Download Models of a four-species annual weed community : growth

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. General models of crop yield loss due to the
presence of weeds: a) a sigmoid response model,
described by Zimdahl (1980), and b) a hyperbolic
response model, described by Cousens (1985).
46
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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.
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surasammi ImINIFIIII11111111111.111
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4
1040"+1044
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ril._. .,...
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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
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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
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i
I Sim
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o 11 11.
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OM MI
easagsioar.iaticA
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rani
.
.
.
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-
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-
-
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-
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
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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.
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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.
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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.
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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. Further
developments of this approach and this model will contribute both to the development of efficient weed management
strategies and to an understanding of the mechanisms that
regulate plant communities.
211
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