Ideal Free Dispersal under General Spatial heterogeneity and Time Periodicity

TL;DR

This paper extends the concept of ideal free distribution to environments with general spatial heterogeneity and time periodicity, demonstrating the evolutionary advantage of such dispersal strategies and providing a criterion for their feasibility.

Contribution

It introduces a mathematical framework for ideal free distributions in time-periodic environments and identifies conditions under which these strategies are evolutionarily stable.

Findings

Dispersal strategies that produce ideal free distributions have a competitive advantage.

A necessary and sufficient criterion for the feasibility of ideal free distributions in periodic environments.

Existence of evolutionarily stable, time-periodic dispersal strategies.

Abstract

A population is said to have an ideal free distribution in a spatially heterogeneous but temporally constant environment if each of its members have chosen a fixed spatial location in a way that optimizes its individual fitness, allowing for the effects of crowding. In this paper, we extend the idea of individual fitness associated with a specific location in space to account for the full path that an individual organism takes in space and time over a periodic cycle, and extend the mathematical formulation of an ideal free distribution to general time periodic environments. We find that, as in many other cases, populations using dispersal strategies that can produce a generalized ideal free distribution have a competitive advantage relative to populations using strategies that do not produce an ideal free distribution. A sharp criterion on the environmental functions is found to be necessary and sufficient for such ideal free distribution to be feasible. In the case the criterion is met, we showed that there exist dispersal strategies that can be identified as producing a time-periodic version of an ideal free distribution, and such strategies are evolutionarily steady and are neighborhood invaders from the viewpoint of adaptive dynamics. Our results extend previous works in which the environments are either temporally constant, or temporally periodic but the total carrying capacity is temporally constant.