Geoff Wild

The genetical theory of kin selection

Natural selection operates both directly, via the impact of a trait upon the individual’s own fitness, and indirectly, via the impact of the trait upon the fitness of the individual’s genetically related social partners. These effects are often framed in terms of Hamilton’s rule, rb − c > 0, which provides the central result of social‐evolution theory. However, a number of studies have questioned the generality of Hamilton’s rule, suggesting that it requires restrictive assumptions. Here, we use Fisher’s genetical paradigm to demonstrate the generality of Hamilton’s rule and to clarify links between different studies. We show that confusion has arisen owing to researchers misidentifying model parameters with the b and c terms in Hamilton’s rule, and misidentifying measures of genotypic similarity or genealogical relationship with the coefficient of genetic relatedness, r. More generally, we emphasize the need to distinguish between general kin‐selection theory that forms the foundations of social evolution, and streamlined kin‐selection methodology that is used to solve specific problems.

Evolution of cooperation in a finite homogeneous graph

Recent theoretical studies of selection in finite structured populations have worked with one of two measures of selective advantage of an allele: fixation probability and inclusive fitness. Each approach has its own analytical strengths, but given certain assumptions they provide equivalent results. In most instances the structure of the population can be specified by a network of nodes connected by edges (that is, a graph), and much of the work here has focused on a continuous-time model of evolution, first described by ref. 11. Working in this context, we provide an inclusive fitness analysis to derive a surprisingly simple analytical condition for the selective advantage of a cooperative allele in any graph for which the structure satisfies a general symmetry condition (‘bi-transitivity’). Our results hold for a broad class of population structures, including most of those analysed previously, as well as some for which a direct calculation of fixation probability has appeared intractable. Notably, under some forms of population regulation, the ability of a cooperative allele to invade is seen to be independent of the nature of population structure (and in particular of how game partnerships are specified) and is identical to that for an unstructured population. For other types of population regulation our results reveal that cooperation can invade if players choose partners along relatively ‘high-weight’ edges.

Adaptation and the evolution of parasite virulence in a connected world

Adaptation is conventionally regarded as occurring at the level of the individual organism, where it functions to maximize the individual’s inclusive fitness. However, it has recently been argued that empirical studies on the evolution of parasite virulence in spatial populations show otherwise. In particular, it has been claimed that the evolution of lower virulence in response to limited parasite dispersal provides proof of Wynne-Edwards’s idea of adaptation at the group level. Although previous theoretical work has shown that limited dispersal can favour lower virulence, it has not clarified why, with five different suggestions having been given. Here we show that the effect of dispersal on parasite virulence can be understood entirely within the framework of inclusive fitness theory. Limited parasite dispersal favours lower parasite growth rates and, hence, reduced virulence because it (1) decreases the direct benefit of producing offspring (dispersers are worth more than non-dispersers, because they can go to patches with no or fewer parasites), and (2) increases the competition for hosts experienced by both the focal individual (‘self-shading’) and their relatives (‘kin shading’). This demonstrates that reduced virulence can be understood as an individual-level adaptation by the parasite to maximize its inclusive fitness, and clarifies the links with virulence theory more generally.

Direct fitness or inclusive fitness: how shall we model kin selection?

Two standard mathematical formulations of kin‐selection models can be found. Inclusive fitness is an actor‐centred approach, which calculates the fitness effect on a number of recipients of the behaviour of a single actor. Direct fitness is a recipient‐centred approach, which calculates the fitness effect on the recipient of the behaviour of a number of actors. Inclusive fitness offers us a powerful heuristic, of choosing behaviour to maximize fitness, but direct fitness can be mathematically easier to work with and has recently emerged as the preferred approach of theoreticians. In this paper, we explore the fundamental connection between these two approaches in both homogeneous and class‐structured populations, and we show that under simple assumptions (mainly fair meiosis and weak selection) they provide equivalent formulations, which correspond to the predictions of Prices equation for allele frequency change. We use a couple of examples to highlight differences in their conception and formulation, and we briefly discuss a two‐species example in which we have a class of ‘actor’ that is never a ‘recipient’, which the standard direct fitness method can handle but the usual inclusive fitness cannot.

Fitness and evolutionary stability in game theoretic models of finite populations

We investigate two methods of measuring fitness in evolutionary games played among members of a finite population. Classical notions of stability account for the action of selection only, and use immediate reproductive gains as a measure of fitness. This classical interpretation of fitness is what we call reproductive fitness (RF), and is found in the early studies of evolutionary stability in finite populations. More recent work has incorporated the influence of random genetic drift by applying fixation probability (FP) as a measure of fitness. When defined in this way, fitness represents a measure of ultimate evolutionary success. Our main result describes an equivalence between candidate evolutionarily stable strategies under both the RF and FP interpretations of fitness. We apply this result to matrix games in which the use of mixed strategies is permitted, and find here an equivalence between the RF and FP conditions for evolutionary stability.

A Sex Allocation Theory for Vertebrates: Combining Local Resource Competition and Condition‐Dependent Allocation

Tests of sex allocation theory in vertebrates are usually based on verbal arguments. However, the operation of multiple selective forces can complicate verbal arguments, possibly making them misleading. We construct an inclusive fitness model for the evolution of condition‐dependent brood sex ratio adjustment in response to two leading explanations for sex ratio evolution in vertebrates: the effect of maternal quality on the fitness of male and female offspring (the Trivers‐Willard hypothesis [TWH]) and local resource competition (LRC) between females. We show (1) the population sex ratio can be either unbiased or biased in either direction (toward either males or females); (2) brood sex ratio adjustment can be biased in either direction, with high‐quality females biasing reproductive investment toward production of sons (as predicted by the TWH) or production of daughters (opposite to predictions of the TWH); and (3) selection can favor gradual sex ratio adjustment, with both sons and daughters being produced by both high‐ and low‐quality mothers. Despite these complications, clear a priori predictions can be made for how the population sex ratio and the conditional sex ratio adjustment of broods should vary across populations or species, and within populations, across individuals of different quality.

Genomic Imprinting and Sex Allocation

Genomic imprinting allows maternally and paternally derived alleles to have different patterns of expression (one allele is often silent). Kin selection provides an explanation of genomic imprinting because conflicts of interest can arise between paternally and maternally inherited alleles when they have different probabilities of being present in other individuals. Our aim here is to examine the extent to which conflicts between paternally and maternally inherited alleles could arise over the allocation of resources to male and female reproduction (sex allocation), for example, conflict over the offspring sex ratio. We examine the situations in which sex allocation is influenced by competitive or cooperative interactions between relatives: local resource competition, local mate competition, and local resource enhancement. We determine solutions for diploids and haplodiploids when either the mother or the offspring controls sex allocation. Our results suggest that the greatest conflict between paternally and maternally inherited alleles and therefore the strongest selection for genomic imprinting will occur in haplodiploid species where the offspring can control sex allocation, such as the social hymenoptera and the polyembryonic parasitoid wasps. Within the social hymenoptera, we expect especially strong selection for genomic imprinting in species subject to local resource competition, such as honeybees and army ants.

Promiscuity and the evolution of cooperative breeding

Empirical data suggest that low levels of promiscuity have played a key role in the evolution of cooperative breeding and eusociality. However, from a theoretical perspective, low levels of promiscuity can favour dispersal away from the natal patch, and have been argued to select against cooperation in a way that cannot be explained by inclusive fitness theory. Here, we use an inclusive fitness approach to model selection to stay and help in a simple patch-structured population, with strict density dependence, where helping increases the survival of the breeder on the patch. Our model predicts that the level of promiscuity has either no influence or a slightly positive influence on selection for helping. This prediction is driven by the fact that, in our model, staying to help leads to increased competition between relatives for the breeding position—when promiscuity is low (and relatedness is high), the best way to aid relatives is by dispersing to avoid competing with them. Furthermore, we found the same results with an individual-based simulation, showing that this is not an area where inclusive fitness theory ‘gets it wrong’. We suggest that our predicted influence of promiscuity is sensitive to biological assumptions, and that if a possibly more biologically relevant scenario were examined, where helping provided fecundity benefits and there was not strict density dependence, then low levels of promiscuity would favour helping, as has been observed empirically.

SEX RATIOS WHEN HELPERS STAY AT THE NEST

Abstract This study investigates the evolution of the sex ratio (parental investment in sons) when breeding adults are supported by help provided by non breeding individuals of one sex. The study also assumes that the helping sex remains on its natal site to compete for the opportunity to breed, whereas the nonhelping sex disperses. Two kin‐selection models are presented, both of which incorporate the age structure found in many natural populations where such helping occurs. The first model assumes that helpers increase the survival of their parents. The second model assumes that helpers are indiscriminant: a helper chooses to increase the survival of a random pair of adults breeding on its natal patch. In both models, sex ratios are not always biased toward the sex that provides the most help. When helpers do not discriminate (second model), the direction of sex‐ratio bias is determined solely by the size of the benefit of helping behavior. When this benefit is small, sex‐ratio evolution is primarily influenced by local resource competition and sex ratios are biased toward the nonhelping (dispersive) sex. If the benefit of help is large enough, the effect of local resource competition is reduced and sex‐ratio bias favors the helpful sex. When helpers help only their parents, the same qualitative relationship exists between the direction of sex‐ratio bias and the benefit of helping. In this case, however, the direction of sex‐ratio bias is also influenced by the size of the social group, mortality, and which individual (mother or father) controls the sex ratio. This study also investigates a sex‐ratio conflict that exists between mates. Helping behavior of nonbreeders can act to alleviate the disparities between the optimal sex ratio from the perspective of a mother and that from the perspective of a father. This consequence of helping has not been previously recognized.

Fixation Probabilities When Generation Times Are Variable: The Burst–Death Model

Estimating the fixation probability of a beneficial mutation has a rich history in theoretical population genetics. Typically, to attain mathematical tractability, we assume that generation times are fixed, while the number of offspring per individual is stochastic. However, fixation probabilities are extremely sensitive to these assumptions regarding life history. In this article, we compute the fixation probability for a “burst–death” life-history model. The model assumes that generation times are exponentially distributed, but the number of offspring per individual is constant. We estimate the fixation probability for populations of constant size and for populations that grow exponentially between periodic population bottlenecks. We find that the fixation probability is, in general, substantially lower in the burst–death model than in classical models. We also note striking qualitative differences between the fates of beneficial mutations that increase burst size and mutations that increase the burst rate. In particular, once the burst size is sufficiently large relative to the wild type, the burst–death model predicts that fixation probability depends only on burst rate.