Ideal Free Distributions, Evolutionary Games, and Population Dynamics in Multiple‐Species Environments

Cressman, Ross; Křivan, Vlastimil; Garay, József

doi:10.1086/423827

Cited by 119 publications

(107 citation statements)

References 32 publications

(23 reference statements)

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“…Thus in foraging models, the value of food patches depends directly on the intensity of their use by foragers within the population, as we saw from (Parker, 1978). More recent and realistic models of this phenomenon are given in Cressman et al (2004); Křivan et al (2008) for example.…”

Section: Discussionmentioning

confidence: 99%

Nonlinear and Multiplayer Evolutionary Games

Broom

Rychtář

2016

Advances in Dynamic and Evolutionary Games

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract Classical evolutionary game theory has typically considered populations within which randomly selected pairs of individuals play games against each other, and the resulting payoff functions are linear. These simple functions have led to a number of pleasing results for the dynamic theory, the static theory of evolutionarily stable strategies, and the relationship between them. We discuss such games, together with a basic introduction to evolutionary game theory, in Section 1. Realistic populations, however, will generally not have these nice properties, and the payoffs will be nonlinear. In Section 2 we discuss various ways in which nonlinearity can appear in evolutionary games, including pairwise games with strategy-dependent interaction rates, and playing the field games, where payoffs depend upon the entire population composition, and not on individual games. In Section 3 we consider multiplayer games, where payoffs are the result of interactions between groups of size greater than two, which again leads to nonlinearity, and a breakdown of some of the classical results of Section 1. Finally in Section 4 we summarise and discuss the previous sections. Permanent repository link

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Section: Discussionmentioning

confidence: 99%

Nonlinear and Multiplayer Evolutionary Games

Broom

Rychtář

2016

Advances in Dynamic and Evolutionary Games

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“…Finally, using the results of Poincaré-Bendixson theorem [12], we show that these equilibria are globally stable. We conclude with a brief discussion our results, noting their biological implications in the context of evolutionary stable strategies (ESSs; Maynard Smith [13]) and ideal free distributions (IFDs; Fretwell & Lucas [14]) of fitness-optimizing animals in population games [15]. Proofs of our main analytical results are presented in the appendix.…”

Section: Introductionmentioning

confidence: 93%

“…Periodic solutions are not uncommon in asymmetric fitness games with co-evolving strategies (e.g., predator-prey games [15]). Like predator-prey conflicts, mating conflicts between males and females may also generate a co-evolutionary cycling especially if the value of adaptations exhibits negative frequency-dependence (i.e., rare strategies have higher fitness than common types).…”

Section: Ruling Out Closed Orbitsmentioning

confidence: 99%

On the evolutionary stability of male harassment in a coercive mating game

Udiani¹,

Lou²,

Hamilton³

2016

Tamkang J. Math.

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Abstract. In many animals, males employ coercive mating strategies to help them maximize their expected number of offspring. In such systems, selection will favor behavioral adaptations in females that help them mitigate harassment costs and maximize their reproductive fitness. Previously, Bokides et al.[1] presented a model showing how male harassment strategies can co-evolve with female habitat preferences in a mating game. Their results indicated that if females dispersed freely between habitats where males were present and where males were excluded, selection could favor males who strategically harassed at high (or low) levels, depending on the proximity of their phenotype to a threshold level h * . This article is a continuation of that work addressing the questions of stability at equilibria where males harass at the threshold level (i.e., h * ). We show these states are both locally and globally asymptotically stable. Further, we argue based on these results that h * is an evolutionary stable male harassment level at which females will be ideally distributed to match the resource quality and social environments of their alternative habitats.

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“…These conflicting goals give rise to a spatial game that has been termed a space race (Sih 2005). Studies of space race games and other habitat selection games, have derived evolutionary stable distributions and investigated whether or not density-dependent movements lead to such distributions (Iwasa 1982;Cressman et al 2004;Schreiber and Vejdani 2006;Abrams 2007;Krivan et al 2008). Studies of the effects of space races on large scale population dynamics have focused on the Lotka-Volterra predatorprey model and the Nicholson-Bailey host-parasitoid model.…”

Section: Introductionmentioning

confidence: 99%

“…Studies of the effects of space races on large scale population dynamics have focused on the Lotka-Volterra predatorprey model and the Nicholson-Bailey host-parasitoid model. The effects on stability are variable, although stabilizing effects seem to predominate (van Baalen and Sabelis 1993;Krivan 1997Krivan , 1998van Baalen and Sabelis 1999;Cressman et al 2004;Mchich et al 2007). An interesting exception is the tri-trophic model of Abrams (2007), which differs from other models in that it assumes that the timescales of the studied movements are similar to those for the rates of birth and death.…”

Section: Introductionmentioning

confidence: 99%

Population-level consequences of heterospecific density-dependent movements in predator–prey systems

Sjödin

Brännström

Söderquist

et al. 2014

Journal of Theoretical Biology

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In this paper we elucidate how small-scale movements, such as those associated with searching for food and avoiding predators, affect the stability of predator-prey dynamics. We investigate an individual-based Lotka-Volterra model with density dependent movement, in which the predator and prey populations live in a very large number of coupled patches. The rates at which individuals leave patches depend on the local densities of heterospecifics, giving rise to one reaction norm for each of the two species. Movement rates are assumed to be much faster than demographics rates. A spatial structure of predators and prey emerges which affects the global population dynamics. We derive a criterion which reveals how demographic stability depends on the relationships between the per capita covariance and densities of predators and prey. Specifically, we establish that a positive relationship with prey density and a negative relationship with predator density tend to be stabilizing. On a more mechanistic level we show how these relationships are linked to the movement reaction norms of predators and prey. Numerical results show that these findings hold both for local and global movements, i.e., both when migration is biased towards neighboring patches and when all patches are reached with equal probability.

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Ideal Free Distributions, Evolutionary Games, and Population Dynamics in Multiple‐Species Environments

Cited by 119 publications

References 32 publications

Nonlinear and Multiplayer Evolutionary Games

Nonlinear and Multiplayer Evolutionary Games

On the evolutionary stability of male harassment in a coercive mating game

Population-level consequences of heterospecific density-dependent movements in predator–prey systems

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