Spatial variation and density-dependent dispersal in competitive coexistence

Abstract

It is well known that dispersal from localities favourable to a species' growth and reproduction (sources) can prevent competitive exclusion in unfavourable localities (sinks). What is perhaps less well known is that too much emigration can undermine the viability of sources and cause regional competitive exclusion. Here, I investigate two biological mechanisms that reduce the cost of dispersal to source communities. The first involves increasing the spatial variation in the strength of competition such that sources can withstand high rates of emigration; the second involves reducing emigration from sources via density-dependent dispersal. I compare how different forms of spatial variation and modes of dispersal influence source viability, and hence source-sink coexistence, under dominance and pre-emptive competition. A key finding is that, while spatial variation substantially reduces dispersal costs under both types of competition, density-dependent dispersal does so only under dominance competition. For instance, when spatial variation in the strength of competition is high, coexistence is possible (regardless of the type of competition) even when sources experience high emigration rates; when spatial variation is low, coexistence is restricted even under low emigration rates. Under dominance competition, density-dependent dispersal has a strong effect on coexistence. For instance, when the emigration rate increases with density at an accelerating rate (Type III densitydependent dispersal), coexistence is possible even when spatial variation is quite low; when the emigration rate increases with density at a decelerating rate (Type II density-dependent dispersal), coexistence is restricted even when spatial variation is quite high. Under pre-emptive competition, density-dependent dispersal has only a marginal effect on coexistence. Thus, the diversity-reducing effects of high dispersal rates persist under pre-emptive competition even when dispersal is density dependent, but can be significantly mitigated under dominance competition if density-dependent dispersal is Type III rather than Type II. These results lead to testable predictions about source-sink coexistence under different regimes of competition, spatial variation and dispersal. They identify situations in which density-independent dispersal provides a reasonable approximation to species' dispersal patterns, and those under which consideration of density-dependent dispersal is crucial to predicting long-term coexistence.

Coexistence of competitive species with a stage‐structured life cycle

“…Two-patch two-competing-species models with interpatch migrations (Levin 1974;Nishimura and Kishida 2001;Amarasekare 2004) have similar topological configurations of model structure to our stage-structured competition model. The adult and juvenile stages in our model correspond to the two patches, and maturation and birth processes correspond to migrations between the patches.…”

“…In two-patch models, stable coexistence of the competing species is accomplished partly by refuge patch effects via certain migration rates between patches when a destabilizing competition effect is embedded in either or both patches (Levin 1974;Nishimura and Kishida 2001;Amarasekare 2004). Our stage-structured model is analogous to the patch models (Levin 1974;Nishimura and Kishida 2001;Amarasekare 2004) in that refuge effects lead to stable coexistence with sufficiently low migration rates. However, a complete source-sink structure of our model (wherein the adult stage is the source patch and the juvenile stage is only a sink patch) provides a unique mechanism for stable coexistence.…”

Wind mediated dispersal of freshwater invertebrates in a rock pool metacommunity: differences in dispersal capacities and modes

“…We did not relate relative abundances of taxa in the dispersing community to relative abundances in active communities as these do not reliably reflect the relative abundance of different corresponding propagules in the propagule bank (Brendonck & De Meester, 2003). Differences in magnitude of observed dispersal rates among taxa can be a consequence of variation in size of their corresponding propagule banks (density dependent dispersal; Amarasekare, 2004). However, as detailed information about the relative composition of propagule banks is unavailable for our study site, we could not simply use measured dispersal rates to infer taxon-specific dispersal capacity.…”

Two-time scales in spatially structured models of population dynamics: A semigroup approach

“…Most models consider the simplest case of density-independent migrations (see [1,19,29]) and, to our knowledge, still, few works have addressed the effects of density-dependent dispersal. We could, nevertheless, cite the following ones: [3,2,9,20]. In a more recent work [21], some of us considered a predator-prey model with two patches connected by density-dependent migrations.…”