Ecological Invasion, Roughened Fronts, and a Competitor's Extreme Advance: Integrating Stochastic Spatial-Growth Models

Both community ecology and conservation biology seek further understanding of factors governing the advance of an invasive species. We model biological invasion as an individual-based, stochastic process on a two-dimensional landscape. An ecologically superior invader and a resident species compete for space preemptively. Our general model includes the basic contact process and a variant of the Eden model as special cases. We employ the concept of a "roughened" front to quantify effects of discreteness and stochasticity on invasion; we emphasize the probability distribution of the front-runner's relative position. That is, we analyze the location of the most advanced invader as the extreme deviation about the front's mean position. We find that a class of models with different assumptions about neighborhood interactions exhibit universal characteristics. That is, key features of the invasion dynamics span a class of models, independently of locally detailed demographic rules. Our results integrate theories of invasive spatial growth and generate novel hypotheses linking habitat or landscape size (length of the invading front) to invasion velocity, and to the relative position of the most advanced invader.Comment: The original publication is available at www.springerlink.com/content/8528v8563r7u2742

Metabolic rate models and the substitutability of predator populations

• Much of the debate surrounding the consequences of biodiversity loss centres around the issue of whether different species are functionally similar in their effects on ecological processes. In this study, we examined whether populations consisting of smaller, more abundant individuals are functionally similar to populations of the same species with larger, fewer individuals. • We manipulated the biomass and density of banded sunfish (Enneacanthus obesus) and measured their impact on populations of Southern leopard frog (Rana sphenocephala) larvae. We also evaluated the ability of models relating metabolic rate to body size to predict the relative impacts of populations that differ in average body size and population density. • Our results indicate that population biomass, density and their interaction each play a large role in determining the effect of a predator population on its food resource. Populations with smaller but more abundant individuals had effects as large or larger than those populations with larger but fewer individuals. • Although we found qualitative agreement between the observed relative effects of populations with that predicted by allometric models, we also found that density-dependence can cause effects of a population to differ from that expected based on allometry. • The substitutability of populations differing in average body size appears to depend on complex relationships between metabolic rate, population density and the strength of density-dependence. The restrictive conditions necessary to establish functional equivalence among different populations of the same species suggests that functional equivalence should be rare in most communities