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I derive a population-dynamic model of sedentary consumers that compete exploitatively for sedentary resources. The area over which each individual uses resources is an explicit parameter of the model. In the limit as this area approaches infinity, the model converges to previously studied models of consumer-resource dynamics. I then examine the evolution of resource partitioning among the consumer species. The principal finding is that the amount of evolved resource partitioning decreases to zero as resource use becomes increasingly local. This results from an effect of the spatial scale of resource use on the spatial pattern of resource availability that increases the evolutionary contribution of intraspecific competition relative to interspecific competition.

Population dynamic models are developed for communities of annual plants in spatially heterogeneous environments. These models are constructed from submodels of the survivorship, fecundity, germination, and dispersal of individual plants. The submodels include the effects of spatially local interactions on plant performance and the spatial variation in performance caused by spatial heterogeneity in the physical environment. It is possible to estimate the submodels from data on experimental communities in either the field or greenhouse and so it is possible to empirically calibrate the population dynamic models developed. Each population dynamic model explicitly includes the spatial distribution of individuals in a plant community. Several two-species models for plants in patchy environments are studied to examine the community-level consequences of spatial heterogeneity in the physical environment. The results fall into two classes. First, community structure is in part determined by a relation between patch size and mean seed dispersal distance. Specifically, coexistence is, in some cases, possible only if patches are sufficiently larger than the mean dispersal distance. Second, community structure is also affected by relations between patch size and the maximum distance over which two plants interact (termed the neighborhood radius). In some cases, coexistence is possible only if patch size is sufficiently larger than the neighborhood radius. In others, the species coexist only if patch size is sufficiently smaller than the neighborhood radius. In still other cases, coexistence is possible only if patch sizes are within critical bounds, where the sizes of the critical bounds are in units of the neighborhood radius. All results involving relations between the neighborhood radius and patch size are direct consequences of the sedentary nature of plants and the fact that individual plants interact primarily with nearby plants.

Models are developed for the dynamics of multi-species communities of annual plants that lack seed dormancy. These models explicitly include plastic plant growth, the spatial distribution of individuals, and the fact that individuals interact primarily with nearby individuals. Because the models are based on submodels of individual plants (fecundity, survivorship and dispersal, and how these are affected by inter-individual interactions), they provide explanations of community-level phenomena in terms of the biology of individuals. All model parameters and functional forms may be estimated from data obtained in simple experiments of a single years's duration. The models are used to examine the community-level consequences of some types of inter-individual interactions that have been reported in the ecological literature. In addition, the models are used to demonstrate that dispersal may markedly influence the outcome of competition among plant species, even in a physically homogeneous environment, due to an effect of dispersal on the spatial distribution of individuals.

Neighborhood population-dynamic models are developed for single-species and multispecies communities of annual plants with seeds that may lie dormant through one or more growing seasons. Dormancy-induced changes in lifetime germination successes affect the equilibrium densities of plants and the local stability of equilibria. Dormancy-induced population-dynamic time lags, in contrast, do not affect equilibrium densities of post-germination plants or the ability of an invader to successfully colonize a multispecies community. In single-species populations, time lags are never destabilizing but may be stabilizing. Specifically, some strategies of dormancy (a way to partition lifetime germination success among the various age classes of seeds) cause an otherwise oscillatory monoculture (eigenvalue less than negative one) to have a locally stable positive equilibrium. The maximum distance over which a plant of one species can interfere with a plant of another species is termed the neighborhood radius. The pop...

A model of two competing species is presented in which each species is able to disperse over a single spatial axis. The spatial axis is composed of two intervals with different carrying capacities. We ask the question: If species one is alone and at population dynamic equilibrium, then when can species two successfully invade when rare? We say that an interval is “suitable” if the interval can be invaded by species two in the absence of dispersal by both species, and we say an interval is “unsuitable” if the interval cannot be invaded by species two in the absence of dispersal by both species. We offer three findings: (I) If one interval is suitable and the other is unsuitable, then the success of invasion depends upon the length of the suitable interval. Invasion succeeds if the suitable interval is larger than a threshold minimum and fails otherwise. (II) It is possible for species two to invade even though both intervals are unsuitable. (III) It is possible for species two to fail to invade even though both intervals are suitable.

We present tractable formulations for neighborhood models of annual plant population dynamic processes. These models are constructed from submodels, termed predictors, of individual plants. Fecundity and survivorship predictors give the fecundity and survivorship of an individual as a function of local population density. Dispersal predictors predict the dispersal pattern of a plant's maternal progeny and the survivorship of plants from seed to seedlings. We develop both computer models and analytically tractable models. Our computer models are designed to determine the population dynamic consequences of specific fecundity, survivorship and dispersal predictors. The analytical models are valid when dispersal is sufficiently large, and are used to explain the predictions of analogous computer models. We show through examples that the predictions of corresponding computer and analytical models may be virtually identical. Empirical tests of these models are practical because all model parameters and function...

The evolution of resource partitioning in a multidimensional resource space is studied for two and three competing species. Optimal patterns of resource partitioning are determined by simultaneously maximizing the fitness of each species with respect to its own niche position, conditional on the positions of all other species. We find that there are only a finite number of possible solutions, and several of these may be optimal simultaneously. Some solutions of the three-species model involve partitioning along more resource axes than any solutions of the two-species model. The results are related to empirical resource partitioning phenomena in Anolis lizard populations.

During 1980 and 1981 population experiments were performed with two two-species guilds of Anolis lizards: A. gingivinus and A. wattsi pogus on the island of St. Maarten (Netherlands Antilles) and A. bimaculatus and A. wattsi schwartzi on the island of St. Eustatius (Netherlands Antilles). These experiments were designed to test the hypothesis that the strength of interspecific competition is inversely related to the degree of interspecific resource partitioning. The experimental design consisted of four field-enclosures (12 x 12 m) on St. Maarten and four on St. Eustatius. On each island two enclosures contained only the larger native species (A. gingivinus or A. bimaculatus), and two contained both native species. Resource partitioning was measured inside each of the two- species enclosures. There was more interspecific partitioning of space and prey (arthropods) on St. Eustatius than on St. Maarten. A comparison of the one- and two-species enclosures on St. Maarten revealed five competitive effects of A. wattsi pogus on A. gingivinus. In the presence of A. wattsi pogus, A. gingivinus individuals had lower growth rates and increased perch heights. Also, dissected A. gingivinus from the two-species enclosures contained smaller volumes of developing eggs per female, smaller volumes of insect prey per lizard, and smaller mean prey sizes than A. gingivinus from the single-species enclosures. In contrast, no consistent and significant competitive effects of A. wattsi schwartzi on A. bimaculatus were observed on St. Eustatius. These results support a central assumption of competition theory: the strength of interspecific competition increases as the amount of interspecific resource partitioning decreases.

The two Anolis lizard species of St. Eustatius (Neth. Antilles) have large effects on the abundance of arthropods. Over a six-month period, we excluded Anolis lizards from three experimental areas and maintained three other areas with natural densities of lizards. Exclusion of anoles resulted in a two to three-fold increase in the abundance of arthropods on the forest floor (mainly Dipterans), and a twenty to thirty-fold increase in the abundance of three large web-building spiders. These abundant web-building spiders, in turn, caused approximately a 25% decrease in the abundance of insects between the forest floor and canopy. Exclusion of anoles had no observed effect on the degree of herbivory as assayed by the amount of leaf damage on two plant species.

Population experiments with Anolis lizard species demonstrate a relation between the amount of between-species competition and the degree of interspecific resource partitioning (the more the partitioning the less the competition). Specifically, the amount of resource partitioning between the two species (Anolis gingivinus and Anolis wattsi pogus) on the island of St. Maarten is less than that between the two species (Anolis bimaculatus and Anolis wattsi schwartzi) on the island of St. Eustatius. The presence of Anolis wattsi both lowers the growth rates and raises the perch heights of Anolis gingivinus individuals. In contrast, Anolis wattsi has no effect on Anolis bimaculatus. Thus, when there is less resource partitioning, Anolis wattsi has a greater competitive effect. This verifies, for these species, a central assumption of competition theory: the strength of between-species competition is inversely related to the amount of interspecific resource partitioning.

SUMMARYWe examined dynamical factors that shape the distribution of the number of parasites/host in constant or temporally varying environments, and with or without host-age dependent variation in host susceptibility and parasite mortality. We predict properties of the parasite distribution in the absence of density-dependent factors such as densitydependent mortality or recruitment and parasite-induced host mortality. These properties provide a criterion for the detection of density dependence in temporally variable systems with host-age dependent interactions. We have then introduced methods to estimate and statistically evaluate the effects of host age or size on the distribution of parasites/host. The methods are based on a maximum likelihood protocol for linear and non-linear regression when data are negatively binomially distributed. We have illustrated the use of the theoretical results and statistical methods by re-analysing the data of Halvorsen & Andersen (1984) on cestode infections in Norwegian arctic charr and by analysing new data on nematode infections in Caribbean Anolis lizards.

We developed models of inter-individual interference to predict the fecundity of individuals in populations of the annual plant species, Arabidopsis thaliana. An individual plant is modeled as having a neighborhood which is a circular area of fixed radius with the plant at its center. Other plants which share the circle with the focal plant are termed neighbors of the focal plant. We developed an index of neighborhood interference which is the independent variable in a non-linear regression model that predicts individual plant fecundity. We present methods of exploratory data analysis that are useful in determining a best neighborhood radius, defined as that radius which minimizes residual sum of squares, and in deciding on the functional form of the interference index. In developing the interference index for Arabidopsis, we focus on aspects of the spatial distribution of neighbors: their number, distance and angular dispersion. We found that a best (or optimal) neighborhood radius can be resolved, which provides the best predictor of plant performance. Fecundity predictors based on adult neighbors were noticeably better than those based on neighbors at the seedling stage. Rosettes of Arabidopsis may change location during development (they fall over) and the new “fallen” positions do provide some improvement in the predictor. Taking into account distance to neighbors within the neighborhood provided only negligible improvement in the model. Finally, the incorporation of angular dispersion in the crowding index produced a considerably better fit. The fecundity predictor that included number of neighbors and angular dispersion in the crowding index explained about 70% of the variation in individual seed set.

James S. Clark, Jason Lynch, and Peter Wyckoff are in the Department of Botany, Duke University, Durham, NC 27708; Chris Fastie and Stephen T. Jackson are in the Department of Botany, University of Wyoming, Laramie, WY 82701; George Hurtt and Stephen Pacala are in the Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ 08544-1003; Carter Johnson is in the Department of Horticulture and Forestry, South Dakota State University, Brookings, SD 57007; George A. King is at Dynamic Corporation, US EPA National Health and Environmental Effects Research Laboratory, Corvallis, OR 97333; Mark Lewis is in the Math Department, University of Utah, Salt Lake City, UT 84112; Colin Prentice is at the School of Ecology, Lund University, Lund, Sweden; Eugene W. Schupp is in the Department of Rangeland Resources, Utah State University, Logan, UT 84322; and Thompson Webb III is in the Department of Geological Sciences, Brown University, Providence, RI 029121846. ? 1998 American Institute of Biological Sciences. A plausible explanation

Spatially local interference among pigweed (Amaranthus retroflexus) and velvet leaf (Abutilon theophrasti) individuals was studied in experimental two species stands. Although survivorship was density-independent for both species, individual fecundities were affected by the local population density of velvet leaf and pigweed near each plant. We estimated the functional forms of the spatially local density dependence and the distances over which plants interfere with one another. For both species hyperbolic functions provided better fits than either linear or log-linear functions. The apparent significance of higher-order interaction terms from the linear and log-linear regressions appears to be an artifact of the hyperbolic form of the data. We explain aspects of the functional forms of the relations between fecundity and local densities in terms of morphological attributes of each species. We also describe some statistical problems associated with estimating the effects of spatially local interindividual interference.

Calibrated neighbourhood population dynamic models had predicted that monocultures of Abutilon theophrasti (velvet leaf) can exhibit oscillatory and chaotic dynamics. This hypothesis was tested both in field experiments and under controlled-environment conditions. The effect of soil nutrient levels on the population dynamics was observed in glasshouse experiments