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Modern evolutionary game theory typically deals with the evolution of continuous, quantitative traits under weak selection, allowing the incorporation of rich biological detail and complicated nonlinear interactions. While these models are commonly used to find candidates for evolutionary endpoints and to approximate evolutionary trajectories, a less appreciated property is their potential to expose and clarify the causal structure of evolutionary processes. The mathematical step of differentiation breaks a nonlinear model into additive components which are more intuitive to interpret, and when combined with a proper causal hypothesis, partial derivatives in such models have a causal meaning. Such an approach has been used in the causal analysis of game-theoretical models in an informal manner. Here we formalize this approach by linking evolutionary game theory to concepts developed in causal modelling over the past century, from path coefficients to the recently proposed causal derivative. There is a direct correspondence between the causal derivative and the derivative used in evolutionary game theory. Some game theoretical models (e.g. kin selection) consist of multiple causal derivatives. Components of these derivatives correspond to components of the causal derivative, to path coefficients, and to edges on a causal graph, formally linking evolutionary game theory to causal modelling. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'. [ABSTRACT FROM AUTHOR]

The article focuses on evolutionary game theory, which provides a powerful toolkit and conceptual framework for modelling adaptation in biotic interactions. It highlights the difference between adaptation via natural selection in static, abiotic environments and in biotic environments. It also explains how game theory can be used to solve problems where the pay-off for adopting a given strategy depends on the strategies adopted by others.

Colonies of insects such as ants and honeybees are commonly viewed as 'superorganisms', with division of labour between reproductive 'germline-like' queens and males and 'somatic' workers. On this view, properties of the superorganismal colony are comparable with those of solitary organisms to such an extent that the colony itself can be viewed as a unit analogous to an organism. Thus, the concept of a superorganism can be useful as a guide to thinking about life history and allocation traits of colonies as a whole. A pattern that seems to reoccur in insects with superorganismal societies is size dimorphism between queens and males, where queens tend to be larger than males. It has been proposed that this is analogous to the phenomenon of anisogamy at the level of gametes in organisms with separate sexes; more specifically, it is suggested that this caste dimorphism may have evolved via similar selection pressures as gamete dimorphism arises in the 'gamete competition' theory for the evolution of anisogamy. In this analogy, queens are analogous to female gametes, males are analogous to male gametes, and colony survival is analogous to zygote survival in gamete competition theory. Here, we explore if this question can be taken beyond an analogy, and whether a mathematical model at the superorganism level, analogous to gamete competition at the organism level, may explain the caste dimorphism seen in superorganismal insects. We find that the central theoretical idea holds, but that there are also significant differences between the way this generalized 'propagule competition' theory operates at the levels of solitary organisms and superorganisms. In particular, we find that the theory can explain superorganismal caste dimorphism, but compared with anisogamy evolution, a central coevolutionary link is broken, making the requirements for the theory to work less stringent than those found for the evolution of anisogamy. [ABSTRACT FROM AUTHOR]

The Price equation has been entangled with social evolution theory from the start. It has been used to derive the most general versions of kin selection theory, and Price himself produced a multilevel equation that provides an alternative formulation of social evolution theory, dividing selection into components between and within groups. In this sense, the Price equation forms a basis for both kin and group selection, so often pitted against each other in the literature. Contextual analysis and the neighbour approach are prominent alternatives for analysing group selection. I discuss these four approaches to social evolution theory and their connections to the Price equation, focusing on their similarities and common mathematical structure. Despite different notations and modelling traditions, all four approaches are ultimately linked by a common set of mathematical components, revealing their underlying unity in a transparent way. The Price equation can similarly be used in the derivation of streamlined, weak selection social evolution modelling methods. These weak selection models are practical and powerful methods for constructing models in evolutionary and behavioural ecology; they can clarify the causal structure of models, and can be easily converted between the four social evolution approaches just like their regression counterparts. This article is part of the theme issue 'Fifty years of the Price equation'. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses article in the issue on the topics including the link between evolution and information theory; human cultural evolution [13], the evolution of multicellularity; and empirically oriented topics such as animal breeding.

Facultative sex combines sexual and asexual reproduction in the same individual (or clone) and allows for a large diversity of life-history patterns regarding the timing, frequency and intensity of sexual episodes. In addition, other life-history traits such as a diapause stage may become linked to sex. Here, we develop a matrix modelling framework for addressing the cost of sex in facultative sexuals, in constant, periodic and stochastically fluctuating environments. The model is parametrized using life-history data from Brachionus calyciflorus, a facultative sexual rotifer in which sex and diapause are linked. Sexual propensity was an important driver of costs in constant environments, in which high costs (always > onefold, and sometimes > twofold) indicated that asexuals should outcompete facultative sexuals. By contrast, stochastic environments with high temporal autocorrelation favoured facultative sex over obligate asex, in particular, if the penalty to fecundity in 'bad' environments was large. In such environments, obligate asexuals were constrained by their life cycle length (i.e. time from birth to last reproductive adult age class), which determined an upper limit to the number of consecutive bad periods they could tolerate. Nevertheless, when facultative asexuals with different sexual propensities competed simultaneously against each other and asex, the lowest sex propensity was the most successful in stochastic environments with positive autocorrelation. Our results suggest that a highly specific mechanism (i.e. diapause linked to sex) can alone stabilize facultative sex in these animals, and protect it from invasion of both asexual and pure sexual strategies. This article is part of the themed issue 'Weird sex: the underappreciated diversity of sexual reproduction'. [ABSTRACT FROM AUTHOR]

Isogamy is a reproductive system where all gametes are morphologically similar, especially in terms of size. Its importance goes beyond specific cases: to this day non-anisogamous systems are common outside of multicellular animals and plants, they can be found in all eukaryotic super-groups, and anisogamous organisms appear to have isogamous ancestors. Furthermore, because maleness is synonymous with the production of small gametes, an explanation for the initial origin of males and females is synonymous with understanding the transition from isogamy to anisogamy. As we show here, this transition may also be crucial for understanding why sex itself remains common even in taxa with high costs of male production (the twofold cost of sex). The transition to anisogamy implies the origin of male and female sexes, kickstarts the subsequent evolution of sex roles, and has a major impact on the costliness of sexual reproduction. Finally, we combine some of the consequences of isogamy and anisogamy in a thought experiment on the maintenance of sexual reproduction. We ask what happens if there is a less than twofold benefit to sex (not an unlikely scenario as large short-term benefits have proved difficult to find), and argue that this could lead to a situation where lineages that evolve anisogamy--and thus the highest costs of sex--end up being associated with constraints that make invasion by asexual reproduction unlikely (the 'anisogamy gateway' hypothesis). This article is part of the themed issue 'Weird sex: the underappreciated diversity of sexual reproduction'. [ABSTRACT FROM AUTHOR]

The article presents a study of the heritability of the human offspring sex ratio, based on data from the entire Swedish population born from 1932 onwards. Topics discussed include the central empirical finding of Zietsch et al. is in itself fascinating, particularly given that observed variation in the majority of studied human traits; and the heritability argument is subtle, and the principle is in fact theoretically consistent with both outcomes.

A large proportion of studies in systems science focus on processes involving a mixture of positive and negative feedbacks, which are also common themes in evolutionary ecology. Examples of negative feedback are density dependence (population regulation) and frequency-dependent selection (polymorphisms). Positive feedback, in turn, plays a role in Fisherian 'runaway' sexual selection, the evolution of cooperation, selfing and inbreeding tolerance under purging of deleterious alleles, and the evolution of sex differences in parental care. All these examples feature self-reinforcing processes where the increase in the value of a trait selects for further increases, sometimes via a coevolutionary feedback loop with another trait. Positive feedback often leads to alternative stable states (evolutionary endpoints), making the interpretation of evolutionary predictions challenging. Here, we discuss conceptual issues such as the relationship between self-reinforcing selection and disruptive selection. We also present an extension of a previous model on parental care, focusing on the relationship between the operational sex ratio and sexual selection, and the influence of this relationship on the evolution of biparental or uniparental care. [ABSTRACT FROM AUTHOR]

Social monogamy predominates in avian breeding systems, but most socially monogamous species engage in promiscuous extra-pair copulations (EPCs). The reasons behind this remain debated, and recent empirical work has uncovered patterns that do not seem to fit existing hypotheses. In particular, some results seem to contradict the inbreeding avoidance hypothesis: females can prefer extra-pair partners that are more closely related to them than their social partners, and extra-pair young can have lower fitness than within-pair young. Motivated by these studies, we show that such results can become explicable when an asymmetry in inbreeding tolerance between monogamy and polygamy is extended to species that combine both strategies within a single reproductive season. Under fairly general conditions, it can be adaptive for a female to choose an unrelated social partner, but inbreed with an extra-pair partner. Inbreeding depression is compensated for by inclusive fitness benefits, which are only fully realized in EPCs. We also show that if a female has already formed a suboptimal social bond, there are scenarios where it is beneficial to engage in EPCs with less related males, and others where EPCs with more related males increase her inclusive fitness. This has implications for detecting general relatedness or fitness trends when averaged over several species. [ABSTRACT FROM AUTHOR]

Both gamete competition and gamete limitation can generate anisogamy from ancestral isogamy, and both sperm competition (SC) and sperm limitation (SL) can increase sperm numbers. Here, we compare the marginal benefits due to these two components at any given population level of sperm production using the risk and intensity models in sperm economics. We show quite generally for the intensity model (where N males compete for each set of eggs) that however severe the degree of SL, if there is at least one competitor for fertilization (N − 1 ≥ 1), the marginal gains through SC exceed those for SL, provided that the relationship between the probability of fertilization (F) and increasing sperm numbers (x) is a concave function. In the risk model, as fertility F increases from 0 to 1.0, the threshold SC risk (the probability q that two males compete for fertilization) for SC to be the dominant force drops from 1.0 to 0. The gamete competition and gamete limitation theories for the evolution of anisogamy rely on very similar considerations: our results imply that gamete limitation could dominate only if ancestral reproduction took place in highly isolated, small spawning groups. [ABSTRACT FROM AUTHOR]