Extending our current understanding of spatial competition
Two of the obvious needs for future work on spatially structured competition are to better understand spatial dynamics in systems with multiple patches and in systems with continuous (or more nearly continuous) spatial structure.
Both of these would bring the models closer to reality. Unfortunately, progress in both cases is somewhat limited for technical reasons.Most studies dealing with multiple-patch systems of interacting species have assumed random movement. This is true of an early analysis of predator-prey systems with type II responses by Jansen and de Roos (2000). They assumed a linear chain of 90 patches, and found that random movement tended to stabilize abundances, as the patches were out of synchrony. One attempt to compare 2- and multiple-patch versions of competition was Wilson and Abrams' (2005) study of two different spatial versions of the Armstrong-McGehee (AM) model, in which the consumer-resource interaction generated cycles in each patch. This was also restricted to random movement. The 2-patch version was based on the continuous time AM model with a single logistic resource and consumers with type II responses. The consumer parameters were identical across patches, but the resource parameters could differ. The 2-patch model typically had a coexistence bandwidth (range of relative mortality rates allowing coexistence) that was approximately 40% greater than that of comparable 1-patch models. Differences in parameter values between patches or the presence of antisynchronized dynamics both resulted in enhanced coexistence. The multi-patch version was based on simulations that attempted to mimic the 2-patch differential equation model with an individual-based approach, but did have several subtle differences. Because the simulations were based on discrete individuals, there was much more scope for random processes to affect dynamics.
The cycles generated by the type II functional response with efficient consumers periodically produce very small population sizes, which enhanced the role of stochasticity in determining the outcome of competition. In any event, these explorations suggest that the analysis of multipatch systems with variation are likely to have some unique features not present in the 2-patch models that have been discussed here.The study of spatial competition suffers from some of the other characteristics that have commonly been omitted from most published models based on a single homogeneous habitat. Those omissions include: (1) the lack of interactions between resources within a patch, particularly in cases where the resources are biological species; (2) the lack of trophic levels beyond the consumer and resource; and (3) the lack of stage/age structure or intraspecific variation in competition-related traits in both consumers and resources. While much more work is needed, it seems likely that at least some of the qualitative findings regarding random vs adaptive movement revealed by the simple 2-patch models reviewed here will apply to many of these more complex scenarios.