Evolutionary Games and Population Dynamics

Hofbauer, Josef; Sigmund, Karl

doi:10.1017/cbo9781139173179

Cited by 4,079 publications

(5,081 citation statements)

References 57 publications

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“…Theorem 4.1 is a well-known result for evolutionary games without time constraints, forming one part of the folk theorem of evolutionary game theory (Hofbauer and Sigmund, 1998;Cressman, 2003). Another part of the folk theorem states that an interior ESS (i.e.…”

Section: Evolutionary and Dynamic Stability In The Pure-strategy Modelmentioning

confidence: 99%

“…For classical matrix games (i.e. matrix games without time constraints), these two concepts are connected by one part of the folk theorem of evolutionary game theory (Hofbauer and Sigmund, 1998;Cressman, 2003;Broom and Rychtar, 2013): An ESS is a locally asymptotically stable rest point of the replicator equation. The fundamental question of this paper is then: What is the connection between ESSs and stable rest points of the standard replicator equation in the class of matrix games under time constraints?…”

Section: Introductionmentioning

confidence: 99%

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The ESS and replicator equation in matrix games under time constraints

et al. 2018

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Recently, we introduced the class of matrix games under time constraints and characterized the concept of (monomorphic) evolutionarily stable strategy (ESS) in them. We are now interested in how the ESS is related to the existence and stability of equilibria for polymorphic populations. We point out that, although the ESS may no longer be a polymorphic equilibrium, there is a connection between them. Specifically, the polymorphic state at which the average strategy of the active individuals in the population is equal to the ESS is an equilibrium of the polymorphic model.Moreover, in the case when there are only two pure strategies, a polymorphic equilibrium is locally asymptotically stable under the replicator equation for the pure-strategy polymorphic model if and only if it corresponds to an ESS. Finally, we prove that a strict Nash equilibrium is a pure-strategy ESS that is a locally asymptotically stable equilibrium of the replicator equation in n-strategy time-constrained matrix games.

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Section: Evolutionary and Dynamic Stability In The Pure-strategy Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The ESS and replicator equation in matrix games under time constraints

et al. 2018

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“…Originally, this equation was introduced to describe evolution in a population consisting of n different types. The replicator equation then models the changes in the frequency of each type, depending on their fitness in comparison with the average fitness within the population (Hofbauer and Sigmund, 1998). Here foraging on resource i is increased (decreased), if the potential energy gain from consuming that resource alone is greater (lower) than the expected energy gain from feeding on both resources.…”

Section: Food Web Modelmentioning

confidence: 99%

Environmental weakening of trophic interactions drives stability in stochastic food webs

Ruokolainen

McCann

2013

Journal of Theoretical Biology

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A 3-species food web model is analysed, with stochastic variation in parameters. Noise affects either resource growth or consumer intake as a Gaussian function. Noise variance, colour, and the consumers foraging adaptation rate is varied. Environmental characteristics impact on the consumer-resource interaction strength. Noise impact on population variability depends on where it hits in the food web. a r t i c l e i n f o t r a c tThe physiological performance and behaviour of organisms are contingent on environmental conditions. When these conditions vary over time, this can have important consequences for the dynamics of individual populations and entire species communities. While the importance of environmental variation on the structuring and stability of natural food webs is recognised, little work has been done so far to build up a theoretical understanding of these processes. Here we investigate a simple model food web, where a consumer species forages flexibly upon two distinct, inter-competing resource species. Resource productivities or the resource intake rates by the consumer are assumed to depend on environmental conditions in a realistic manner. Fluctuations in these parameters drive variation in the strength of consumer-resource interactions, depending on whether the resource or the consumer is sensitive to environmental noise. The way resources and the consumer respond to changes in environmental conditions stems from the deterministic influence of each stochastic parameter on food web dynamics, which interact with the consumer adaptation process as well as between-resource competition. According to recent empirical reports, the mechanisms behind our results are likely to be relevant in natural systems and thus the model predictions are of potential importance in understanding food web responses to environmental stochasticity in general.

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“…The theory of dynamic systems has mainly influenced models of population development in biology (see e.g. Maynard Smith, 1974;Hofbauer and Sigmund, 1998). Some studies focused on dispersal patterns in metapopulations to predict spatio-temporal variations (Ferrière and Michod, 1996;Ferrière and Le Galliard, 2001) and build a bridge from population dynamics to cooperative breeding (Pen and Weissing, 2000;Le Galliard et al, 2005).…”

Section: Population Dynamicsmentioning

confidence: 99%

Cooperation theory of cooperative breeding

Skubic

2007

Behavioural Processes

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Evolutionary Games and Population Dynamics

Cited by 4,079 publications

References 57 publications

The ESS and replicator equation in matrix games under time constraints

The ESS and replicator equation in matrix games under time constraints

Environmental weakening of trophic interactions drives stability in stochastic food webs

Cooperation theory of cooperative breeding

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