The ideal free distribution: a review and synthesis of the game-theoretic perspective

The Ideal Free Distribution (IFD), introduced by Fretwell and Lucas in [Fretwell, D.S., Lucas, H.L., 1970. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheoretica 19, 16-32] to predict how a single species will distribute itself among several patches, is often cited as an example of an evolutionarily stable strategy (ESS). By defining the strategies and payoffs for habitat selection, this article puts the IFD concept in a more general game-theoretic setting of the "habitat selection game". Within this game-theoretic framework, the article focuses on recent progress in the following directions: (1) studying evolutionarily stable dispersal rates and corresponding dispersal dynamics; (2) extending the concept when population numbers are not fixed but undergo population dynamics; (3) generalizing the IFD to multiple species. For a single species, the article briefly reviews existing results. It also develops a new perspective for Parker's matching principle, showing that this can be viewed as the IFD of the habitat selection game that models consumer behavior in several resource patches and analyzing complications involved when the model includes resource dynamics as well. For two species, the article first demonstrates that the connection between IFD and ESS is now more delicate by pointing out pitfalls that arise when applying several existing game-theoretic approaches to these habitat selection games. However, by providing a new detailed analysis of dispersal dynamics for predator-prey or competitive interactions in two habitats, it also pinpoints one approach that shows much promise in this general setting, the so-called "two-species ESS". The consequences of this concept are shown to be related to recent studies of population dynamics combined with individual dispersal and are explored for more species or more patches.

A Lyapunov function for piecewise-independent differential equations: stability of the ideal free distribution in two patch environments

In this article we construct Lyapunov functions for models described by piecewise-continuous and independent differential equations. Because these models are described by discontinuous differential equations, the theory of Lyapunov functions for smooth dynamical systems is not applicable. Instead, we use a geometrical approach to construct a Lyapunov function. Then we apply the general approach to analyze population dynamics describing exploitative competition of two species in a two-patch environment. We prove that for any biologically meaningful parameter combination the model has a globally stable equilibrium and we analyze this equilibrium with respect to parameters.

Local- and landscape-level den selection of striped skunks on the Canadian prairies

We examined the seasonal landscape and habitat use patterns of striped skunks ( Mephitis mephitis Schreber, 1776). We tracked 52 male and 72 female skunks from September 1999 to June 2003 in Saskatchewan, Canada. At the local level, den structures differed by sex and season. In autumn/winter, all skunks preferred buildings, whereas in spring/summer females selectively used underground burrows and rock piles for parturition and rearing of young, and males used aboveground retreats. Den sites were closer to crop fields, roads, water sources, and macrohabitat edges than random sites. At the landscape level, den sites were associated positively with weighted mean shape index of crop fields, mean patch size of water bodies, total edge of water bodies, and weighted mean fractal dimensions of grassland, woodland, and farmsteads, suggesting that wetland edges and habitat complexity are important in den selection by skunks. Compositional analysis revealed sex- and season-specific differences at the population level. Both sexes preferred grassland/pastures and farmstead habitats for establishing den sites. In autumn/winter, skunks preferred grassland/pastures for winter dens. However, in spring/summer skunks preferred farmsteads for resting sites. Our results suggest that skunks respond to landscape and habitat features surrounding den sites, and not just specific den or local habitat characteristics.

Aposematism: what should our starting point be?

The evolution of aposematism is considered to be a major evolutionary problem because if new aposematic forms emerged in defended cryptic populations, they would face the dual problems of rarity and conspicuousness. We argue that this commonly assumed starting point might not have wide validity. We describe a novel evolutionary computer model in which prey evolve secondary defences and become conspicuous by moving widely over a visually heterogeneous habitat. Unless crypsis imposes high opportunity costs (for instance, preventing prey from efficient foraging, thermoregulation and communication), costly secondary defences are not predicted to evolve at all. However, when crypsis imposes opportunity costs, prey evolve secondary defences that facilitate raised behavioural conspicuousness as prey exploit opportunities within their environment. Optimal levels of secondary defence and of behavioural conspicuousness increase with population sizes and the costs imposed by crypsis. When prey are already conspicuous by virtue of their behaviours, the evolution of aposematic appearances (bright coloration, etc.) is much easier to explain because aposematic traits add little further costs of conspicuousness, but can bring large benefits.

Ideal free distributions, evolutionary games, and population dynamics in multiple-species environments

In this article, we develop population game theory, a theory that combines the dynamics of animal behavior with population dynamics. In particular, we study interaction and distribution of two species in a two-patch environment assuming that individuals behave adaptively (i.e., they maximize Darwinian fitness). Either the two species are competing for resources or they are in a predator-prey relationship. Using some recent advances in evolutionary game theory, we extend the classical ideal free distribution (IFD) concept for single species to two interacting species. We study population dynamical consequences of two-species IFD by comparing two systems: one where individuals cannot migrate between habitats and one where migration is possible. For single species, predator-prey interactions, and competing species, we show that these two types of behavior lead to the same population equilibria and corresponding species spatial distributions, provided interspecific competition is patch independent. However, if differences between patches are such that competition is patch dependent, then our predictions strongly depend on whether animals can migrate or not. In particular, we show that when species are settled at their equilibrium population densities in both habitats in the environment where migration between habitats is blocked, then the corresponding species spatial distribution need not be an IFD. Thus, when species are given the opportunity to migrate, they will redistribute to reach an IFD (e.g., under which the two species can completely segregate), and this redistribution will also influence species population equilibrial densities. Alternatively, we also show that when two species are distributed according to the IFD, the corresponding population equilibrium can be unstable.

Can animals use foraging behaviour to combat parasites?

Host-parasite interactions are often seen as an arms race, with parasites attempting to overcome host resistance to infection. Herbivory is a common route of transmission of parasites that represents the most pervasive challenge to mammalian growth and reproduction. The present paper reviews the foraging skills of mammalian herbivores in relation to their ability to exploit plant properties to combat parasites. The starting point is that foraging behaviour may ameliorate the impact of parasitism in three ways; hosts could: (1) avoid foraging in areas contaminated with parasites; (2) select diets which increase their resistance to parasites; (3) select for foods containing anti-parasitic properties (self-medication). Details are given of the pre-requisite skills needed by herbivores if they are to combat parasitism via behaviour, i.e. herbivores are able to: (a) determine their parasitic state and alter their behaviour in relation to that state (behaviours 1, 2 and 3); (b) determine the environmental distribution of parasites (behaviour 1); (c) distinguish plant species or plant parts that increase their resistance to parasites (behaviour 2) or have anti-parasitic properties (behaviour 3). Mammalian herbivores cannot detect the presence of the parasites themselves and must rely on cues such as faeces. Despite the use of these cues contacting parasites may be inevitable and so mechanisms to combat parasitism are necessary. Mammalian herbivores have the foraging skills needed to exploit the heterogeneous distributions of nutrients and parasites in complex foraging environments in order to avoid, and increase their resistance to, parasites. Current evidence for the use of plant secondary metabolites (PSM) by herbivores for self-medication purposes remains equivocal. PSM have both positive (anti-parasitic) and negative (toxic) effects on herbivores. Here details are given of an experimental approach using tri-trophic (plant-herbivore-parasite) interactions that could be used to demonstrate self-medication in animals. There is strong evidence suggesting that herbivore hosts have developed the foraging skills needed to take advantage of plant properties to combat parasites and thus use behaviour as a weapon in the host-parasite arms race.

Ideal free distributions when resources undergo population dynamics

This study examines the influence of optimal patch choice by consumers on resource population dynamics and on consumer distribution in a two patch environment. The evolutionarily stable strategy which describes animal distributions across habitat patches is called the ideal free distribution (IFD) strategy. Two mechanisms that lead to the IFD are: (1) direct consumer competition such as interference, and (2) exploitative competition for resources. This article focuses on the second mechanism by assuming that resources undergo population dynamics while consumer abundance is fixed. Two models of resource growth are considered in detail: the exponential and the logistic. The corresponding consumer IFD is derived for each of these two models, assuming that consumers behave adaptively by moving to the patch which provides them with the highest fitness. This derivation does not require that resources are at an equilibrium, and it provides, for each resource density, the corresponding distribution of consumers. The article suggests that adaptive patch choice by consumers decreases between patch heterogeneity in resource levels and weakens the apparent competition between resources. The results for a single consumer population are extended for two competing consumer populations. The corresponding IFD is computed as a function of the two consumer densities. This allows for the analytical description of isolegs which are the boundary lines, in the two consumer density phase space, separating regions where qualitatively different habitat preferences are predicted.