The Ideal Free Distribution and Evolutionary Stability in Habitat Selection Games with Linear Fitness and Allee Effect

Cressman, Ross; Tran, Tan

doi:10.1007/978-3-319-12307-3_66

Cited by 10 publications

(7 citation statements)

References 7 publications

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“…Similarly, the remaining individuals with P π (2) in their territory have to go to P π (2) and so on. So, the above procedure with the permutation π indeed recovers the stable occupancy function D, and any stable distribution which satisfies (15) must have an occupancy function defined by (12) and (13).…”

Section: All Solutions To the Predator Dilution Gamementioning

confidence: 91%

“…Once the permutation π is defined, we use it to construct the occupancy function O as done earlier in Sect. 4.2 by (14) together with (12) and (13). The occupancy function O is clearly stable.…”

Section: Existence Of Stable Occupancy Functions For the Predator Dilmentioning

confidence: 99%

“…The simplest single species model was developed by Fretwell and Lucas [14], Fretwell [13] (see also [10]), with a closely related model developed by Parker [35]. More complex cases, including for multi-species [15,23], individuals with different abilities [19,40] and for more complex payoff functions, including the Allee effect [12,25], have also been considered.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Ideal Cost-Free Distributions in Structured Populations for General Payoff Functions

Broom

Rychtář

2016

Dyn Games Appl

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The important biological problem of how groups of animals should allocate themselves between different habitats has been modelled extensively. Such habitat selection models have usually involved infinite well-mixed populations. In particular, the model of allocation over a number of food patches when movement is not costly, the ideal free distribution (IFD) model, is well developed. Here we generalize (and solve) a habitat selection game for a finite structured population. We show that habitat selection in such a structured population can have multiple stable solutions (in contrast to the equivalent IFD model where the solution is unique). We also define and study a "predator dilution game" where unlike in the habitat selection game, individuals prefer to aggregate (to avoid being caught by predators due to the dilution effect) and show that this model has a unique solution when movement is unrestricted.

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Section: All Solutions To the Predator Dilution Gamementioning

confidence: 91%

Section: Existence Of Stable Occupancy Functions For the Predator Dilmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ideal Cost-Free Distributions in Structured Populations for General Payoff Functions

Broom

Rychtář

2016

Dyn Games Appl

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“…This is called the Allee effect. The IFD for the Allee effect has been studied in the literature (Fretwell and Lucas, 1969;Morris, 2002;Křivan, 2014;Cressman and Tran, 2015). It has been shown that for hump shaped patch payoffs, up to three IFDs can exist for a given overall population abundance.…”

Section: Some Extensions Of the Habitat Selection Gamementioning

confidence: 99%

Biology and Evolutionary Games

Broom

Křivan

2018

Handbook of Dynamic Game Theory

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“…(b) ( *   * ) is convergence stable if and only if, for all non-zero ( ) ∈ R 2 , either (( + )  + )  0 or  ( + ( +  ) )  0 if and only if  +   0  +   0 and ( + ) ( +  )  . 39 In Sections 3.1 and 3.4, it was shown that a CSS for symmetric games is a neighborhood strict NE that is convergence stable under all adaptive dynamics (e.g. Theorem 6 (a)).…”

mentioning

confidence: 99%

Evolutionary Game Theory

Cressman¹,

Apaloo²

2016

Handbook of Dynamic Game Theory

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Evolutionary game theory developed as a means to predict the expected distribution of individual behaviors in a biological system with a single species that evolves under natural selection. It has long since expanded beyond its biological roots and its initial emphasis on models based on symmetric games with a finite set of pure strategies where payoffs result from random one-time interactions between pairs of individuals (i.e. on matrix games). The theory has been extended in many directions (including non-random, multi-player or asymmetric interactions, and games with continuous strategy (or trait) spaces) and has become increasingly important for analyzing human and/or social behavior as well. This chapter initially summarizes features of matrix games before showing how the theory changes when the two-player game has a continuum of traits or interactions become asymmetric. It's focus is on the connection between static game-theoretic solution concepts (e.g. ESS, CSS, NIS) and stable evolutionary outcomes for deterministic evolutionary game dynamics (e.g. the replicator equation, adaptive dynamics).

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The Ideal Free Distribution and Evolutionary Stability in Habitat Selection Games with Linear Fitness and Allee Effect

Cited by 10 publications

References 7 publications

Ideal Cost-Free Distributions in Structured Populations for General Payoff Functions

Ideal Cost-Free Distributions in Structured Populations for General Payoff Functions

Biology and Evolutionary Games

Evolutionary Game Theory

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