Spatial and nonspatial evolutionary games and their applications

Li, You

doi:10.26481/dis.20180207yl

Cited by 2 publications

(4 citation statements)

References 152 publications

(259 reference statements)

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“…Evolutionary games can also exhibit non-equilibrium strategy dynamics. Games with continuous-trait strategies have shown other sorts of such as limit cycles, as noted for variants of the rock-scissors-paper game, and evolutionary suicide (Weissing, 1991;You, 2018). While the four equilibrial properties of the ESS, convergence stability, NIS, and mutual invisibility are well formalized (Apaloo et al, 2009), these non-equilibrium evolutionary dynamics have thus far defied clear context or intuition.…”

Section: E Discussionmentioning

confidence: 99%

Non-Equilibrial Dynamics in Under-Saturated Communities

Halloway

Staňková

Brown

2019

Preprint

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A. AbstractThe concept of the evolutionary stable strategy (ESS) has been fundamental to the development of evolutionary game theory. It represents an equilibrial evolutionary state in which no rare invader can grow in population size. With additional work, the ESS concept has been formalized and united with other stability concepts such as convergent stability, neighborhood invasion stability, and mutual invisibility. Other work on evolutionary models, however, shows the possibility of unstable and/or non-equilibrial dynamics such as limit cycles and evolutionary suicide. Such "pathologies" remain outside of a well-defined context, especially the currently defined stability concepts of evolutionary games. Ripa et al. (2009) offer a possible reconciliation between work on non-equilibrial dynamics and the ESS concept. They noticed that the systems they analyzed show non-equilibrial dynamics when under-saturated and "far" from the ESS and that getting "closer" to the ESS through the addition of more species stabilized their systems. To that end, we analyzed three models of evolution, two predator-prey models and one competition model of evolutionary suicide, to see how the degree of saturation affects the stability of the system. In the predator-prey models, stability is linked to the degree of saturation.Specifically, a fully saturated community will only show stable dynamics, and unstable dynamics occur only when the community is under-saturated. With the competition model, we demonstrate it to be permanently under-saturated, likely showing such extreme dynamics for this reason.Though not a general proof, our analysis of the models provide evidence of the link between community saturation and evolutionary dynamics. Our results offer a possible placement of these evolutionary "pathologies" into a wider framework. In addition, the results concur with previous results showing greater evolutionary response to less biodiversity and clarifies the effect of extrinsic vs. intrinsic non-equilibrial evolutionary dynamics on a community.

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Section: E Discussionmentioning

confidence: 99%

Non-Equilibrial Dynamics in Under-Saturated Communities

Halloway

Staňková

Brown

2019

Preprint

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“…They assume well-mixed popu-lations and no spatial restrictions on the interaction of agents. However, examples show that results from this non-spatial approach may differ from results achieved by modeling the same scenario assuming a heterogeneous population without individual aspects like aging or local competitions for space [Kerr et al, 2002, Laird, 2014, Schüller, 2014, Schreiber and Killingback, 2013, You, 2018. Nevertheless, spatial aspects should only be included in the model if they have an impact on the modeled phenomenon, as spatial models are usually harder to analyze than their non-spatial variants.…”

Section: Spatial Vs Non-spatial Modelsmentioning

confidence: 99%

“…• Variability in Space: Classical models may contain implicit spatial aspects, but they cannot typically model distinct individuals that create local nonuniformity in populations. Many authors could observe differences between predictions of spatially explicit and non-spatial models [Chesson, 1981, Durrett and Levin, 1994, You, 2018].…”

Section: Advantages Of Abmsmentioning

confidence: 99%

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On Agent-Based Models of Sex, Plants and Sustainability

Schüller¹

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Spatial and nonspatial evolutionary games and their applications

Cited by 2 publications

References 152 publications

Non-Equilibrial Dynamics in Under-Saturated Communities

Non-Equilibrial Dynamics in Under-Saturated Communities

On Agent-Based Models of Sex, Plants and Sustainability

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