How Life History Can Sway the Fixation Probability of Mutants

Evolutionary stability is sensitive on the conflict between reproduction and survival: proofs

Evolutionary game theory is a powerful mathematical framework to study how phenotypes evolve by natural selection. Both birth and death are key in classic models in evolutionary games. The conflict between the two is fundamental in life history theory. The conflict between birth and death has been shown to change the evolutionary outcome for continuous traits. However, it is not clear how the conflict reshapes the evolutionary outcome for discrete strategies. An allocation model is proposed, in which part of the payoff is mapped to reproduction and the rest is mapped to illness. For non-evolving allocation, it is proved that the allocation does not change the fixation probability if and only if the illness is an inverse exponential function and the product of reproduction function and illness function is a constant. The necessary and sufficient condition implies that the allocation dramatically alters the evolutionary stability for a wide class of evolutionary processes. This is also verified by alternative construction proofs and numerical examples. Furthermore, the illness and reproduction function also ensures that every allocation is a neutral stable regime, if the allocation evolves to maximize the invasion probability. A deviation can lead to a non-trivial evolutionary branching. These results explicitly show that the reproduction and illness functions are restrictive to ensure the invariance of evolutionary outcome. Thus it implies that the demographic and life history need to be considered together to understand patterns of evolutionary dynamics.

Diffusion approximation for an age-class-structured population under viability and fertility selection with application to fixation probability of an advantageous mutant

In this paper, we ascertain the validity of a diffusion approximation for the frequencies of different types under recurrent mutation and frequency-dependent viability and fertility selection in a haploid population with a fixed age-class structure in the limit of a large population size. The approximation is used to study, and explain in terms of selection coefficients, reproductive values and population-structure coefficients, the differences in the effects of viability versus fertility selection on the fixation probability of an advantageous mutant.

Which facilitates the evolution of cooperation more, retaliation or persistence?

The existence of cooperation in this world is a mysterious phenomenon. One of the mechanisms that explain the evolution of cooperation is repeated interaction. If interactions between the same individuals repeat and individuals cooperate conditionally, cooperation can evolve. A previous study pointed out that if individuals have persistence (i.e., imitate its "own" behavior in the last move), cooperation can evolve. However, retaliation and persistence are not mutually exclusive decisions, but rather a trade-off in the decision making process of individuals. Players can refer to the opponent's behavior and if the actor and the opponent opted for the different alternative in the last move, conditional cooperators have to give up either retaliation or persistence. The previous study also investigated this, and has revealed that the individual should give more importance to retaliation than to persistence. However, this study has assumed that the errors in perception are absent. In this world, errors in perception are present, and trying to imitate the opponent player can sometimes end in failure. And, it might be that imitating the focal player, which definitely ends in success, is more beneficial than trying to imitate the opponent player, which can end in failure especially when the error rate in recognition is large. Here, this paper uses evolutionarily stable strategy (ESS) analysis and analyzes the stability for reactive strategies against the invasion by unconditional defectors in the iterated prisoner's dilemma game. And our analysis reveals that even if we take errors in perception into consideration, retaliation facilitates the evolution of cooperation more than persistence unexpectedly. In addition, we analyze the stability for reactive cooperators against the invasion by a strategy other than unconditional defectors. Moreover, we also analyze the deterministic model in which unconditional cooperators, unconditional defectors, and the reactive strategy at the same time.

Unified and simple understanding for the evolution of conditional cooperators

Cooperation is a mysterious phenomenon which is observed in this world. The potential explanation is a repeated interaction. Cooperation is established if individuals meet the same opponent repeatedly and cooperate conditionally. Previous studies have analyzed the following four as characters of conditional cooperators mainly. (i) niceness (i.e., when a conditional cooperator meets an opponent in the first place, he (she) cooperates or defects), (ii) optimism (when a conditional cooperator meets an opponent in the past, but he (she) did not get access to information about the opponent's behavior in the previous round, he (she) cooperates or defects), (iii) generosity (even when a conditional cooperator knows that an opponent defected in the previous round, he (she) cooperates or defects) and (iv) retaliation (a conditional cooperator cooperates with a cooperator with a higher probability than with a defector). Previous works deal with these four characters mainly. However, these four characters basically have been regarded as distinct topics and unified understanding has not been done fully. Here we, by studying the iterated prisoner's dilemma game (in particular, additive games) and using evolutionarily stable strategy (ESS) analysis, find that when retaliation is large, the condition under which conditional cooperators are stable against the invasion by an unconditional defector is loose, while none of "niceness", "optimism", and "generosity" makes impact on the condition under which conditional cooperators are stable against an invasion by an unconditional defector. Furthermore, we show that we can understand "niceness", "optimism", and "generosity" uniformly by using one parameter indicating "cooperative", and when the conditional cooperators have large "retaliation" enough to resist an invasion by an unconditional defector, natural selection favors more "cooperative" conditional cooperators to invade the resident conditional cooperative strategy. Moreover, we show that these results are robust even when taking the existence of mistakes in behavior into consideration.