The impact of random frequency-dependent mutations on the average population fitness

Huang, Weini; Werner, Benjamin; Traulsen, Arne

doi:10.1186/1471-2148-12-160

Cited by 13 publications

(12 citation statements)

References 39 publications

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“…In this paper we have shown that a heuristic approach, based on the assumption of the existence of a scaling factor, can provide a way to make analytic conclusions without specifying any precise form for the distribution of mutations. Interestingly, a similar observation has been made for a game theoretic model of the evolution of average population fitness [45], although the analytic form of the observed scaling function was distinct. An important avenue for further investigations will be to determine if this approach can be used to as a general method for addressing problems involving stochastic mutation events.…”

Section: Discussionsupporting

confidence: 72%

Fitness differences suppress the number of mating types in evolving isogamous species

2020

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Sexual reproduction is not always synonymous with the existence of two morphologically different sexes; isogamous species produce sex cells of equal size, typically falling into multiple distinct self-incompatible classes, termed mating types. A long-standing open question in evolutionary biology is: what governs the number of these mating types across species? Simple theoretical arguments imply an advantage to rare types, suggesting the number of types should grow consistently, however, empirical observations are very different. While some isogamous species exhibit thousands of mating types, such species are exceedingly rare, and most have fewer than ten. In this paper, we present a mathematical analysis to quantify the role of fitness variation -characterised by different mortality rates -in determining the number mating types emerging in simple evolutionary models. We predict that the number of mating types decreases as the variance of mortality increases. the sexes. However unlike true sexes, the number of mating types is not restricted to two; D. discoideum has three mating types [5].A natural question that then arises is what drives the evolution of the number or mating types? Within anisogamous species, a series of trade-offs (it is difficult to produce gametes that are both small and well-provisioned or large and numerous) restrict the number of morphological types to two [6]. In contrast, isogamous species, in which such trade-offs are absent, do not face such a restriction. In fact, simple evolutionary reasoning suggests that a population with two mating types should be a very unstable configuration.To explain this idea, let us discuss the following scenario: An isogamous population with two distinct self-incompatible mating types A and B of equal frequencies. Assuming massaction encounter rates, individuals of each type have a 50% chance of locating an individual of the opposite complementary type within the population. Now a mutation occurs, leading to a novel self-incompatible mating type C. An individual of this rare type C is now able to mate with all individuals of type A and B (a large proportion of the population) and thus is selected for, until the population reaches a new equilibrium in which all three types have equal frequencies. This "rare sex advantage" to novel isogamous mating types leads to the prediction that their number should consistently grow [7]. In a very extreme case, we might imagine as many distinct mating types as there are individuals in the population.By the above theoretical argument, one might predict that D. discoideum, with its three mating types, should be an evolutionary outlier, restricting its opportunities for sexual reproduction to a mere two thirds of the population. In fact, the empirical data paints rather the opposite picture. The majority of isogamous species (including the yeast Saccharomyces cerevisiae [8], the ciliate Blepharisma japonicum [9] and the green algae Chlamydomonas reinhardtii [10]) have two mating types [11]. A smaller variety of species have ...

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Section: Discussionsupporting

confidence: 72%

Fitness differences suppress the number of mating types in evolving isogamous species

2020

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“…In order to determine how frequent such rank changes occur or how generic these games are, we analyze changes in the ranking of strategies in random games [36] – [39] . In particular, we compute the probability that rank changes occur and determine the number of changes in the rank of strategies, see Figure 3 .…”

Section: Resultsmentioning

confidence: 99%

“…Naturally this also holds for games with more strategies. To determine the probability and numbers of such rank changes in random games [36] – [39] , we generalize the numerical procedure described above.…”

Section: Resultsmentioning

confidence: 99%

Extrapolating Weak Selection in Evolutionary Games

et al. 2013

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In evolutionary games, reproductive success is determined by payoffs. Weak selection means that even large differences in game outcomes translate into small fitness differences. Many results have been derived using weak selection approximations, in which perturbation analysis facilitates the derivation of analytical results. Here, we ask whether results derived under weak selection are also qualitatively valid for intermediate and strong selection. By “qualitatively valid” we mean that the ranking of strategies induced by an evolutionary process does not change when the intensity of selection increases. For two-strategy games, we show that the ranking obtained under weak selection cannot be carried over to higher selection intensity if the number of players exceeds two. For games with three (or more) strategies, previous examples for multiplayer games have shown that the ranking of strategies can change with the intensity of selection. In particular, rank changes imply that the most abundant strategy at one intensity of selection can become the least abundant for another. We show that this applies already to pairwise interactions for a broad class of evolutionary processes. Even when both weak and strong selection limits lead to consistent predictions, rank changes can occur for intermediate intensities of selection. To analyze how common such games are, we show numerically that for randomly drawn two-player games with three or more strategies, rank changes frequently occur and their likelihood increases rapidly with the number of strategies . In particular, rank changes are almost certain for , which jeopardizes the predictive power of results derived for weak selection.

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“…We define the fitness of a strategy S as f S = exp[wπ S ] [29]. We follow the usual assumption that mutations only switch between the pre-existing strategies but do not generate an entirely novel strategy; for such a model we refer to [30][31][32]. The non-negative parameter w measures the intensity of selection [33].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Properties of Evolutionary Multi-player Games in Finite Populations

Traulsen

Gokhale

2013

Games

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William D. Hamilton famously stated that "human life is a many person game and not just a disjoined collection of two person games". However, most of the theoretical results in evolutionary game theory have been developed for two player games. In spite of a multitude of examples ranging from humans to bacteria, multi-player games have received less attention than pairwise games due to their inherent complexity. Such complexities arise from the fact that group interactions cannot always be considered as a sum of multiple pairwise interactions. Mathematically, multi-player games provide a natural way to introduce non-linear, polynomial fitness functions into evolutionary game theory, whereas pairwise games lead to linear fitness functions. Similarly, studying finite populations is a natural way of introducing intrinsic stochasticity into population dynamics. While these topics have been dealt with individually, few have addressed the combination of finite populations and multi-player games so far. We are investigating the dynamical properties of evolutionary multi-player games in finite populations. Properties of the fixation probability and fixation time, which are relevant for rare mutations, are addressed in well mixed populations. For more frequent mutations, the average abundance is investigated in well mixed as well as in structured populations. While the fixation properties are generalizations of the results from two player scenarios, addressing the average abundance in multi-player games gives rise to novel outcomes not possible in pairwise games.

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The impact of random frequency-dependent mutations on the average population fitness

Cited by 13 publications

References 39 publications

Fitness differences suppress the number of mating types in evolving isogamous species

Fitness differences suppress the number of mating types in evolving isogamous species

Extrapolating Weak Selection in Evolutionary Games

Dynamic Properties of Evolutionary Multi-player Games in Finite Populations

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