The effect of the opting-out strategy on conditions for selection to favor the evolution of cooperation in a finite population

Li, Cong; Lessard, Sabin

doi:10.1016/j.jtbi.2020.110543

Cited by 3 publications

(2 citation statements)

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“…Finally, the island model with the possibility of extinction and recolonization can be extended to study groups distributional dynamics stemming from the possibility of opting out in repeated games (Cressman and Krivan [9], Krivan and Cressman [21], Li and Lessard [35], Zhang et al [62]). In the general case, however, the extinction probability or rate depends on the group composition, which makes the analysis more challenging.…”

Section: Case 3: σmentioning

confidence: 99%

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Evolutionary game with stochastic payoffs in a finite island model

Kroumi,

Lessard

2024

JDG

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In this paper, we consider a two-player two-strategy game with random payoffs in a population subdivided into d demes, each containing N individuals at the beginning of any given generation and experiencing local extinction and recolonization with some fixed probability m after reproduction and selection among offspring. Within each deme, offspring engage in random pairwise interactions, and the payoffs are assumed to have means and variances proportional to the inverse of the population size. By verifying the conditions given in Ethier and Nagylaki (1980) to approximate Markov chains with two timescales, we establish that the discrete-time evolutionary dynamics with N d generations as unit of time converges to a continuous-time diffusion as d → ∞. The infinitesimal mean and variance of this diffusion are expressed in terms of the population-scaled means and variances of the payoffs besides identity-by-descent measures between offspring in the same deme in a neutral population. We show that the probability for a strategy to fix in the population starting from an initial frequency (N d) −1 generally increases as the payoffs to that strategy exhibit less variability or the payoffs to the other strategy more variability. As a result, differences in variability can make this fixation probability for cooperation larger than the corresponding one for defection. As the deme-scaled extinction rate ν = mN decreases for N large enough and m small enough, creating a higher level of identity among offspring within demes, the differences between the population-scaled variances of the payoffs for interacting offspring of different types increases this effect to a greater extent than the differences for interacting offspring of the same type. Furthermore, assuming no variability in the payoffs to cooperation, we explore in more details the relationships between the levels of variability in the payoffs to defection as functions of ν that are necessary for the fixation probability of cooperation to be above (N d) −1 , the corresponding fixation probability of defection to be below (N d) −1 , and the former fixation probability to exceed the latter.

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Section: Case 3: σmentioning

confidence: 99%

“…where I 1 and J 1 are randomly chosen offspring produced in demes chosen at random and independently before viability selection and recolonization. The stated result is obtained by substituting these identities into (35) and then using ( 2) and (1).…”

Section: Case 3: σmentioning

confidence: 99%