Two-Locus Epistasis With Sexually Antagonistic Selection: A Genetic Parrondo's Paradox

Reed, Floyd A.

doi:10.1534/genetics.106.069997

Cited by 58 publications

(37 citation statements)

References 32 publications

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“…In particular, despite suggestions of their potentially broad utility [15,19,44], Parrondo games have received little explicit attention in the ecology or evolutionary biology literatures. However, given the applications they have found thus far [48,49], history-dependent Parrondo games might be a novel and integrative framework for modelling a host of phenomena involving nonlinear genetic interactions.…”

Section: Discussionmentioning

confidence: 99%

Paradoxical persistence through mixed-system dynamics: towards a unified perspective of reversal behaviours in evolutionary ecology

Williams

Hastings

2011

Proc. R. Soc. B.

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Counterintuitive dynamics of various biological phenomena occur when composite system dynamics differ qualitatively from that of their component systems. Such composite systems typically arise when modelling situations with time-varying biotic or abiotic conditions, and examples range from metapopulation dynamics to population genetic models. These biological, and related physical, phenomena can often be modelled as simple financial games, wherein capital is gained and lost through gambling. Such games have been developed and used as heuristic devices to elucidate the processes at work in generating seemingly paradoxical outcomes across a spectrum of disciplines, albeit in a field-specific, ad hoc fashion. Here, we propose that studying these simple games can provide a much deeper understanding of the fundamental principles governing paradoxical behaviours in models from a diversity of topics in evolution and ecology in which fluctuating environmental effects, whether deterministic or stochastic, are an essential aspect of the phenomenon of interest. Of particular note, we find that, for a broad class of models, the ecological concept of equilibrium reactivity provides an intuitive necessary condition that must be satisfied in order for environmental variability to promote population persistence. We contend that further investigations along these lines promise to unify aspects of the study of a range of topics, bringing questions from genetics, species persistence and coexistence and the evolution of bet-hedging strategies, under a common theoretical purview.

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Section: Discussionmentioning

confidence: 99%

Paradoxical persistence through mixed-system dynamics: towards a unified perspective of reversal behaviours in evolutionary ecology

Williams

Hastings

2011

Proc. R. Soc. B.

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“…Nevertheless, differential or antagonistic selection between sexes can lead to a new class of stable internal equilibria in the diploid systems (Owen 1953;Bodmer 1965;Mandel 1971;Kidwell et al 1977;Reed 2007), and I make use of this property in the haploid models developed below. In the experiment by Chippindale and colleagues (Chippindale et al 2001), $75% of the total fitness variation in the adult stage of Drosophila melanogaster was negatively correlated between males and females, which suggests that a substantial portion of the fruit fly expressed genome is under sexually antagonistic selection.…”

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confidence: 99%

One- and Two-Locus Population Models With Differential Viability Between Sexes: Parallels Between Haploid Parental Selection and Genomic Imprinting

Yanchukov

2009

Genetics

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A model of genomic imprinting with complete inactivation of the imprinted allele is shown to be formally equivalent to the haploid model of parental selection. When single-locus dynamics are considered, an internal equilibrium is possible only if selection acts in the opposite directions in males and females. I study a two-locus version of the latter model, in which maternal and paternal effects are attributed to the single alleles at two different loci. A necessary condition for the allele frequency equilibria to remain on the linkage equilibrium surface is the multiplicative interaction between maternal and paternal fitness parameters. In this case the equilibrium dynamics are independent at both loci and results from the single-locus model apply. When fitness parameters are additive, analytic treatment was not possible but numerical simulations revealed that stable polymorphism characterized by association between loci is possible only in several special cases in which maternal and paternal fitness contributions are precisely balanced. As in the single-locus case, antagonistic selection in males and females is a necessary condition for the maintenance of polymorphism. I also show that the above two-locus results of the parental selection model are very sensitive to the inclusion of weak directional selection on the individual's own genotypes.

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“…The possible relevance of the paradox to other situations of interest in fields such as Biology, Economy and Physics has been pointed out [13][14][15][16][17][18][19][20][21][22][23][24]. Parrondo's paradox not only can be used to explain a large number of nonlinear phenomena [5], but also presents its own rich nonlinear characteristics.…”

Section: Introductionmentioning

confidence: 99%

Random Walks in the Presence of Absorbing Barriers in Parrondo's Games

et al. 2014

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Communicated by Stefania ResidoriFor a multi-agent spatial Parrondo's model that it is composed of games A and B, we use the discrete time Markov chains to derive the probability transition matrix. Then, we respectively deduce the stationary distribution for games A and B played individually and the randomized combination of game A + B. We notice that under a specific set of parameters, two absorbing states instead of a fixed stationary distribution exist in game B. However, the randomized game A + B can jump out of the absorbing states of game B and has a fixed stationary distribution because of the "agitating" role of game A. Moreover, starting at different initial states, we deduce the probabilities of absorption at the two absorbing barriers.

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Two-Locus Epistasis With Sexually Antagonistic Selection: A Genetic Parrondo's Paradox

Cited by 58 publications

References 32 publications

Paradoxical persistence through mixed-system dynamics: towards a unified perspective of reversal behaviours in evolutionary ecology

Paradoxical persistence through mixed-system dynamics: towards a unified perspective of reversal behaviours in evolutionary ecology

One- and Two-Locus Population Models With Differential Viability Between Sexes: Parallels Between Haploid Parental Selection and Genomic Imprinting

Random Walks in the Presence of Absorbing Barriers in Parrondo's Games

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