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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

Pairwise invisibility plots (PIPs) for the continuous snowdrift game. Each panel shows a sign plot of invasion fitness S(x,y) in Eq. (11). Due to the linearity of the payoff difference with respect to the strategy frequency, the sign pair (S(x2,x1),S(x1,x2)) can indicate the frequency dynamics between the strategies with x1 and x2. Panel (x) exemplifies the case of (S(x2,x1),S(x1,x2)) = (+,−) which leads to a unilateral evolution: x2 dominates x1. The five sign plots are representative corresponding to the five cases of adaptive dynamics in the continuous snowdrift game: (a), (b), (c), (d), and (e) are for (ii-B), (i-B), (iii-B), (iv-B), and (iv-A), respectively. Parameters: c1 = 4.6, c2 = −1; (d1,d2) = (0.3, −0.3) for (a), (0.7, −0.3) for (b), (0.3, −0.7) for (c), (0.7, −0.7) for (d), and (1.7, −1.7) for (e).
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fig0015: Pairwise invisibility plots (PIPs) for the continuous snowdrift game. Each panel shows a sign plot of invasion fitness S(x,y) in Eq. (11). Due to the linearity of the payoff difference with respect to the strategy frequency, the sign pair (S(x2,x1),S(x1,x2)) can indicate the frequency dynamics between the strategies with x1 and x2. Panel (x) exemplifies the case of (S(x2,x1),S(x1,x2)) = (+,−) which leads to a unilateral evolution: x2 dominates x1. The five sign plots are representative corresponding to the five cases of adaptive dynamics in the continuous snowdrift game: (a), (b), (c), (d), and (e) are for (ii-B), (i-B), (iii-B), (iv-B), and (iv-A), respectively. Parameters: c1 = 4.6, c2 = −1; (d1,d2) = (0.3, −0.3) for (a), (0.7, −0.3) for (b), (0.3, −0.7) for (c), (0.7, −0.7) for (d), and (1.7, −1.7) for (e).

Mentions: We note that in the model, invasion fitness has already been resolved into two linear components: one variable as b2(3x + y) + b1 − c2(x + y) − c1 and a fixed diagonal as y − x. This leads to the so-called pairwise invasibility plot (PIP) (Geritz et al., 1997, 1998), a sign plot of invasion fitness S(x,y) on (x,y)-space, which can be separated by lines (Fig. 3). The PIP diagram can provide a useful overview to determine the sign pair for any (S(x2,x1),S(x1,x2)) and thus the replicator dynamics in any dimorphic population. The adaptive dynamics of the population, once degenerated to monomorphism, can then be predicted by the four adaptive dynamics criteria in Table 2. In certain cases its dimorphism is protected, otherwise, we shall consider adaptive dynamics in dimorphic populations.


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

Sasaki T, Okada I - BioSystems (2015)

Pairwise invisibility plots (PIPs) for the continuous snowdrift game. Each panel shows a sign plot of invasion fitness S(x,y) in Eq. (11). Due to the linearity of the payoff difference with respect to the strategy frequency, the sign pair (S(x2,x1),S(x1,x2)) can indicate the frequency dynamics between the strategies with x1 and x2. Panel (x) exemplifies the case of (S(x2,x1),S(x1,x2)) = (+,−) which leads to a unilateral evolution: x2 dominates x1. The five sign plots are representative corresponding to the five cases of adaptive dynamics in the continuous snowdrift game: (a), (b), (c), (d), and (e) are for (ii-B), (i-B), (iii-B), (iv-B), and (iv-A), respectively. Parameters: c1 = 4.6, c2 = −1; (d1,d2) = (0.3, −0.3) for (a), (0.7, −0.3) for (b), (0.3, −0.7) for (c), (0.7, −0.7) for (d), and (1.7, −1.7) for (e).
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fig0015: Pairwise invisibility plots (PIPs) for the continuous snowdrift game. Each panel shows a sign plot of invasion fitness S(x,y) in Eq. (11). Due to the linearity of the payoff difference with respect to the strategy frequency, the sign pair (S(x2,x1),S(x1,x2)) can indicate the frequency dynamics between the strategies with x1 and x2. Panel (x) exemplifies the case of (S(x2,x1),S(x1,x2)) = (+,−) which leads to a unilateral evolution: x2 dominates x1. The five sign plots are representative corresponding to the five cases of adaptive dynamics in the continuous snowdrift game: (a), (b), (c), (d), and (e) are for (ii-B), (i-B), (iii-B), (iv-B), and (iv-A), respectively. Parameters: c1 = 4.6, c2 = −1; (d1,d2) = (0.3, −0.3) for (a), (0.7, −0.3) for (b), (0.3, −0.7) for (c), (0.7, −0.7) for (d), and (1.7, −1.7) for (e).
Mentions: We note that in the model, invasion fitness has already been resolved into two linear components: one variable as b2(3x + y) + b1 − c2(x + y) − c1 and a fixed diagonal as y − x. This leads to the so-called pairwise invasibility plot (PIP) (Geritz et al., 1997, 1998), a sign plot of invasion fitness S(x,y) on (x,y)-space, which can be separated by lines (Fig. 3). The PIP diagram can provide a useful overview to determine the sign pair for any (S(x2,x1),S(x1,x2)) and thus the replicator dynamics in any dimorphic population. The adaptive dynamics of the population, once degenerated to monomorphism, can then be predicted by the four adaptive dynamics criteria in Table 2. In certain cases its dimorphism is protected, otherwise, we shall consider adaptive dynamics in dimorphic populations.

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