Subsistence of sib altruism in different mating systems and Haldane’s arithmetic

Garay, József; Csiszár, Villő; Móri, Tamás F.

doi:10.1016/j.jtbi.2022.111330

Cited by 5 publications

(25 citation statements)

References 42 publications

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“…In other word, here we consider frequency dependent, survival game-theoretic conflicts between siblings (cf. Garay 2009;Garay and Varga, 2011) within monogamous and exogamous families (Garay et al, 2019(Garay et al, , 2023. We emphasize that the game theoretical conflict is well mixed between full siblings, but is not in the whole population.…”

Section: Introductionmentioning

confidence: 81%

“…Furthermore, our population genetics model can handle the basic ideas of the kin and the group selection theories at the same time, i.e. the genetic relatedness and the group effect on survival probability of sibling together determine the evolutionary stability in genotype centred population genetics model of familiar selection (Garay et al, 2019(Garay et al, , 2023. The speciality of familial selection is that the interactions only take place within the families, thus an open question arises: What will be the endpoint of such a selection regime when the game theoretical conflicts take place simultaneously within the family and between the members of different families, which can either belong to the same group or to different groups, too?…”

Section: Discussionmentioning

confidence: 99%

“…Now we ask when a genotype distribution is an evolutionarily stable genotype distribution (ESGD) in an arbitrarily large sexual population. Following Maynard Smith and Price (1973), we say that a homozygote is ESGD if the rare mutant gene cannot invade the resident population (Garay at al., 2019(Garay at al., , 2023. Mathematically, this means that the (relative) frequency of the resident homozygote increases from generation to generation, provided mutation is sufficiently rare.…”

Section: Evolutionary Stability Of Genotype Distributionsmentioning

confidence: 99%

“…The genotype centred population genetics models have already been used to study the evolution of altruism within the families (e.g. Cavalli-Sforza and Feldman, 1978;Garay et al, 2019Garay et al, , 2023Maynard Smith, 1980;Uyenoyama and Feldman 1980;Uyenoyama et al, 1981). We recall some results about these population genetics models, which can be considered as preliminaries of the present paper.…”

Section: Introductionmentioning

confidence: 99%

“…Firstly, the fixation probability of the altruistic behaviour depends on the genotype-phenotype mapping (Garay et al, 2019;Toro et al, 1982;Uyenoyama and Feldman, 1980). Secondly, in the presence of additive cost and benefit functions the population genetics models give the same results that Hamilton's method gives (Garay et al, 2019(Garay et al, , 2023Hamilton, 1964), but does not in the non-additive situation (Cavalli-Sforza and Feldman, 1978;Garay et al, 2019Garay et al, , 2023. All of these published models focus on the evolutionary stability of the monomorphic altruistic population.…”

Section: Introductionmentioning

confidence: 99%

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Game of full siblings in Mendelian populations

Garay¹,

Szilágyi²,

Varga

et al. 2022

Preprint

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We adapt the concept of evolutionary stability to familial selection when a game theoretic conflicts between siblings determines the survival rate of each sibling in monogamous, exogamous families in a diploid, panmictic population. Similarly to the classical evolutionary game theory, the static condition of evolutionary stability of mixed Nash equilibrium implies the local stability of the genotype dynamics, in spite of that the mating table based genotype dynamics is not a replicator dynamics. We apply our general result to the case where a matrix game determines the survival rate of siblings. In our numerical studies we consider the prisoners dilemma between siblings, when the cooperator and defector behaviour are unequally determined by a recessive-dominant allele pair at an autosomal locus. When the prisoners dilemma game is strict (cf. iterated one) and the cooperator phenotype is recessive resp. dominant, then the cooperator and defector phenotypes are the unique stable phenotypes, respectively. When the prisoners dilemma game is not strict, both phenotypes coexist, independently of the genotype-phenotype mapping. However, the frequencies of the phenotypes are different according to which phenotype is dominant.

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Section: Introductionmentioning

confidence: 81%

Section: Discussionmentioning

confidence: 99%

Section: Evolutionary Stability Of Genotype Distributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Game of full siblings in Mendelian populations

Garay¹,

Szilágyi²,

Varga

et al. 2022

Preprint

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Nonlinear social evolution and the emergence of collective action

Allen,

Khwaja,

Donahue

et al. 2024

PNAS Nexus

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Organisms from microbes to humans engage in a variety of social behaviors, which affect fitness in complex, often nonlinear ways. The question of how these behaviors evolve has consequences ranging from antibiotic resistance to human origins. However, evolution with nonlinear social interactions is challenging to model mathematically, especially in combination with spatial, group, and/or kin assortment. We derive a mathematical condition for natural selection with synergistic interactions among any number of individuals. This result applies to populations with arbitrary (but fixed) spatial or network structure, group subdivision, and/or mating patterns. In this condition, nonlinear fitness effects are ascribed to collectives, and weighted by a new measure of collective relatedness. For weak selection, this condition can be systematically evaluated by computing branch lengths of ancestral trees. We apply this condition to pairwise games between diploid relatives, and to dilemmas of collective help or harm among siblings and on spatial networks. Our work provides a rigorous basis for extending the notion of “actor”, in the study of social evolution, from individuals to collectives.

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Matrix game between full siblings in Mendelian populations

Garay,

Varga,

Csiszár

et al. 2024

Preprint

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We demonstrate that static evolutionary stability implies the stability of the corresponding interior equilibrium point in genotype dynamics, while a certain form of monotonicity ensures the global stability of a homozygote state. We apply our findings to familial selection in a diploid, panmictic population, where the survival rates of siblings within monogamous and exogamous families are determined by a matrix game, and the behavior is uniquely determined by an autosomal recessive-dominant or intermediate allele pair. We provide conditions for the existence of each homozygote. In our numerical investigations of the Prisoner's Dilemma between siblings, we distinguish two scenarios: cooperation (collaborating case) or defector-cooperator strategy pair (alternating case) that maximizes the siblings' survival rates. Based on the stability of the pure cooperator and defector states, we provide a potential classification of genotype dynamics. We find that the pure cooperator population cannot fixate in the alternating case. However, in the collaborating case, fixation is possible but not necessary, since bistability, coexistence, moreover, the monostable fixation of pure defector state can also occur due to the interplay between the phenotypic payoff function and the genotype-phenotype mapping, which collectively determine the outcome of natural selection. In donation game, the classical Hamilton’s rule implies the fixation of the cooperation in all considered genotype-phenotype mappings.

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Subsistence of sib altruism in different mating systems and Haldane’s arithmetic

Cited by 5 publications

References 42 publications

Game of full siblings in Mendelian populations

Game of full siblings in Mendelian populations

Nonlinear social evolution and the emergence of collective action

Matrix game between full siblings in Mendelian populations

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