Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Lesson 5: Population structure and plant demography • Density and pattern – Random, clumped, regular distribution patterns • Plant demography – Modular growth – Plant age vs. stages – Population growth models – Transition Matrix Models – Density dependence • The law of constant yield • Self-thinning rule – Life tables and survivorship curves • Fecundity • Net reproductive rate • Reproductive value • Metapopulation studies Billings focus on the individual plant Billings focus was the individual plant within a complex of environmental factors, which he called a holocoenosis. This diagram summarizes an autecological approach to plant ecology, with focus being individual species and their adaptations to the environment. W.D. Billings, 1952. The environmental complex in relation to plant growth and distribution. Quaterly Review of Biology 27: 251-265. Plant population “A group of plants of the same species occupying a particular space at the same time.” Based on Krebs 1972 The components from which plant communities are constructed. Factors influencing plant populations: • The same factors influencing the presence of a plant in our original question “Why are organisms absent some places and abundant in others?” – – – – – Environmental conditions Resource availability Competition Disturbance Availability of propagules (biogeography) Measurement and description of plant population structure and dynamics • Distribution of plants on the landscape (density and pattern) • Measurement of plant demography (changes in plant population size and structure through time) • Distribution of suites of populations within landscapes (metapopulation dynamics) Density • “Number of individuals per unit area (e.g., trees per ha, or plants per m2).” • Most easily used for populations of discreet individuals such as trees. • Less useful for species that reproduce vegetatively, such as grasses. Patterns of Distribution • • • • Can give more information on a populations habitat preference, competitive dynamics, microhabitat distribution than density alone. In random distribution patterns, the location of one individual has no bearing on anothers. In clumped and regular patterns, the presence of one plant may be affecting another, possibly through competition or allelopathy or clumped distribution of propagules from a parent plant. A chi-square test can be used to test for random distribution. Clumped patterns may also be due to the presence of special microhabitats. • • • • Braya purpurascens. www.mun.ca/biology/ delta/arcticf/images/l314.jpg Non-sorted circles, Howe Island, AK. Example of regular distribution of habitats that causes clumped distribution of certain species. Centers of circles have high evapotranspiration and salts accumulate. Halophytic species, such as Braya purpurascens, are distributed mainly on the barren circles. Plant demography • “The study of changes in population structure through time.” • Plant populations increase or decrease through birth and death processes as well as immigration and emigration, and by and vegetative sprouting. • It includes counting: – Number of genetically distinct individuals, – Number of vegetatively reproduced individuals, – Number of leaves, branches, tillers, stems, flowers, etc., – Movement of seeds into and out of the population and storage in the soil. The influence of John Harper on plant population ecology • The study of population biology was almost solely a topic of zoologists until John Harper really created the field in the late 1940s and 1950s after he met Charles Elton, a famous animal ecologist who was noted primarily for his studies of small mammal populations. • Harper made the field of plant population biology quite accessible through Population Biology of Plants, which was first published in 1977. Major chapters in Harpers book Dispersal, dormancy and recruitment seed rain, dormancy, seed bank, recruitment of seedlings Effects of neighbors effects of density on yield and mortality, form and reproduction Mixtures of species: space, proportions, changes with time Effects of predators Defoliation Seasonality, search and choice Grazing animal effects Predation of seeds and fruits Pathogens Natural dynamics of populations Annual and biennials Herbaceous perennials Woody plants Plants, vegetation, and evolution Reproduction and growth Life cycles and fertility schedules Community structure and diversity Natural selection and population biology Idealized plant history (Harper 1977) • • • • J.L. Harper 1977 Starting with seed pool (the dormant phase), some of the seeds will not sprout and become seedlings due to various factors, such as unfavorable site, seed herbivory, or climate (the environmental sieve). Of the seedlings that sprout (the seedling cohort), only a few will reach maturity and set seed. The diagram also allows for vegetative reproduction, shown as the vegetative daughter connected to the parent plant, (these vegetative shoots are called ramets). Each genetically distinct parent plant is a genet. The mature plants will produce seeds, which in turn must pass through the environmental filter. Genets, clones and ramets • Genet: a single genetic individual. • Clone: a group of distinct individuals that are part of a single genet (e.g., aspen trees) • Ramet: a single member of a clone (a branch of genet). Plants have very different growth from animals • Animals have determinant growth (e.g. only one heart, two lungs, a liver, two arms, etc.) and usually determinant size. • Plants have indeterminant growth, (i.e., their size and abundance of parts can vary a lot because of the different environmental conditions. Different number of shoots, leaves, roots, flowers, fruits or seeds in response to favorable conditions. Similarly, their size can vary markedly, depending on the location.) They may react to stress by varying the number of parts. For example, Chenopodium album (lambs quarter) under nutrient deficiency or if grown at high density, flowers and sets seed when only 50 cm high, but, given ideal growth conditions it may produce 50,000 times as many seeds and grow to 1 m height. Thus, plant demographers are often more interested counting leaves or flowers, or individual stems, than they are in trying to count individual plants. Modular growth (White 1979) • Concept of a plant being a population of parts (roots, leaves, stems, flowers, fruits) or modules. • Plants may independently allocate growth to different modules, depending on availability of resources and environmental conditions. Fitness • Fitness = the lifetime reproductive success of an organism. • This concept is much easier to apply to animals than to plants. • The ability of plants to reallocate reproductive effort to vegetative modules during times of stress makes analysis of fitness difficult without following the reproduction among all its vegetative shoots. Another important difference between plants and animals for population studies: Size distribution • Unlike animals, mature plant sizes are rarely distributed as a normal curve, in which most individual are of moderate size. • Plant sizes normally have an L-shaped frequency distribution of sizes . • Furthermore, the size of plants is rarely a direct function of age. • Age is also often not a good predictor of reproductive status in plants. Barbour et al. Fig. 4.4 Population dynamics of plant modules • To get around some of these unique properties of plants, population ecologists often examine modules of the plants. • For example, in this study Harper examined the survivorship of cohorts of leaves of three species of grass during one growing season. • Cohorts of leaves were marked at different times during the summer and the percent surviving from previous markings noted. Harper 1977, p. 22 Number of leaves of each cohort (Linum usitatissimum) (Bazzaz and Harper, 1976) • Here Bazzaz and Harper counted the number of leaves in each cohort and followed their history. • Early leaves were longest lived, but more leaves were produced in later cohorts. Bazzaz and Harper, 1976 Morphological and physiological changes during the life cycle of a plant module Area, photosynthesis and respiration Sucrose and phosphorus concentration Milthorpe and Moorby 1974, cited in Harper 1977 • Just like with whole organisms or complete ecosystems, it is possible to study the ecophysiological processes of plant modules. • These diagrams show the changes in size, respiration rate, photosynthesis rate, and concentrations of phosphorus and sucrose, through the life history of cucumber leaves. Tree growth as the development of a population of modules Terminal shoots of Rhus typhina with age • • • • Each point on the graph represents the number of terminal growing points on a tree of a particular age. The borken line indicates the number of shoots expected if each growing shoot give rise to two new shoots in the next growth period. (The terminal meristem in this species aborts.) The dark line shows the actual number of shoots, which is less than expected because some of the shoots die. Solid dots are trees in unshaded habitats. From J. White, unpublished, reproduced in Harper, 1977 Photo: http://ispb.univ-lyon1.fr/cours/botanique/photos_dicoty/dico%20Q%20a%20Z/Rhus%20typhina.jpg Population growth models Used to predict populations of plants at some future time. Discrete models: Based on Harpers diagram, we can derive the simple equation: N t+1 = Nt + B - D + I - E N t+1 = Number of plants at some future time. Nt = Number of plants at present time. B = Number of plants established from the seed bank. D = Number of plants that die. I = Number of seeds immigrating to the site. E = Number of seeds emigrating (dispersing) from the site. The rate of the population growth, , in this discrete model is equal to the population at some future time divided by the present population. = N t+1 / N t However, it is not so simple to make these calculations because we rarely have all the information needed, and in many cases the data are impossible to obtain. Continuous-time growth models • Useful for predicting population at any time in the future. • Need to know the rate of population increase, r, where r = b - d (number of births minus the number of deaths). • With r, we can calculate rate of change in a population N: dN/dt = rN. What is r for the Curve A (<0, 0, >0)? Continuous-time growth models Exponential growth: Curve A: r>0. • • • If r > 0, the population will grow exponentially. If r = 0, the rate of change in the population is zero (stable population). If r<0, the population will decline. What type of growth does Curve B show? Continuous-time growth models Logistic growth: Curve B. In this case the population is constrained by some environmental limitation to a carrying capacity (K). The population will slow as it reaches K. The equation for Curve B is: dN/dt = rN(K - N)/K, the Verhulst-Pearl equation. Limitation of resources in the alga Chlorella • • Gause (1924) showed that the Verhulst-Pearl equations fit population growth of Paramecium reasonably well. An example from the plant world is the alga Chlorella (regarded as a superfood): – • • “Help your body remove the heavy metals and other pesticides in your body, improve your digestive system, including decreasing constipation, help you focus more clearly and for greater duration, balance your body's pH, and help eliminate bad breath”. Joseph Merkola http://www.mercola.com/forms/chlorella.htm This alga forms clumps and so experiences the effects of density when there are still available resources in the medium. The initially exponential growth rate declines after 8 days (dashed curve). If the lumping is prevented by shaking, the exponential rate continues for four more days before the nutrient limitation of the solution is reached. Pearsall and Bengry 1940, cited in Harper 1977, http://www.bioschool.co.uk/bioschool.co.uk/images/images/chlorella%20culture%201_JPG.jpg The exponential and logistic growth curves well express the ideas of Malthus regarding the limitation of resources Through the animal and vegetable kingdoms, nature has scattered the seeds of life abroad with the most profuse and liberal hand. She has been comparatively sparing in the room and nourishment necessary to rear them. Their germs of existence contained in this spot of earth, with ample food, and ample room to expand in would fill millions of worlds in the course of a few thousand years. Necessity, that imperious all pervading law of nature, restrains them within the prescribed bounds. The race of plants, and race of animals shrink under this great restrictive law. Malthus, 1798, “An essay in the principal of population” What are some reasons Verhulst-Pearl might not apply to real plant populations? Why Verhulst-Pearl equation does not usually apply to the real world of plants • • • • Carrying capacities are rarely constant. They vary with environmental conditions. Birth and death rates are not constant. Therefore, r is not constant. Biomass of plants may have more impact on the carrying capacity than the number of individuals. Population boundaries are usually poorly defined. Transition Matrix Models • Often the stage of life history of a plant is a more useful representation of survivorship and reproductive performance than age. • Transition matrix models are used to estimate the birth growth and death probabilities for individuals within different age classes or stages of a plant population. • Using discrete time steps populations of individuals within each age class may be projected into the future. • The matrix above shows is a general matrix that presents the probability values that represent the chance that a plant in a given stage of development will arrive at a different (or remain at the same) stage during the census interval. The matrix is for a plant with a 3-stage growth cycle (a biennial with seed, rosette, and flower stages). • For example: in the rosette column, if 60% of the rosettes of a plant die, and of these 25% remain as rosettes, and 75% become flowers. Then probabilities in the Rosette column are ars = 0, arr = .4 x 0.25=0.1, and arf = 0.4 x 0.75 = 0.3. Present Census Leslie, P.H. (1945) The use of matrices in certain populations mathematics. Biometrika 33: 183212. Calculating future population size with transition matrices Transition matrix for a biennial. Seeds cannot produce flowers in the first year; and rosettes cannot produce seeds. Therefore, asf and ars are 0. 1. To calculate the population structure of a future population. A census of the number of individuals in each stage of the present population is taken and portrayed in a column matrix ( B1). 2. This matrix is multiplied by the transition matrix (A). This matrix was obtained by monitoring the probability of individuals in each stage class (s = seed, i= immature, f = flowering) making the transition to another stage class or remaining at the same stage class. The resulting matrix ( B2) shows the number of individuals that make the transition from one stage to the next. 3. A new column matrix that portrays the future population structure is obtained by summing the values in each row to arrive at the total number of seeds, immature, and flowering plants. 4. This new column matrix, which shows the population structure of the future population, can then be multiplied by the transition matrix to find the population structure at the next time interval. This assumes that the transition probabilities remain constant for future generations (which they dont). 5. This is repeated until the population structure stabilizes (stable stage distribution). Transition matrix model application to study of Dipsacus sylvestris (Teasel) • Werner and Caswell studied teasel populations in open field and shrubland. • Teasel is a weedy invasive biennial species with a stem up to 2 m tall, that is increasingly prickly toward the tip. It has a huge eggshaped head that is armed with numerous, sharppointed bracts. The mature plants are much sought after for dry flower arrangements. The plants occur mostly on disturbed soil with high soil moisture. Native to Europe but is common throughout most of the lower 48 states. Wilde Karde 212.185.118.226/ bilddb/Bild.asp?I=119 www.chicagobotanic.org/.../ dipfu05.jp http://bailey.aros.net/nature/images/ Teasel%20reduced.jpg Example of the use of transition matrices in the study of teasel populations (Dipsacus sylvestris) r = 0.957 Upper: Transition matrix for the open field. Lower: Transition matrix for the shrub-covered field. Lowest row: Percent occurrence of each stage in the open field. r = -0.465 Shrub covered field has lower seed production and lower probabilities of plants reaching the flowering stage. Result shows an increasing population for the open field (r = 0.957), and declining population in the shrub covered field (r = -0.465). Werner, P.A. & Caswell, H. 1977. Population growth rates and age versus state-distribution models for teasel…Ecol. 58: 11-3-1111. Law of constant yield • Biomass is a better estimate of carrying capacity for plants than density of plants or seeds. • When the number of plants are high enough for interspecific interference to be important, the yield is constant regardless of planting density. • McDonald (1951) showed that the yield of Trifolium subteraneum and Bromus was constant regardless of the number of seeds or seedlings. (Seeds of Trisub in upper diagram varied across three orders of magnitude.) • The yield, however, is dependent on the availability of resources. The lower figure shows the response to three different levels of nitrogen. Trifolium subteraneum Bromus uniloides (3 levels of nitrogen in soil) McDonald 1951, cited in Barbour et al. 1999. Self-thinning rule Biomass vs. number of individuals B = CN-1/2, where B = biomass, and N is the population density, and C is a constant. Yoda et al. 1963, Westoby 1981. Cited in Barbour et al. 1999. • With plants large individuals usurp greater amounts of resources, which tends to eliminate smaller individuals. Thus large indviduals have a greater competitive effect on small individuals than small individuals have on large. This leads to size hierarchies. • Plant populations are thus dependent on a combination of biomass and density (crowding dependent). • Yoda et al. (1963) presented a self-thinning rule that describes the interaction between biomass and population density. This diagram is from another study by Westoby (1981), whereby the original equation of Yoda et al. takes another form. • Below the line, biomass will tend to increase toward the line(vertical, up pointing arrows). Above the line, plant mortality will reduce density (horizontal left pointing arrow) toward the line. • Once at the self-thinning line, individuals will die at a rate related to biomass accumulation rates. Application of self-thinning rule to plants of various sizes • Plant mass vs. density J.White 1985, cited in Barbour et al. 1999. • The equation appears to hold for plants of all sizes. The slope of the line = 1/2 for trees, shrubs, and herbs, across 12 orders of magnitude in size! Life tables: cohort table for Phlox drummondii www.eeob.iastate.edu/.../ Phlox_drummondii.jpg • Used for short-lived species, where the investigator can follow the survivorship of each individual. Leverich & Levin 1979 cited in Barbour et al. 1999. Examples of survivorship curves Eurterpe globosa (= Prestoea acuminata) Phlox drummondii Van Valen 1975 for Eurterpe globosa and Leverich and Levin 1979 for P. drummondii. Cited in Barbour et al. 1999. Survivorship curves (Deevey, 1947) Type I: characteristic of organisms with mortality concentrated in the later stages of life (e.g., annuals with seed dormancy). Type II: characteristic of organisms with constant mortality rates. Type III: characteristic of organisms with high juvenile mortality (e.g., most trees). Note that large animals tend to have Type I survivorship and small animals tend to have Type III; whereas the opposite is true of large and small plants. Deevey 1947. Cited in Barbour et al. 1999. Fecundity and net reproductive rate Fecundity (bx) is the age-specific birthrate of individuals. It is a measure of the average number of seeds produced by individuals of a single size or age cohort during an interval (x). Net reproductive rate (Ro) is a combination of the fecundity and the probability of that an individual will survive to the necessary age category. It is the product of the survivorship (lx) times fecundity, summed for the cohort over its life time: Ro = lxbx. Reproductive value of an individual of age x Reproductive value (Vx) is the relative contribution that individuals of age x are likely to make to the seed pool before they die. It is calculated as the sum of the average number of seeds it produces in the current year (bx) plus the the average number of seeds produced by an individual in each age class older than bx (e.g., bx+1, bx+2, etc.) times the probability that an individual will survive to each older age category (lx+1/lx): Vx = bx + (lx+i/lx) bx+i Example: reproductive value of Phlox drummondii through its lifetime Leverich & Leven 1979 Size or age distribution of trees • • • • Heyward 1939, cited in Barbour et al. 1999. Size (dbh) or age (no. of tree rings) can be used. Used to examine the population dynamics of longer lived species. Diagram shows the number of plants in each size category for hardwoods and pines in one stand of trees. What does this distribution suggest? Metapopulations “The suite of populations in a region that are semi-isolated from each other because of habitat heterogeneity, but which show significant interchange of pollen and/or propagules.” (paraphrased from Levin, 1970) Species are patchily distributed because of habitat heterogeneity. Ericksons (1945) study showed that plant showed patchy distribution at all scales he mapped. Patches that are interconnected and show significant interchange are considered metapopulations. Ralph O. Erickson, 1945. The Clematis fremontii var. riehlii population in the Ozarks,” Annals of the Missouri Botanical Garden, vol. 32 Adding complexity to Harpers original model Regional seed pool • Local populations Numerous studies have examined the exchange of propagules between local populations. Colonization at new sites can be a function of a variety of factors. For example: – – • Availability of open sites. Good sites may be going extinct through climate change, succession, or anthropogenic disturbances. All good sites are currently occupied. These and other factors can influence whether a species will expand into new areas, maintain itself in the landscape, or go extinct. Metapopulations Pulliam (1989) recognized two distinct types of populations: Source populations: Populations in favorable areas that produce a lot of seed and potential emigrants. Sink populations: Populations in unfavorable habitats that must receive an constant influx in immigrants to maintain themselves. Models of movement of species between populations • • • Infinite island models: Sewall Wright's (1943) infinite island model is a "landscapeneutral" model that assumes equal population size and equal exchange of migrants across all populations. Metapopulation models: (Levins 1970), is a demographic model that describes a set of populations with certain extinction probabilities that are connected by migration of colonists. Landscape models: Use spatially explicit information about the mosaic of habitat types to describe the landscape. This model can be combined with a metapopulation model or any model that describes a set of connected populations that occur within a landscape. For further discussion of metapopulation models and landscape approaches see Harrison and Taylor 1997, Wiens 1997. (For all models, lines indicate gene flow or migration, solid patches are populations; dotted patches indicate extinct populations.) From: Proceedings from a Workshop on Gene Flow in Fragmented, Managed, and Continuous PopulationsJanuary 5-9, 1998. National Center for Ecological Analysis and SynthesisUniversity of California-Santa BarbaraProceedings written byV. L Sork, D. Campbell, R. Dyer, J. Fernandez, J. Nason, R. Petit, P. Smouse, and E. Steinberg. Two recent studies of metapopulation genetics Giles, B.E. and J. Goudet. 1997. Genetic differentiation in Silene dioica metapopulations: Estimation of spatiotemporal effects in a successional plant species. American Naturalist, 149: 507-526. Olson M.S. and D.E. McCauley. 2002. Mitochondrial DNA diversity, populaiton structure, and gender association in the gynodioecious plant Silene vulgaris. Evolution, 56: 253262. Summary • Density and pattern – • Random, clumped, regular distribution patterns Plant demography (Harper 1977) – – – Modular growth (White 1979) Plant age vs. stages Population growth models • • • • – – Transition Matrix Models (Leslie 1975) Density dependence • • – • The law of constant of yield (Kira et al. 1975) Self-thinning rule (Yoda et al. 1963) Life tables and survivorship curves (Deevey 1947, Phlox example from Leverich and Levin 1975) • • • – Discrete-time model: difficult to apply Continuous time model: exponential growth equation Limitation of resources: Verhulst-Pearl logistic equation Exponential vs. logistic population growth Fecundity Net reproductive rate Reproductive value Forest population dynamics (Examples from Heyward 1939, Oosting and Billings 1952) Metapopulations – – – Interchange of propagules between local populations (Levin 1970). Source and sink populations (Pulliam 1989). Different models of gene flow between populations. Literature for Lesson 5 Werner, P.A. and J. Caswell. 1977. Population growth rates and age versus stage-distribution models for teasel (Dipsacus sylvestris Huds.) Ecology 58: 1103-1111. Giles, B.E. and J. Goudet. 1997. Genetic differentiation in Silene dioica metapopulations: Estimation of spatiotemporal effects in a successional plant species. American Naturalist, 149: 507-526. Leverich, W.J. and D.A. Levin,. Age-specific survivorship and reproduction in Phlox drummondii. American Naturalist 113: 881-903. Platt, W.J. and M. Weiss. 1985. An experimental study of competition among fugitive prairie plants. Ecology 66: 708-720. Olson M.S. and D.E. McCauley. 2002. Mitochondrial DNA diversity, populaiton structure, and gender association in the gynodioecious plant Silene vulgaris. Evolution, 56: 253-262. Westoby, M. 1981. The place of the self-thinning rule in population dynamics. American Naturalist 118: 581-587.