Spatial Heterogeneity, Indirect Interactions, and the Coexistence of Prey Species.

Predation may generate patterns in the structure of communities similar to those produced by competition. The potential role of spatial heterogeneity in promoting the coexistence of prey species is explored with both analytical and graphical models. In these models, prey interact indirectly through their effect on predator numbers: an interaction that leads to "apparent competition" and a problem in species coexistence. A model of prey coexistence in a homogeneous habitat is explored. If prey grow logistically, prey abundance is measured by the effect prey have on predator growth, and the predator consumes prey in a finegrained manner, the criterion for species k to remain in the community takes a simple form: its sensitivity to predation (ak/rk) cannot exceed the average sensitivity to predation of the entire community, ( $$\overline {a/r}$$ ), divided by a measure of the intensity of predation on the community (Δ). At high Δ, species must have very similar values for ai/ri to coexist. This suggests that in spatially homogeneous environments, prey coexistence is difficult to achieve at high intensities of predation. There are two distinct ways in which spatial segregation may promote prey coexistence. First, habitat selection by the predator may provide each prey with an implicit refuge in the presence of the alternative prey, because predators will tend to leave a habitat in which their foraging yields are relatively low. If predators can select their habitats optimally without cost, and without interference from other predators, it is shown that at equilibrium no prey suffers a reduction in density because other prey are present in the diet. Nonoptimal habitat selection or interference between predators makes prey that have either low intrinsic growth rates (ri) or high rates of predator attack (ai) vulnerable to density reductions or extinction, as a result of predator "spillover" between patches. Second, if prey are spatially segregated, the predator population may be broken into two, partially independent subpopulations coupled by random predator movement. If each prey grows exponentially in the absence of predation, the permissible difference in their sensitivities to predation (ai/ri) is bounded by a measure of spatial coupling; the more tightly the two patches are linked by predator movement, the more similar the values for ai/ri must be if the prey are to continue to coexist. This model also provides a simple illustration of how spatial heterogeneity may stabilize an otherwise unstable predator-prey system. The evolutionary stability of segregation between prey is briefly discussed. Even if habitat partitioning relaxes apparent competition between prey occupying separate patches, the segregational pattern itself may persist because of apparent competition within each patch. Several examples from field studies suggest that habitat partitioning and the movement behavior of both predators and prey are important factors affecting coexistence in prey communities.