in 1985. Lines represent the fitted models for each species (1/W=A+BN). 168. b) C.album a) A.retroflexus 10 tn 0 10 20 30 40 Density (plants per 0.1 m ) c) E.crus-galli 0 4 8 12 16 20 242 Density (plants per 0.1 m2) d) L.multiflorum 10 3 8 2 6 31 : 2 0 0 0 2 4 6 8 Density (plants per 0.1 m2) 0 10 20 30 40 Density (plants per 0.1 m2) Figure 4.4. Monoculture responses of mean biomass per plant (Wi) for A. retroflexus, C. album, E.crus-cialli, and L. multiflorum described by nonlinear regression, using the model: Wi = Wmf (1+aiNi)-1". In this model, (Watkinson 1980). N is the monoculture density of the species. 169 LITERATURE CITED Bleasdale, J.K.A., and J.A. Nelder. 1960. Plant population and crop yield. Nature, 188, 342. Connolly, J. 1987. On the use of response models in mixture experiments. Oecologia, 72, 95-103. Cousens, R.D. 1986. The use of population models in the study of the economics of weed control. European Weed Research Society Symposium Proceedings. 1986, Economic Weed Control, 269-276. Firbank, L.G. and A.R. Watkinson. 1985. On the analysis of competition within two-species mixtures of plants. Journal of Applied Ecology, 22, 503-517. Holliday, R. 1960. Plant population and crop yield. Nature, 186, 22-24. Levins, R. 1973. Fundamental and applied research in Science, 181, 523-524. agriculture. Radosevich, S.R., and M.L. Roush. 1988. The role of competition in agriculture. in: Perspectives in Plant Competition, D. Tilman and J. Grace (eds). Academic Press. (in press) Ratkowsky, D.A. 1983. Nonlinear Regression Modeling, A Unified Practical Approach. Statistics, textbooks and monographs, v. 48. Marcel Dekker, Inc. New York. 276 pages. Roush, M.L., and S.R. Radosevich. 1987. A weed community model of germination, growth and competitin of annual weed species. WSSA abstracts, St.Louis. SAS Institute Inc. 1985. SAS/STATTM Guide for Personal Computers, Version 6 Edition. Cary, NC:SAS Institute Inc. 378 pp. Shinozaki, K. and T.Kira. 1956. Intraspecific competition among higher plants. VII. Logistic theory of the C-D effect. Journal of the Institute of Poytechnics, Osaka City University 7:35-72. Spitters, C.J.T. 1983a. An alternative approach to the analysis of mixed cropping experiments. 1. Estimation of competition effects. Netherlands Journal of Agricultural Science, 31, 1-11. 170 Statistical Graphics Corp. 1987. Statgraphics statistical graphics system. STSC Inc. Rockville, MD. Watkinson, A.R. 1980. Density dependence in singlespecies populations of plants. Journal of Theoretical Biology. 83: 345-357. Watkinson, A.R. 1981. Interference in pure and mixed populations of Agrostemma aithago. Journal of Applied Ecology, 18, 967-976. Welden,C.W. and competition distinction Biology 61, W.L. Slauson. 1986. The intensity of versus its importance: an overlooked and some implications.Ouarterly Review of 23-44. Wit, C.T. de. 1960. On Competition. Verslagen Landbouwk Onderz. The Hague. 66, 8. Zimdahl, R.L. 1980. Weed Crop Competition: A review. International Plant Protection Center, Corvallis, OR. 171 APPENDIX RECRUITMENT Recruitment data are presented in Figure A4.1 and Table A4.1. Plant frequencies (densities) varied significantly among census dates (p=.0001, and Table A4.1) for all species. Patterns of emergence varied among the species (p=.0001, and Figure A4.1), and among series types (p=.0001, and Table A4.1). The significance of these data for developing the weed community model will be evaluated more fully when data for recruitment in the continuing weed community in 1987 and 1988 have been collected and analyzed. The data then will be integrated with data that describe environmental conditions (ie. temperature) and with seed germination data from controlled-environment studies. COMPETITION MODELS Several models were summarized in the text. The models themselves are presented in Tables A4.2-5. The significance of the models for characterizing the importance of competition was discussed in the text. The model coefficients describe the contributions of proximity factors and reproduction in 1985 to the intensity of competition in 1986. 172 Table A4.1. Significance (p values) of pre-planned comparisons between plant frequencies measured at varying census dates and harvests, by species and series typea. p-value for comparison species: series AMRE:AC AE AL CE CL EL CHAL:AC AE AL CE CL EL ECCR:AC AE AL CE CL EL LOMU:AC AE AL CE CL EL final 1985 vs final 1986 pre-till vs 5/14/86 6/3/86 final 1986 vs vs 6/3/86 5/14/86 .0707 .4027 .1170 .1010 .3811 .2482 .7462 .0910 .8715 .9511 1.0000 .5357 .0418 .0001 .0001 .0942 .0001 .0001 .0246 .0001 .0001 .1469 .0038 .0001 .5091 .0532 .9491 .9270 .0747 .0001 .7721 .0009 .0445 .0001 .0019 .0001 .4586 .7607 .6889 .3369 .7031 .1470 .4717 .7031 .6093 .1562 .1146 .3169 .0938 .0007 .0114 .0002 .0499 .0002 .8585 .0068 .1870 .0012 .6687 .0001 .9148 .1252 .3726 .0588 .2847 .0169 .7214 .6687 .4121 .1437 .5443 .0297 .0001 .0001 .0001 .0001 .0001 .0001 .7096 .3519 .2639 .7902 .5232 .0045 .5407 .9576 .6511 .7902 .7906 .9153 .9788 1.0000 .9153 1.0000 1.0000 .9576 a The p-values for pairwise comparisons were generated from a general linear models (SAS Inst. 1985) procedure that tested densities of each species for influences of census date (p=.0001 for each species), series (p=.0001 for each species),and interactions among series and census date (p=.0001 forA. retroflexus (AMRE), C. album (CHAL), and L. multiflorum (LOMU), p=.0009 for E. crus(lain (ECCR)). Data represent censuses of one block of the experiment. Final harvests in 1985 and 1986 occurred 1 Aug. and 25 July, respectively. 173 Table A4.2. 1986 yield-density models for a community of four annual weed speciesa. In Wi = B10 + Bij Nj +.... R2 In Wa = 0.16 - .013 Na - .027 Nc .38 In We = 0.31 - .013 N c .18 ln W e = 0.22 - .022 N c .13 In W1 = 0.16 - .412 N1 1 .32 lnWi= Bio + B..N. 13 3 Bik85Nk854--+ Bim85Ym85 R2 lnWa=.20-.013Na-.028Nc+.018Ne85-.013N185 .39 lnWc=.47-.012Nc-.139111-.01411185-.003Yc85-.013Y185 .22 1nWe=.67-.019Nc-.044Ne85-.036N185-.010Ya85-008Yc85 .18 1nW1=.79-.125Nc-.367N1+.059Ye85-.063Y185 .53 a In these models, W1 is the mean weight per individual of species i, Bio is the natural log of the theoretical maximum size of an individual of species i, B.1 is the influence of the 1986 density of species j (N1) on species i, Bik85 is the influence of the 1985 detisity of species k TNk85) on species i, and Bim85 is the influence of the 1985 yield of species m (Ym851 on species i. The species were A. retroflexus (a), C. album (c), E. crus-galli (e), and 1. mgltiflorum (1). Adjusted coefficients of determination (114) are indicated for each model. 174 Table A4.3: Correlations among 1985 densities and yields of each species. CORR NAMRE NCHAL NECCR NLOMU NA85 NC85 NE85 NL85 YA85 YC85 YE85 YL85 NA85 NC85 NE85 NL85 0.2891 -0.1297 -0.1405 -0.0513 1.0000 -0.0703 -0.0310 -0.0791 0.6848 -0.2387 -0.2002 -0.1905 -0.2461 0.3743 -0.1686 -0.0720 -0.0703 1.0000 -0.1202 -0.1246 -0.3412 0.7345 -0.2748 -0.2727 -0.0020 -0.0592 0.1396 -0.0475 -0.0310 -0.1202 1.0000 -0.1160 -0.0536 -0.1275 0.5791 -0.0779 -0.0140 -0.0986 0.0207 0.0821 -0.0791 -0.1246 -0.1160 1.0000 -0.0915 -0.1217 -0.1186 0.7204 CORR YA85 YC85 YE85 YL85 NAMRE NCHAL NLOMU NECCR NA85 NC85 NE85 NL85 YA85 YC85 YE85 YL85 0.4324 -0.2329 -0.0154 -0.1177 0.6848 -0.3412 -0.0536 -0.0915 1.0000 -0.4713 -0.1687 -0.1728 -0.2910 0.5246 -0.0867 -0.1779 -0.2387 0.7345 -0.1275 -0.1217 -0.4713 1.0000 -0.3194 -0.2974 -0.0245 -0.1277 -0.0243 0.3992 -0.2002 -0.2748 0.5791 -0.1186 -0.1687 -0.3194 1.0000 -0.0114 -0.0521 -0.1890 0.1998 0.1141 -0.1905 -0.2727 -0.0779 0.7204 -0.1728 -0.2974 -0.0114 1.0000 175 a. A. retroflexus b. C. album 60 ISO 40 100 rl 0 40 C. SO es E 7/27/55 3/12/56 3/6/54 6/3/46 7/25/56 5/14/46 7/27/55 3/22/56 5/14/56 3/6/56 camas data 6/3/46 7/25/46 census date d. L. multiflorum c. E. crus-galli 1 erE a a z 3/22/64 7/27/55 3/4/56 6/3/56 S/14/56 census data 3/22/86 7/27/55 7/25/56 3/6/66 6/2/66 5/14/56 7/25/04 census data Figure A4.1. Recruitment patterns of A. retroflexus (a), C. album (b), E. crus-galli (c), and L. multiflorum (d) fall 1985 through final harvest, July, 1986. Data are mean densities at each harvest or census date. Standard deviations also are indicated. 176 Part 4: Epilogue. SYNOPSIS, SPECULATION AND SYNTHESIS This section is my opportunity to do three things: 1) to review some of the high points from the body of the thesis, 2) to go out on a limb and speculate about some of the results that were found, and 3) to integrate the results and conclusions of the dissertation and propose new directions for this research approach. Because this section will be unique to the thesis and will not be published elsewhere, it stands primarily as a reflective sketch of the accomplishments and possibilities of this body of research. This epilogue is my opportunity to respond in depth to the inevitable question: "so what?". 177 SYNOPSIS The dissertation was directed to address the question: what is the role of competition in the regulation of weed communities? The first two chapters reviewed the pertinent literature for developing a rational approach to measuring the intensity and importance of competition in weed communities. The second two chapters applied that approach to a specific four-species annual weed community. What I described in the literature reviews was a general disagreement about how to go about measuring competition. There have been, as yet, no definitive experimental approaches developed to measure the intensity and importance of competition. Competition models vary, designs for competition experiments vary, and results and interpretations of competition studies vary. Obviously, the choice of models and experimental designs must address the specific objectives of an investigation. Thus all of the approaches and experimental designs that I described for measuring competition are useful, given certain research objectives and constraints. However, recent advances and renovations in the use of yield-density models and of competition designs that vary multiple proximity factors promise to make significant contributions to the study of plant competition. 178 I focused much of the review, and all of the actual research, on evaluating and advancing yield-density models and systematic experimental designs because I am convinced of their potential value in weed-competition research. The original models for monocultures (eg. Shinozaki and Kira 1956) have been in the literature for over 30 years. The recent use of these models and experimental methods for evaluating mixtures began in the early 1980's. Although numerous authors have promoted the use of these mixture models (ie. Watkinson 1981, Connolly 1983, Spitters 1983, Radosevich 1987, Radosevich and Roush 1988), actual applications and evaluations have only begun. In other words, the potential is there but the jury is still out. In Chapter II, I focused on a new topic for agricultural ecology: how do we determine the importance of competition in weed-crop systems? Although the importance of competition in plant communities is currently a hot topic in basic ecological research, this question has not yet been approached or addressed in agricultural systems. This topic has not been avoided by agronomists; it simply has been overlooked because of the strong focus on measuring the intensity of weed competition in crop systems. Recent developments in the modelling of economic thresholds (eg. Cousens 1985) have awaken in weed scientists an interest in the modelling of 179 weed populations and communities. In order to model weed populations and communities, weed ecologists must understand the key processes that regulate them. Thus agricultural ecologists now must pose their own version of a question that mystifies more basic ecologists: how important is competition in agricultural communities? The research in this thesis was devoted to evaluating the use of yield-density models to measure the intensity and importance of competition. If these models were successful in describing the processes of plant growth and competition, and the influence of those processes on community dynamics, then they will be valuable for developing the plant growth, development, and competition components of a weed community model. In Chapter III, the models were used to integrate plant growth processes with competition processes, by explaining relationships between growth and competition. In Chapter IV, the models were used to integrate the processes of competition with community dynamics, by describing relationships between competition factors (ie. proximity factors) and the dynamics of the populations in a community. The experiments linking plant growth and competition indicated strong relationships between measurable plant growth traits and competitive abilities of the four species studied. Comparison with similar data from Davis, 180 CA, indicated that although the relationships were always strong, actual predictions of competitiveness from growth traits varied with variations in the environment (ie. variations in temperature and light intensity). Thus this set of experiments suggest that growth and competition can be linked; however, considerable experimentation will be necessary to develop models that are predictive over a range of environments. The experiments for linking competition with community dynamics indicated that while the yield density models may provide valuable estimates of the relative importance of competition in weed populations, they cannot precisely quantify the role of competition in agricultural communities. Further, they indicated that the predictive ability of competition models was greatly reduced in a naturally recruited community. Thus estimates of the importance of competition in highly controlled competition experiments may be poor estimates of the role of competition in 'real' weed communities. Models directly relating proximity factors with the dynamics of weed populations indicated that interspecific competition may have been important in determining the dynamics of the species populations. Further, the predictive ability of weed population models (1986 density, PGR, and RGR) based on competition (proximity factors) was negatively correlated with the importance of 181 competition for determining weed biomass and/or the competitive ability of the species. Thus, population models indicated that competition was most important for the weed species populations whose biomass responses were least predictable; biomass models indicated that competition was most important for the species that experienced the most intense competition and whose population dynamics were least predictable My approach to describing community dynamics was primarily a population-level approach. Influences of competition on community traits such as species diversity were not directly evaluated. Results suggested that various components of species diversity decreased between the two years of the experiment; however, direct evaluation of the role of competition was not possible. This subject will be addressed further in the speculations section. Results from the two sets of experiments suggested potential relationships between growth, competition and community dynamics. The precise role of competition in the regulation of weed populations and communities must be addressed from a broader perspective, including lifehistory processes other than competition. 182 SPECULATION Plant Growth Analysis I would like to comment on the potential for using plant growth analysis in investigations of plant competition. I believe that plant growth serves as an ideal integrator of the physiological and morphological processes that contribute to plant competition. Plant growth analysis quantifies those processes at the level where plant-plant interactions occur: the whole plant. Thus growth analysis contributes to an understanding of the mechanisms of competition among plants. (The tools.) Developments during the last 10 years in the field of plant growth analysis have contributed significantly to describing and understanding plant growth and development at the whole-plant level. In particular, R. Hunt (eg. 1982) has advanced the "functional" (continuous) approachto mathematical description of plant growth. This approach uses curve-fitting techniques to describe instantaneous rates of change in plant growth from observations conducted at frequent, short intervals. The "classical" (as labelled by Hunt, 1982) approach is best reflected by the methods of G.C. Evans (1965). This approach calculates growth rates as discrete changes during relatively long harvest intervals. The functional 183 approach brings the Calculus to the classical approach, and collapses harvest interval calculations to instantaneous values. Much of Hunt's (1982) recent book on growth curves is devoted to promoting (prosaically) the functional approach. Rather than reiterate Hunt's (1982) arguments, I will simply and heartily endorse functional plant growth analysis for measuring plant growth and development. (The Growth-Competition Story.) I have twice told the story that relates growth ability of isolated individuals with competitive ability in mixture: the research for my M.S. at Davis, CA, and Chapter II in this dissertaiton. Despite my investment in this approach, further investigations along the same line may not be much more profitable for this particular system, except to test and/or validate the predictive ability of the established relationships. Future contributions of the growth-competition story will come from more direct and specific investigations of the linkages between resources, growth, and competition. Some examples will be discussed below. I have spoken with other researchers who have investigated similar scenarios of growth and competition to the one that we have studied (ie. D.T. Patterson and J.S. Holt). From these discussions, I have concluded that 184 we were either very lucky or very perceptive in our choice of species. Other researchers have not found the clear relationships between growth parameters and competition that we found with our species. For example, J.S. Holt and associates (pers. comm.) have investigated relationships between growth and competition in perennial species. They, and D.T. Patterson and associates (pers. comm.) found few growth traits that were consistently related with competitive ability. Why did our species conform so well? I believe that we may have enhanced our ability to find relationships because we controlled several biological factors by our choice of species. We chose our species based on both similarities and disimilarities. All are cosmopolitan annual weeds, and most were summer annuals. As summerannual weeds common to virtually all disturbed temperate systems, the species have likey cooccurred worldwide for almost as many years as humans have disturbed soil. Each species displays the characteristic life-history traits of annual colonizers described by Baker (1965) and Grime (1977). In particular, all have fast relative growth rates and very high and rapid reproductive capabilities. In contrast, weedy perennials would probably introduce numerous variations in allocation and other life-history traits that were not present in our set of four annual weeds. 185 Variations in the relative importance of the species in temperate agricultural regions seem to correlate with physiological traits such as photosynthetic pathway (C3 vs. C4) and/or allocation patterns (leaf vs. stem vs. root etc.). The species that we chose varied in traits of morphology (broadleaf vs. grass, root/shoot ratios, etc.) and physiology (e.g. C3 vs. C4); therefore, we could compare variations in growth and competition due to morphology and physiology. Our choice of species was was an initial step to account for (quantify or control) the biological factors involved in competition. A few traits varied, many traits were similar among the species. Beyond this strategy, we were just lucky. Where can we go from here with the growthcompetition story? We have suggested a qualitative link between growth and competition. Further experiments might aim to validate this link by including other species in the Davis and/or Corvallis systems. If hierarchies of growth ability and competitive ability of new species added to the previous systems are consistent and predictive on the basis of the physiological and morphological framework established here, the model (relationship) will be validated. What is needed for expanding the predictive nature of the growth-competition model is a set of quantitative links between the environment, growth, and competition. 186 To establish these links, we need experiments that investigate more than the growth ability of isolated plants and the competitive ability of competing plants. Comparisons of the data from California with the data from Oregon indicated that the results of growth and competition experiments, and relationships between growth and competitin, were highly dependent on the environment. We cannot repeat the experiment in every possible environment. We need experiments that explain how the environment influences growth and competition. We need to perform growth analysis on isolated plants in a range of controlled environments and on plants that are growing in competition. Growth models must be developed to predict growth traits and rates from environmental parameters (ie. temperature and light). Competition growth models need to be developed to describe how growth traits change in response to proximity factors. When these linkages are established, the growth and competition components of the community model may be complete. Designing competition experiments (The Addition series.) The experimental design for varying densities and proportions of four species was borrowed from a grant proposal written to the USDA competitive grants program by Pat Werner and Tom Miller at Michigan State 187 University. They have not yet published the results of their investigations using the addition series. Therefore, there has been no formal review in the literature of the experimental technique. I would like to express some of my observations and 'hunches' about this design in general, and about our implementation of the design in particular. In general, the modified addition series design (Figures 3.2 and 4.2) successfully established in the field a range of densities and proportions using (nearly) all-possible combinations of four plant species. Although the implementation of the design was labor- and spaceintensive, I believe the resulting data were well worth the expense. We used the modified design to investigate interactions among four species. The two extra species do not necessarily need to be plant species. The design also could be used to investigate interactions among two plant species and 'something else'. That 'something else' could be biotic (such as competitors, herbivores, etc.) or abiotic (such as resource level, herbicide, or other management tool). One nuance of the four-species design is that it provides more information about the two background species than about the species in the strips. The study system of Pat Werner and Tom Miller included two 'intercrop' species and two 'weed' species; therefore, 188 they used the two crops as the background and the two weeds as the strip species. For my study, there was no such grouping of the species; therefore, I chose to repeat the series and vary background species to obtain all-possible two-species combinations in the background two-way density gradients. After completing the analysis of the two years of experiments, I feel that this decision was prudent. First, we achieved an overall balance of sample sizes for the first year experiment. Thus, we had a similar set of information for each species in the first year. The unbalanced nature of the experiment in the second year obviously reduced our ability to model competitive interactions. Second, although series type (Table 4.1) did not significantly influence biomass responses, it did influence population responses (Table 4.?). Therefore, we were able to detect influences at two levels of spatial scale: biomass responses to competitive interactions occurred primarily within the 1 m2 experimental units, whereas dispersal, tillage, and other processes 'stretched' population responses beyond the boundaries of the experimental units. (Sytematic or randomized?) The addition series design is strictly systematic only in conception. The design, as illustrated in Figures 2.2 and 3.2, need not be literally translated into the 189 field. The design can be used simply as an indicator of treatments. The treatments can be arranged randomly in the field. The decision to randomize or to plant systematically is left to the experimenter. In our case, a systematic planting design (literal translation of the design to the field) offered numerous advantages. First, a systematic design required less space. Because neighboring experimental units were more similar than would be expected from a random arrangement, we observed minimal edge effect. Therefore, we were satisfied with a smaller unit size than would have been desirable with randomization. This decision becomes more important as the scale or size of experimental plants increases. Second, planting was simpler because of the systematic arrangement. I was able to plant nine or more units at once. With randomization, planting would be limited to one unit at a time. In retrospect, my experiment could have been randomized without significantly increasing the space and time required if the rest of the experimental design were different. With three repeated blocks of the six series types, randomization would have been extremely difficult. However, the repetition probably was 'overkill' with respect to the yield density models. Replication existed throughout the experiment whenever a similar complement of species was generated in experimental units of the six 190 different addition series types (i.e. the series were the replicates). Repetition of each of the six series types enhanced but did not necessarily guarantee more replication of treatments. With nearly 1500 experimental units (thus many degrees of freedom), virtually all statistical models were extremely highly significant (p=.0001). Fewer repetitions of each series type (two, or even one) would probably have been sufficient for the yield density models. The level of replication that we utilized was necessary, however, for evaluation of population dynamics based on the influence of series type. With fewer total series, the choice to randomize or not would have been more difficult. Because the series (the true replicates) were randomly located and oriented in the field, the design was randomized for specieseffects within a single repetition of the six series types. Thus analysis of variance for comparing among species values of competition parameters and statistics would be valid in any case. My sole reservation about the systematic design is that systematic trends may influence the yield-density models. 1 do not believe that field heterogeneity would have played a role in this bias because tillage homogenized much of the field and observed variation occurred on a scale greater than the size of the addition series themselves. Blocking of the replication of the series in 191 the field appeared to account for most of the field heterogeneity. Rather, the design itself may bias the treatment densities according to its location in the series. If I were to perform the experiment again with the same level of repetition, I would add a 1 m wide border strip around each series. My reservation was that units on the periphery of the series experienced neighbor units that were more different that units within the series. I do not feel that this variation in neighbor units was a significant problem in my experiment. However, if I were doing it again, I would plant border strips to remove doubt. In retrospect, I would increase the size of experimental units to at least 1.5 or 2 m2, so that the observational unit could be increased. I had no reason to expect that plants were influencing or being influenced much beyond the 1 m2. However, I would have preferred a larger sample-area (observational unit). The inner 0.1 m2 sample in each unit defined the lowest measurable density as 10 plants m-2 (one plant per 0.1 m2). Even where actual densities in a unit were lower than 1 plant m-2, the density on paper was 10 m-2. Some of the variation at the low end of the density range may have been attributed to this problem of measuring density. Fitting data to the yield-density models may have been significantly enhanced if I had data for densities below 10 plants m-2. 192 Yield-density models: pearls or red herrings? As the title to this section implies, I have some mixed feelings about theoretical yield-density relationships. A red herring is "something used to confuse, or to divert attention from something else" (Webster's New World Dictionary. College edition, 1957, World Publishing Company). In particular, I am skeptical about the use of nonlinear modelling to evaluate the general-form yield density relationships described by Watkinson (1980, 1981) and others: Wi = Wmi (1 + ai (Ni + eij Nj)-b. The biological interpretations ascribed to the parameters in the model were intended to elevate the yield-density models from simple, empirical models to a more theoretical basis for describing competitive interactions. In one sense, the recent resurrection of the yielddensity models seems like the harvesting of an oyster. The grain of sand, first laid down in 1956, may have become a luminous pearl that will enlighten plant ecologists about the processes of interspecific plant competition. A second possibility is that we may spend a huge amount of energy and use a number of tools in opening the oyster, only to realize that the grain of sand is really just a grain of sand. The models 193 themselves probably are no less empirical than they were 30 years ago. After statistically struggling with the models in expectation of pearls, I began to wonder if we had harvested red herrings instead of oysters (potential pearls). I also began to think that perhaps I should be content with the grain of sand. My misgivings are primarily statistical in nature, and primarily concerned with difficulties in evaluating the nonlinear model. Watkinson (1980, 1981) and others have suggested that the nonlinear form is better than the multispecies reciprocal yield model (Spitters 1983) because it is more biologically realistic, primarily because the parameter bi is estimated rather than forced to a value of 1.0. I was persuaded that, by estimating b, I could learn more about the nature of the competitive interactions. Therefore, I needed to pursue statistical tools to analyze the nonlinear model. Colleagues with a statistical bent have cautioned against the numerous pitfalls of nonlinear regression. The nature of yield-density responses was another reason to approach the yield-density models with trepidation. Consider the function that we are trying to mathematically describe (Figure 4.4). First of all, there is no such thing as zero density, yet we are fitting models with intercepts at N=0. Second, residuals indicated that the data for plant biomass (individuals or mean indivi- 194 duals) are disproportionately more variable at low densities; therefore, the data violate the assumption of homogeneity of variance. Third, the nonlinear model is hyperbolic and most sensitive to changes in density precisely in the density range where we have the least amount and greatest variablity of data (density approaching 0). In summary, the nonlinear model was a nice idea but it was nearly impossible to accomodate statistically. Maybe the model should be transformed in some manner. Natural log transformations generally help these hyperbolic, yield-density models (Ratkowsky 1983). Now the model is expressed in a simple, linear form with nonlinear parameters (ai, eij): lnWi = lnWmi - bi ln( ai (Ni + eij Nj)) If we are willing to mechanically iterate the nonlinear parameters, this model can be approximated using linear regression. We then have a few options. We can be happy with approximations; however, this approach only gives us statistics about Wmi and bi, and not about ai and eij. I was more interested in eij than Wmi or bi. Therefore, my options were to go back to nonlinear regression or to find another approach to evaluating relative competitive ability (eij). In my analysis of monocultures, estimates of bi were extremely close to 1.0. In other words, the 'empirical' multispecies reciprocal-yield analysis (Spit- ters 1983) would have been just as good all along! 195 The lesson in this 'oyster opening' was that the effort to open the oyster was probably as valuable as the product inside, and that the pearl was no more valuable than the grain of sand. In other words, there may be no pearl, but neither was the activity strictly a 'red herring'. In my opinion, the greatest contribution of the yield-density models for interspecific competition is the systematic approach that they take to evaluate the influences of various proximity factors. An empirical model is an empirical model is an empirical model. The 'theoretical yield-density model' was a red herring. The grain of sand was the use of regression analysis and empirical models to evaluate the responses of plant biomass to variation in both total density and species proportion. Unlike Spitters (1983) and Watkinson (1980, 1981), who propose specific yield-density models, Connolly (1987) describes his yield-density model in a more genral form: Wi = f(Ni, Ni). Perhaps Connolly (1987) does a service to those of us who look for pearls in the literature when there are really only grains of sand. 196 The importance of competition. (The importance of importance.) Discussions about the importance of competition in Chapters II and IV contain a circular argument. We state that importance is important for developing weed population and community models. In devising a methodology for measuring importance, we indicated that R2 is only an approximation of importance; we need to use a modelling approach to measure the importance of competition. Thus population and community models seem to be both the means and the end of studying the importance of competition. In reality, the whole approach is simply an argument for investigating beyond intensity of competition, for studying more about weed competition than losses of crop yield. The importance of competition seems to be synonymous with weed population model. The value of importance and weed population models will be recognized as we move from responsive, symptomatic weed control practices to predictive, strategic weed management. The responsive approach plans management strategies based on predictions of crop loss due to observed densities of weed species. The over- whelming focus on intensity of competition in weed research reflects the responsive approach to weed control (eg. how much yield will we lose due to the presence of density Ni of species i?). Economic threshold models are 197 a diagnostic tool for this responsive, symptomatic approach to weed control (eg. we have Ni weeds of species i in the field; can we afford to (or not to) spray?). A predictive approach will plan management strategies based on predicted, future weed species densities. The devel- opment and integration of weed population models with economic threshold models will provide tools for predictive, strategic weed management. For example, suppose we currently have Ni, Nj,..Nn densities of species i, j, ....n. Next year, we plan to plant crop X at appro- ximately time T (or when environmental conditions are at level L) and use the set of management techniques M in the field. What species composition and densities can we expect in the field? with the crop? them? Which species will be of concern To what level can we afford to control What additional management strategies will enhance our ability to minimize the economic impact of the weed community now and in the future? These questions form the ultimate objectives of population and economic threshold models of weed-crop systems. (R2 values and the importance of competition.) I have suggested several times that R2 values are 'less-than-perfect' indicators of the importance of competition; however, they may be of considerable value as a comparative tool or in forming hypotheses. 198 Intuitively, R2 values in competition models seem like reasonable estimates of the importance of competition. Obviously, an R2 value is a statistic of the model that is sensitive to other statistics of the model and to interactions between competition and the other processes that regulate plant communities. The question is: how far out on a limb should we go in interpreting the importance of competition from R2 values? It might be argued that, because they were of relatively similar competitive ability, the difference between the R2 values of the two grasses may reflect the different contributions of competition and life-history to regulating the community. Thus, perhaps 60 percent of the variation in population dynamics of both of the species could be explained by proximity factors, while the remaining 40 percent of the observed variation in the response of L. multiflorum may be attributed to its winter-annuality. This argument is, of course, an absurd speculation (ie. I wouldn't venture out on this limb). However, the comparison may form the basis for other experiments aimed at partitioning the role of competition from the roles of other processes and factors. For example, one might impose controlled level(s) of some 'other factor' (eg. biotic, such as herbivore, or abiotic, such as herbicide) on a competiton experiment (using a modified addition series design?). Variation in 199 R 2 values from competition models might then be used to indicate variation in the importance of competition due to the other factor. For a second example, competition experiments might be conducted over several seasons using two closely related species (or biotypes) that vary in some life-history trait, such as some seed bank processes. R 2 values from competition models, and from models that include the influence of the seed bank processes of the species (or biotypes) on the populations, then may partition the importance of influences of competition from the seed bank processes. On the other hand, the partitioning of influences might better be approached using the population models themselves and sensitivity analysis. Key processes and factors other than competition. I propose two general categories of factors/processes, other than competition, that may have contributed to variability in the responses of biomass and population density in my experiments. The first category includes factors that influence the life-history processes depicted in the community model (Figure 1.1), and represents sources external to the plants themselves. The second category includes the genetic and developmental variability of the species themselves, and represents 'internal' sources of variation in those life-history 200 processes. (External sources of variation.) The life-history processes that Iinvestigated were plant growth and competition. In the experiments, I controlled some of the factors that influence growth and competition, I accounted for some, and still other factors I assumed were negligible or benign. For example, consider the competition factors that were defined in Chapter 1: proximity, biology, and environment. We systematically controlled the proximity factors of density and proportion; however, we assumed that spatial arrangement of plants was random and/or of little influence. The influence of growth rate was a biological factor that was experimentally accounted for; the timing of growth (time of emergence) was assumed to be simultaneous for all species. Environment was assumed to be benign, and microenvironments were assumed to be homogenous throughout the field. In all cases, there was evidence that our assumptions were violated. In particular, the timing and nature of the tillage prior to the establishment of the secondyear community resulted in clumped distributions of individuals, variation among the species in emergence time, and possible variation in microenvironment due to variation in microsite topography. How can we account for the influences of these factors in future investigations? We can attempt to 201 control them all; however, we then risk losing reality. The second-year community was unique among weed competition experiments precisely because it was naturally recruited and subject to the processes that influence 'real' weed communities. An alternative is to try to isolate key environmental factors that may have driven the observed variation, isolate the mechanisms by which they influence the processes of growth and competition, and then integrate them into the community model. This is the mechanistic and deterministic approach. For example, if we develop mathematical models to explain the influences of temperature on seed germination and emergence, and on plant growth, we can inject those models into our community-level model. The influences of light intensity and quality on community dynamics may similarly be described by submodels that describe how light intensity and quality influence the individual life-history processes. These submodels then will link the influence of the environment, as a set of driving variables, to the lifehistory processes themselves and ultimately to the dynamics of the community as a whole. This research also ignored plant mortality. We assumed that any mortality that occurred was densityindependent (eg. no self-thinning) and did not influence the outcome of competition. No data were collected to evaluate the amount or type of mortality that occurred in 202 the field. However, based on my observations during the recruitment period in the second year, I would speculate that our assumption of density-independent mortality was valid. There appeared to be significant mortality only during the first few days after emergence of the seedlings, well before plant-plant interactions were likely. Once individuals were established, there appeared to be very little mortality. Because most of the mortality occurred in juveniles, mortality was probably independent of density and primarily influenced by microenvironment (safe site). Density-independence does not necessarily mean that mortality processes were independent of competition processes. For example, density-independent mortality may have significantly influenced the spatial arrangement of individual plants. Thus microenvironment probably influenced spatial arrangement, which in turn may have influenced competitive interactions among the species. Investigations of the influence of environmental factors (such as temperature and light intensity and quality) on the emergence and establishment of seedlings will link these influences with the dynamics of the community. Some selective predation and/or disease was observed in the field. Although data were not collected, I observed that the broadleaf species, A, retro- flexus and C. album, were occasionally injured or killed by insects or 203 pathogens. Injury and mortality were scattered in the field and did not appear to be density-dependent in occurrence; however, data were not collected. I did not observe herbivores or diseases on the two grass species. It is interesting that the two 'losers' were the species that were apparently free of pests. I would speculate that herbivores and diseases did not significantly influence the competitive relationships between the grasses and the broadleafs; however, I cannot rule out possible influences of predation on the compe-titive balance between C. album and A. retroflexus. This research also ignored the processes that occurred in the seed bank. We assumed that processes from seed production to seedling emergence acted as a simple, nonselective seive. Thus we assumed that the number of emerging seedlings was a simple function of the number of seeds produced in the previous year, which in turn was a simple function of the biomass accrued by an individual. These assumptions ignored immigration and dispersal processes, long-term seed viability, processes invoved in the establishment and breaking of dormancy, losses from the seed bank due to senescence, predation, and decay, and the influence of environmental factors on germination and emergence processes. The biggest 'black box' in our weed community model thus far is the seed bank. Obviously, the seed bank of the community is an area that requires 204 intensive and extensive investigation. (Inherent sources of variability.) This research assumed that genetic and ontogenetic control of plant growth was similar for the four species, ie. we assumed that 'inherent' variability was similar for the species. Observations and measurements of the species grown in isolation and in competition indicated that this assumption was violated. For example, both of the grasses, E. crus-galli and L. multiflorum, displayed greater variability in growth traits in the growth analysis and competition experiments than did the broadleafs. Variation in inherent variablity of plant growth and development may have contributed to the growth and competition results. For example, L. multiflorum displayed two distinct growth habits in both the growth and competition experiments. Either a plant allocated a large proportion of its biomass to vegetative growth and became large and leafy, or a plant allocated the bulk of its resources to reproductive structures and was very conservative in leaf production. E. crus-galli displayed distinct growth forms, both at Corvallis, OR., and at Davis, CA. Plants appeared to be either erect (plant axis grew primarily vertically) or prostrate. The E. crus-galli 'complex' has been recognized for its formation of multiple biotypes 205 (Barrett and Wilson 1981). However, I could not determine whether the variations in allocation and morphology observed for the two species (i.e. leafy versus reproductive and vertical versus prostrate) were genetically controlled (eg. biotypes) or developmentally triggered. This on/off behavior contributed to large variability in growth traits and great variability in biomass responses in competition for the two grasses. In contrast to the grasses, plants of A. retroflexus and C. album plants were remarkably similar (to themselves) in growth and development, both in isolation and in mixture. Both species seemed to follow tightly controlled developmental patterns. I collected a wealth of data for calculation of developmental indices. Those data are waiting to be scrutinized; however, I observed tightly synchronized rates of leaf initiation in both broadleafs, and in E. crus-galli, during the growth analysis experiments. No data were collected from the competition experiment; however, visual observations suggested a high degree of uniformity among individuals of the four species in the field. These species are highly plastic in their growth and reproductive responses when exposed to a large range of environmental condition, yet individuals seemed to respond uniformly to the conditions in the field. This observation may be consistent with Baker's 206 (1974) characterization of "general purpose genotypes" of colonizers: a high degree of inbreeding (low variability, due to selfing) coupled with phenotypic plasticity. My observations suggested that developmental and allocation patterns may have been under tight genetic control, but those patterns may be highly plastic with respect to environmental cues. Thus the population would respond plastically, but uniformly, to environmental cues. Partitioning and explaining genetic and developmental controls for traits that contribute to competition for resources may help explain mechanisms for competition within and among plant species. In addition, partitioning the genetic sources of variation may help explain a large proportion of the variation in biomass responses. However, uncoupling the influences of competition and genetics may be a formidable task. Population dynamics versus community dynamics. I have primarily taken a reductionist, population approach to this weed community. I have assumed that community dynamics are the sum of the population dynamics of the four species. In doing so, I have ignored several attributes of communities that might have been addressed with my data. For example, the data indicate that species richness and diversity decreased between the years. One species was virtually eliminated from the summer 207 community, resulting in an apparent decrease in species 'richness' (Whittaker 1975). Species diversity traits such as 'dominance concentration' and species 'equitability' (Whittaker 1975) also differed between years, as seen in the increasing importance (density) of C. album relative to the other species. Even if the community traits had been quantified, the role of competition in influencing the traits would have been difficult to detect. In addition to the problems in quantifying importance that were discussed earlier, we have other confounding factors. For example, data indicating that competition contributed to the elimination of L. multiflorum from the winter component of the community were confounded with the spring 1986 application of glyphosate to the field. L. multiflorum was still a member of the community in Spring 1986 but the species was not present in Summer 1986. Was the species a component of the community in winter 1986-1987? Those data were not directly collected and evaluated. We did not observe a significant population of L. multiflorum in the winters of 1986-1987 or 1987-1988. In any case, whether L. multiflorum was actually eliminated or not, we cannot partition the influences of competition and lifehistory traits from the influence of the herbicide. This population approach to community dynamics stems from my own orientation in ecology. I perceive myself as 208 a population ecologist more than a community ecologist. I tend to believe that communities may be understood from an understanding of the processes that regulate the individual populations and interactions among the populations. In addition, I have assumed that the concerns of agronomists about weed communities are primarily concerns about population densities and species composition (relative densities of each species population). However, a community context may contribute to an understanding of the dynamics of weed-crop systems. Thus measurements of community traits, such as diversity and its components (richness, dominance, equitability, etc.), may be worthwile in further investigations of the dynamics of this community. 209 SYNTHESIS: MODELS OF WEED POPULATIONS AND COMMUNITIES I believe this dissertation contributes to the development of a population and community modelling approach to the study of agricultural systems. The achievements of this dissertation include 1) the development of experimental approaches and designs to quantify the intensity and importance of competition, 2) the establishment of a framework for linking plant growth processes and the process of plant competition, and 3) the conceptual nucleus for integrating plant competition into a comprehensive model of the dynamics of weed populations and communities. The dissertation forms the basis for both extensive and intensive investigations of the life-history processes that regulate plant communities, including plant growth and competition processes and processes that have not yet been scrutinized directly. Experimental results suggested further investigations of specific interactions among light and temperature, plant growth, and competition. Our inability to describe all of the variation in biomass and population dynamics indicated that investigations of other key life-history processes are essential for developing weed community models. In particular, we have targeted seed-bank processes, and interaction 210 between light and temperature and several seed bank processes, as areas for immediate attention. Those experi- ments have begun under continued funding from the USDA competitive grants program, and promise to make significant advances in the development of the weed community model. In addition, future work could include genetic aspects of the population and community dynamics of the system. The population and community modelling approach that I have advanced in this dissertation promises significant contributions to the fields of weed science and plant ecology. The disseration has contributed to a better understanding of how the processes of plant growth and competition influence a specific weed community. 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