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We use a two-species model of plant competition to explore the effect of intraspecific variation on community dynamics. The competitive ability ("performance") of each individual is assigned by an independent random draw from a species-specific probability distribution. If the density of individuals competing for open space is high (e.g., because fecundity is high), species with high maximum (or large variance in) performance are favored, while if density is low, species with high typical (e.g., mean) performance are favored. If there is an interspecific mean-variance performance trade-off, stable coexistence can occur across a limited range of intermediate densities, but the stabilizing effect of this trade-off appears to be weak. In the absence of this trade-off, one species is superior. In this case, intraspecific variation can blur interspecific differences (i.e., shift the dynamics toward what would be expected in the neutral case), but the strength of this effect diminishes as competitor density increases. If density is sufficiently high, the inferior species is driven to extinction just as rapidly as in the case where there is no overlap in performance between species. Intraspecific variation can facilitate coexistence, but this may be relatively unimportant in maintaining diversity in most real communities.

Hierarchical competition-colonization models have been used to explain limiting similarities among species, successional dynamics, and species loss under habitat destruction. This class of models assumes that there is an inverse relationship between competitive ability and colonization ability and that competitively superior species exclude competitively inferior species when both occupy the same site. This hierarchical model of performance trade-offs, however, exhibits some unusual behaviors in the high-diversity limit, including infinitesimally close species packing, pathologically slow dynamics, and fundamentally important regularities in trait-abundance relationships. In particular, under the condition of constant mortality across species, a 3/2-power-law relationship emerges between abundance and fecundity under infinite packing (abundance of a species with fecundity f is inversely proportional to f to the 3/2 power). In this article, we explore the high-diversity limit of the hierarchical competition-colonization model, with particular emphasis on patterns of species packing, species-abundance relationships, and system stability. Because of the potential for pathologically slow dynamics following perturbations and infinitesimally close species packing in the high-diversity limit for this class of models, the models may need to be modified to include more realistic mechanisms governing the extent and timing of interspecific competitive exclusion in order to effectively capture the structure and dynamics of real-world ecosystems.

The effects of three forms of density-dependent regulation were explored in model coral reef fish populations: top-down (predation), bottom-up (competition for food), and pelagic (non-reef-based mechanisms) control. We describe the demographic responses of both biomass and numbers of adult fish, predicting the mean and the variance of temporal fluctuations resulting from stochastic recruitment of juveniles. We find that top-down control acts by suppressing variability of numbers of fish, which in turn suppresses the variability of biomass. Bottom-up control has no effect on fluctuations of numbers of fish, though it strongly reduces fluctuations of biomass. Because fecundity of fish is directly linked to body mass, the regulation of biomass tightly regulates reproductive output independently of the number of individuals in the population. Finally, populations under pelagic control experience bounded fluctuations of biomass and numbers directly proportional to the bounded fluctuations of recruitment. The demographic signatures predicted from both bottom-up and pelagic control are consistent with current evidence supporting the recruitment limitation hypothesis in reef fish ecology. We propose tests to discriminate the dominant mode of density-dependent regulation using qualitative trends in time series demographic data across environmental clines.

Stochastic spatial models are becoming an increasingly popular tool for understanding ecological and epidemiological problems. However, due to the complexities inherent in such models, it has been difficult to obtain any analytical insights. Here, we consider individual-based, stochastic models of both the continuous-time Lotka-Volterra system and the discrete-time Nicholson-Bailey model. The stability of these two stochastic models of natural enemies is assessed by constructing moment equations. The inclusion of these moments, which mimic the effects of spatial aggregation, can produce either stabilizing or destabilizing influences on the population dynamics. Throughout, the theoretical results are compared to numerical models for the full distribution of populations, as well as stochastic simulations.