Population dynamics in spatially complex environments: theory and data

Abstract

Population dynamics and species interactions are spread out in space. This might seem like a trivial observation, but it has potentially important consequences. In particular, mathematical models show that the dynamics of populations can be altered fundamentally simply because organisms interact and disperse rather than being confined to one position for their entire lives. Models that deal with dispersal and spatially distributed populations are extraordinarily varied, partly because they employ three distinct characterizations of space: as 'islands’ (or ‘metapopulations’), as ‘stepping-stones’, or as a continuum. Moreover, there are several different ways of representing dispersal in spatially structured environments, as well as several possibilities for allowing environmental variation to come into play. In spite of this variety, a few common themes emerge from spatial models. First, island and stepping-stone models emphasize that little can be concluded from simply recording patterns of' occupancy, instead a metapopulation’s fate will be determined by the balance between local extinction and recolonization and how that balance interacts with random catastrophes. Island and stepping-stone models also make it clear that the spatial dimension, in particular spatial subdivision, can alter the stability of species interactions and opportunities for coexistence in both predator—prey and competitive systems. Continuum models, which usually take the form of reaction-diffusion equations, address slightly different questions. Reaction-diffusion theory suggests that in uniform environments, certain combinations of local dynamics and dispersal can produce persistent irregularities in the dispersion of species. These striking spatial patterns, which are called diffusive instabilities, can arise from predator—prey interactions, Lotka-Volterra competitive interactions, and from density-dependent population growth in an age-structured population. Moreover, although they differ fundamentally in their structure, the three major classes of spatial models share the common generalization that spatial effects should be expected only for: (i) selected spatial scales; (ii) specific dispersal rates, and (iii) particular patterns of environmental variation relative to the frequency and range of dispersal. The theoretical possibilities are thus contingent on spatial scale and dispersal rates. Although explicit experimental tests of spatial models are non-existent, a handful of studies report general changes in species interactions associated with manipulations of habitat subdivision. Observational studies with adequate data concerning dispersal and scale are also scarce; but those few observational studies with the appropriate supporting information consistently show profound spatial effects, especially effects due to habitat subdivision. The challenge for empiricists is to investigate more rigorously the roles of spatial subdivision and dispersal in natural communities. The challenge for theoreticians is to make the empiricist’s job easier; this can best be done by delineating when spatial effects are most likely to be influential, and by offering guidance on how to design appropriate experiments. Simply saying that the spatial environment is important is to mouth a platitude: what we need to know is whether this presumed importance amounts to much in natural systems.