Migration Dynamics for the Ideal Free Distribution

Abstract

This article verifies that the ideal free distribution (IFD) is evolutionarily stable, provided the payoff in each patch decreases with an increasing number of individuals. General frequency-dependent models of migratory dynamics that differ in the degree of animal omniscience are then developed. These models do not exclude migration at the IFD where balanced dispersal emerges. It is shown that the population distribution converges to the IFD even when animals are nonideal (i.e., they do not know the quality of all patches). In particular, the IFD emerges when animals never migrate from patches with a higher payoff to patches with a lower payoff and when some animals always migrate to the best patch. It is shown that some random migration does not necessarily lead to undermatching, provided migration occurs at the IFD. The effect of population dynamics on the IFD (and vice versa) is analyzed. Without any migration, it is shown that population dynamics alone drive the population distribution to the IFD. If animal migration tends (for each fixed population size) to the IFD, then the combined migrationpopulation dynamics evolve to the population IFD independent of the two timescales (i.e., behavioral vs. population).

Evolutionary ecology of movement by predators and prey

“…The expected payoff for a predator or prey in a patch was defined as the expected per capita birth rate minus the expected per capita death rate for that patch. We also confirmed numerically that the ideal free distribution found using those payoffs was the same as the population dynamics equilibrium that would be predicted in the absence of movement (Cressman and Křivan 2006;Křivan et al 2008;Křivan and Cressman 2009) for a given set of parameters.…”

“…An ideal free distribution (IFD) is a spatial distribution characterized by no individual being able to improve its fitness by moving to a different location in its habitat (Fretwell and Lucas 1969). When applied to just a single species, the IFD has been shown to be a very robust prediction about both behavior and distributions: (a) A population can reach an IFD even when individual organisms (occasionally) move suboptimally, (b) strategies that produce IFDs are evolutionarily stable (sensu Maynard Smith and Price 1973;Maynard Smith 1982), and (c) population dynamics equilibria are also IFDs (Cressman and Křivan 2006;Křivan et al 2008;McPeek and Holt 1992; but see Cressman and Křivan 2010). However, models incorporating multiple species (such as those cited in the previous paragraph) have produced a wide variety of results, which contrast with the simpler view provided by single-species models.…”

Dispersal evolution and resource matching in a spatially and temporally variable environment

“…More generally, the ideal free distribution is the one such that an individual could not attain higher fitness by relocating to another patch. This distribution has been shown to be evolutionarily stable when fitness is a negative function of density (Cressman and Křivan, 2006;Křivan et al, 2008). However, experiments often report undermatching, i.e.…”

Influences of migrations from local competitive pressures on populations between patches

“…de Roos et al [6] and Persson et al [14] studied flexible behaviors in size-structured populations by assuming that the movement rate out of a patch is purely a function of fitness of individuals within that patch. Recently, Cressman and Krivan [5] put forward density-dependent dispersals for ODE models. Abdllaoui et al [1] introduced density-dependent dispersal into predator-prey models in a two-patch environment.…”