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Cheating is evolutionarily assimilated with cooperation in the continuous snowdrift game.

Sasaki T, Okada I - BioSystems (2015)

Bottom Line: Recent theoretical evidence on the snowdrift game suggests that gradual evolution for individuals choosing to contribute in continuous degrees can result in the social diversification to a 100% contribution and 0% contribution through so-called evolutionary branching.Subsequently, conditions are clarified under which gradual evolution can lead a population consisting of those with 100% contribution and those with 0% contribution to merge into one species with an intermediate contribution level.Importantly, this implies that allowing the gradual evolution of cooperative behavior can facilitate social inequity aversion in joint ventures that otherwise could cause conflicts that are based on commonly accepted notions of fairness.

View Article: PubMed Central - PubMed

Affiliation: Faculty of Mathematics, University of Vienna, 1090 Vienna, Austria; Evolution and Ecology Program, International Institute for Applied Systems Analysis (IIASA), 2361 Laxenburg, Austria. Electronic address: tatsuya.sasaki@univie.ac.at.

No MeSH data available.


Related in: MedlinePlus

Evolution of cooperation in snowdrift games. For discrete strategies, on the one hand, the evolution of the strategy frequencies can lead to the coexistence of cooperators and cheaters (upper arrows, X0 to B and X1 to B), yet do not help in understanding whether or not the resultant mixture is stable against continuously small mutations. For continuous strategies, on the other hand, the population converges to an intermediate level of cooperation (lower arrows, X0 to A and X1 to A) and can further undergo evolutionary branching (vertical arrow, A to B). In this case, the population splits into diverging clusters across an evolutionary-branching point  and eventually evolves to an evolutionarily stable mixture of full- and non-contributors (B). Otherwise, it is possible that a point where  has already become evolutionarily stable. In this case, the initially dimorphic population across a point  can be evolutionarily unstable, and thus the population will approach each other and finally merge into one cluster at the point (“evolutionary merging”; vertical arrow, B to A).
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fig0005: Evolution of cooperation in snowdrift games. For discrete strategies, on the one hand, the evolution of the strategy frequencies can lead to the coexistence of cooperators and cheaters (upper arrows, X0 to B and X1 to B), yet do not help in understanding whether or not the resultant mixture is stable against continuously small mutations. For continuous strategies, on the other hand, the population converges to an intermediate level of cooperation (lower arrows, X0 to A and X1 to A) and can further undergo evolutionary branching (vertical arrow, A to B). In this case, the population splits into diverging clusters across an evolutionary-branching point and eventually evolves to an evolutionarily stable mixture of full- and non-contributors (B). Otherwise, it is possible that a point where has already become evolutionarily stable. In this case, the initially dimorphic population across a point can be evolutionarily unstable, and thus the population will approach each other and finally merge into one cluster at the point (“evolutionary merging”; vertical arrow, B to A).

Mentions: In Section 2, we extend the discrete snowdrift game to continuous cooperation. Fig. 1 presents an overview encompassing evolutionary scenarios in the classical and continuous snowdrift games. In Section 3, we then investigate the gradual evolution of cooperation with small mutations. In the continuous extension we consider quadratic payoff functions for interpolating these four payoff values in Eq. (1). It is known that the continuous model with quadratic payoff functions is at minimum, required for full coverage of basic adaptive dynamics for a population monomorphic with the same level of cooperation (Brown and Vincent, 2008; Doebeli et al., 2004) (see also (Boza and Számadó, 2010; Chen et al., 2012; Zhang et al., 2013) for effects of more generalized payoff functions). We show that adaptive dynamics in the snowdrift game analytically provides a solution whether a population is monomorphic or dimorphic. Finally, in Section 4 we provide a summary and discuss the model, results, and future work.


Cheating is evolutionarily assimilated with cooperation in the continuous snowdrift game.

Sasaki T, Okada I - BioSystems (2015)

Evolution of cooperation in snowdrift games. For discrete strategies, on the one hand, the evolution of the strategy frequencies can lead to the coexistence of cooperators and cheaters (upper arrows, X0 to B and X1 to B), yet do not help in understanding whether or not the resultant mixture is stable against continuously small mutations. For continuous strategies, on the other hand, the population converges to an intermediate level of cooperation (lower arrows, X0 to A and X1 to A) and can further undergo evolutionary branching (vertical arrow, A to B). In this case, the population splits into diverging clusters across an evolutionary-branching point  and eventually evolves to an evolutionarily stable mixture of full- and non-contributors (B). Otherwise, it is possible that a point where  has already become evolutionarily stable. In this case, the initially dimorphic population across a point  can be evolutionarily unstable, and thus the population will approach each other and finally merge into one cluster at the point (“evolutionary merging”; vertical arrow, B to A).
© Copyright Policy - CC BY
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4441111&req=5

fig0005: Evolution of cooperation in snowdrift games. For discrete strategies, on the one hand, the evolution of the strategy frequencies can lead to the coexistence of cooperators and cheaters (upper arrows, X0 to B and X1 to B), yet do not help in understanding whether or not the resultant mixture is stable against continuously small mutations. For continuous strategies, on the other hand, the population converges to an intermediate level of cooperation (lower arrows, X0 to A and X1 to A) and can further undergo evolutionary branching (vertical arrow, A to B). In this case, the population splits into diverging clusters across an evolutionary-branching point and eventually evolves to an evolutionarily stable mixture of full- and non-contributors (B). Otherwise, it is possible that a point where has already become evolutionarily stable. In this case, the initially dimorphic population across a point can be evolutionarily unstable, and thus the population will approach each other and finally merge into one cluster at the point (“evolutionary merging”; vertical arrow, B to A).
Mentions: In Section 2, we extend the discrete snowdrift game to continuous cooperation. Fig. 1 presents an overview encompassing evolutionary scenarios in the classical and continuous snowdrift games. In Section 3, we then investigate the gradual evolution of cooperation with small mutations. In the continuous extension we consider quadratic payoff functions for interpolating these four payoff values in Eq. (1). It is known that the continuous model with quadratic payoff functions is at minimum, required for full coverage of basic adaptive dynamics for a population monomorphic with the same level of cooperation (Brown and Vincent, 2008; Doebeli et al., 2004) (see also (Boza and Számadó, 2010; Chen et al., 2012; Zhang et al., 2013) for effects of more generalized payoff functions). We show that adaptive dynamics in the snowdrift game analytically provides a solution whether a population is monomorphic or dimorphic. Finally, in Section 4 we provide a summary and discuss the model, results, and future work.

Bottom Line: Recent theoretical evidence on the snowdrift game suggests that gradual evolution for individuals choosing to contribute in continuous degrees can result in the social diversification to a 100% contribution and 0% contribution through so-called evolutionary branching.Subsequently, conditions are clarified under which gradual evolution can lead a population consisting of those with 100% contribution and those with 0% contribution to merge into one species with an intermediate contribution level.Importantly, this implies that allowing the gradual evolution of cooperative behavior can facilitate social inequity aversion in joint ventures that otherwise could cause conflicts that are based on commonly accepted notions of fairness.

View Article: PubMed Central - PubMed

Affiliation: Faculty of Mathematics, University of Vienna, 1090 Vienna, Austria; Evolution and Ecology Program, International Institute for Applied Systems Analysis (IIASA), 2361 Laxenburg, Austria. Electronic address: tatsuya.sasaki@univie.ac.at.

No MeSH data available.


Related in: MedlinePlus