A geometric approach to the evolution of altruism.

Fisher's geometric model provides a powerful tool for making predictions about key properties of Darwinian adaptation. Here, I apply the geometric model to predict differences between the evolution of altruistic versus nonsocial phenotypes. I recover Kimura's prediction that probability of fixation is greater for mutations of intermediate size, but I find that the effect size that maximises probability of fixation is relatively small in the context of altruism and relatively large in the context of nonsocial phenotypes, and that the overall probability of fixation is lower for altruism and is higher for nonsocial phenotypes. Accordingly, the first selective substitution is expected to be smaller, and to take longer, in the context of the evolution of altruism. These results strengthen the justification for employing streamlined social evolutionary methodologies that assume adaptations are underpinned by many genes of small effect.

Transmission of social status drives cooperation and offspring philopatry.

The evolution of cooperation depends on two crucial overarching factors: relatedness, which describes the extent to which the recipient shares genes in common with the actor; and quality, which describes the recipient's basic capacity to transmit genes into the future. While most research has focused on relatedness, there is a growing interest in understanding how quality modulates the evolution of cooperation. However, the impact of inheritance of quality on the evolution of cooperation remains largely unexplored, especially in spatially structured populations. Here, we develop a mathematical model to understand how inheritance of quality, in the form of social status, influences the evolution of helping and harming within social groups in a viscous-population setting. We find that: (1) status-reversal transmission, whereby parental and offspring status are negatively correlated, strongly inhibits the evolution of cooperation, with low-status individuals investing less in cooperation and high-status individuals being more prone to harm; (2) transmission of high status promotes offspring philopatry, with more cooperation being directed towards the higher-dispersal social class; and (3) fertility inequality and inter-generational status inheritance reduce within-group conflict. Overall, our study highlights the importance of considering different mechanisms of phenotypic inheritance, including social support, and their potential interactions in shaping animal societies.

Sexual antagonism in sequential hermaphrodites.

Females and males may have distinct phenotypic optima, but share essentially the same complement of genes, potentially leading to trade-offs between attaining high fitness through female versus male reproductive success. Such sexual antagonism may be particularly acute in hermaphrodites, where both reproductive strategies are housed within a single individual. While previous models have focused on simultaneous hermaphroditism, we lack theory for how sexual antagonism may play out under sequential hermaphroditism, which has the additional complexities of age-structure. Here, we develop a formal theory of sexual antagonism in sequential hermaphrodites. First, we construct a general theoretical overview of the problem, then consider different types of sexually antagonistic and life-history trade-offs, under different modes of genetic inheritance (autosomal or cytoplasmic), and different forms of sequential hermaphroditism (protogynous, protoandrous or bidirectional). Finally, we provide a concrete illustration of these general patterns by developing a two-stage two-sex model, which yields conditions for both invasion of sexually antagonistic alleles and maintenance of sexually antagonistic polymorphisms.

Kin selection of time travel: the social evolutionary causes and consequences of dormancy.

A basic mechanism of kin selection is limited dispersal, whereby individuals remain close to their place of origin such that even indiscriminate social interaction tends to modify the fitness of genealogical kin. Accordingly, the causes and consequences of dispersal have received an enormous amount of attention in the social evolution literature. This work has focused on dispersal of individuals in space, yet similar logic should apply to dispersal of individuals in time (e.g. dormancy). We investigate how kin selection drives the evolution of dormancy and how dormancy modulates the evolution of altruism. We recover dormancy analogues of key results that have previously been given for dispersal, showing that: (1) kin selection favours dormancy as a means of relaxing competition between relatives; (2) when individuals may adjust their dormancy behaviour to local density, they are favoured to do so, resulting in greater dormancy in high-density neighbourhoods and a concomitant 'constant non-dormant principle'; (3) when dormancy is constrained to be independent of density, there is no relationship between the rate of dormancy and the evolutionary potential for altruism; and (4) when dormancy is able to evolve in a density-dependent manner, a greater potential for altruism is expected in populations with lower dormancy.

W. D. Hamilton and the golden sex ratio.

In his famous two-part paper, published in Journal of Theoretical Biology in 1964, W. D. Hamilton predicted that natural selection acting in male-haploid populations favours a ratio of males to females that is in accordance with the golden ratio. This prediction has found its way into the pages of one of the best-selling books of all time, Dan Brown's 2003 novel The da Vinci Code, and is therefore in the running for the most widely known quantitative result in the history of evolutionary biology. Unfortunately, this golden-ratio result is wrong, and was later corrected by Hamilton, who showed that natural selection actually favours an unbiased sex ratio in this setting. But it has been unclear exactly how Hamilton arrived at the golden-ratio result in the first place. Here I show that the solution to this puzzle is found in unpublished work held in the British Library's W. D. Hamilton Archive. Specifically, in addition to employing a faulty method for calculating relatedness, Hamilton had also employed a faulty method for calculating reproductive value, considering only genetic contributions to the next generation rather than to the distant future. Repeating both mistakes recovers his erroneous golden-ratio result.

A simulation test of the prediction that density-dependent dispersal promotes female-biased sex allocation in viscous populations.

A classic result of sex-allocation theory is that the sex ratio is predicted to be invariant with respect to the rate of dispersal. However, a recent mathematical analysis has suggested that if individuals are able to adjust their probability of dispersal according to the local density of their neighbourhood, then a lower rate of dispersal will be associated with greater female-bias. Here, we perform a computer simulation test of this prediction. Our simulation data provide strong qualitative support for the prediction, and a Monte Carlo randomization test of significance allows us to reject the null hypothesis of the invariance relationship.

The rarer-sex effect.

The study of sex allocation-that is, the investment of resources into male versus female reproductive effort-yields among the best quantitative evidence for Darwinian adaptation, and has long enjoyed a tight and productive interplay of theoretical and empirical research. The fitness consequences of an individual's sex allocation decisions depend crucially upon the sex allocation behaviour of others and, accordingly, sex allocation is readily conceptualized in terms of an evolutionary game. Here, I investigate the historical development of understanding of a fundamental driver of the evolution of sex allocation-the rarer-sex effect-from its inception in the writing of Charles Darwin in 1871 through to its explicit framing in terms of consanguinity and reproductive value by William D. Hamilton in 1972. I show that step-wise development of theory proceeded through refinements in the conceptualization of the strategy set, the payoff function and the unbeatable strategy. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

The geometry of evolutionary conflict.

Conflicts of interest abound not only in human affairs but also in the biological realm. Evolutionary conflict occurs over multiple scales of biological organization, from genetic outlawry within genomes, to sibling rivalry within nuclear families, to collective-action disputes within societies. However, achieving a general understanding of the dynamics and consequences of evolutionary conflict remains an outstanding challenge. Here, we show that a development of R. A. Fisher's classic 'geometric model' of adaptation yields novel and surprising insights into the dynamics of evolutionary conflict and resulting maladaptation, including the discoveries that: (i) conflict can drive evolving traits arbitrarily far away from all parties' optima and, indeed, if all mutations are equally likely then contested traits are more often than not driven outwith the zone of actual conflict (hyper-maladaptation); (ii) evolutionary conflicts drive persistent maladaptation of orthogonal, non-contested traits (para-maladaptation); and (iii) modular design greatly ameliorates conflict-driven maladaptation, thereby facilitating major transitions in individuality.

Density-dependent dispersal promotes female-biased sex allocation in viscous populations.

A surprising result emerging from the theory of sex allocation is that the optimal sex ratio is predicted to be completely independent of the rate of dispersal. This striking invariance result has stimulated a huge amount of theoretical and empirical attention in the social evolution literature. However, this sex-allocation invariant has been derived under the assumption that an individual's dispersal behaviour is not modulated by population density. Here, we investigate how density-dependent dispersal shapes patterns of sex allocation in a viscous-population setting. Specifically, we find that if individuals are able to adjust their dispersal behaviour according to local population density, then they are favoured to do so, and this drives the evolution of female-biased sex allocation. This result obtains because, whereas under density-independent dispersal, population viscosity is associated not only with higher relatedness-which promotes female bias-but also with higher kin competition-which inhibits female bias-under density-dependent dispersal, the kin-competition consequences of a female-biased sex ratio are entirely abolished. We derive analytical results for the full range of group sizes and costs of dispersal, under haploid, diploid and haplodiploid modes of inheritance. These results show that population viscosity promotes female-biased sex ratios in the context of density-dependent dispersal.

Paternal genome elimination promotes altruism in viscous populations.

Population viscosity has long been thought to promote the evolution of altruism. However, in the simplest scenarios, the potential for altruism is invariant with respect to dispersal-a surprising result that holds for haploidy, diploidy, and haplodiploidy (arrhenotoky). Here, we develop a kin-selection model to investigate how population viscosity affects the potential for altruism in species with male paternal genome elimination (PGE), exploring altruism enacted by both females and males, and both juveniles and adults. We find that (1) PGE promotes altruistic behaviors relative to the other inheritance systems, and to a degree that depends on the extent of paternal genome expression. (2) Under PGE, dispersal increases the potential for altruism in juveniles and decreases it in adults. (3) The genetics of PGE can lead to striking differences in sex-specific potentials for altruism, even in the absence of any sex differences in ecology.

Population viscosity promotes altruism under density-dependent dispersal.

A basic mechanism of kin selection is population viscosity, whereby individuals do not move far from their place of birth and hence tend to be surrounded by relatives. In such circumstances, even indiscriminate altruism among neighbours will often involve interactions between kin, which has a promoting effect on the evolution of altruism. This has the potential to explain altruistic behaviour across the whole tree of life, including in taxa for which recognition of kin is implausible. However, population viscosity may also intensify resource competition among kin, which has an inhibitory effect on altruism. Indeed, in the simplest scenario, in which individuals disperse with a fixed probability, these two effects have been shown to exactly cancel such that there is no net impact of viscosity on altruism. Here, we show that if individuals are able to disperse conditionally upon local density, they are favoured to do so, with more altruistic neighbourhoods exhibiting a higher rate of dispersal and concomitant relaxation of kin competition. Comparing across different populations or species, this leads to a negative correlation between overall levels of dispersal and altruism. We demonstrate both analytically and using individual-based simulations that population viscosity promotes the evolution of altruism under density-dependent dispersal.

Sexual antagonism in haplodiploids.

Females and males may face different selection pressures, such that alleles conferring a benefit in one sex may be deleterious in the other. Such sexual antagonism has received a great deal of theoretical and empirical attention, almost all of which has focused on diploids. However, a sizeable minority of animals display an alternative haplodiploid mode of inheritance, encompassing both arrhenotoky, whereby males develop from unfertilized eggs, and paternal genome elimination (PGE), whereby males receive but do not transmit a paternal genome. Alongside unusual genetics, haplodiploids often exhibit social ecologies that modulate the relative value of females and males. Here, we develop a series of evolutionary-genetic models of sexual antagonism for haplodiploids, incorporating details of their molecular biology and social ecology. We find that: (1) PGE promotes female-beneficial alleles more than arrhenotoky, and to an extent determined by the timing of elimination-and degree of silencing of-the paternal genome; (2) sib-mating relatively promotes female-beneficial alleles, as do other forms of inbreeding including limited male-dispersal, oedipal-mating, and the pseudo-hermaphroditism of Icerya purchasi; (3) resource competition between related females inhibits the invasion of female-beneficial alleles; and (4) sexual antagonism foments conflicts between parents and offspring, endosymbionts and hosts, and maternal- and paternal-origin genes.

Reproductive value and the evolution of altruism.

Altruism is favored by natural selection provided that it delivers sufficient benefits to relatives. An altruist's valuation of her relatives depends upon the extent to which they carry copies of her genes - relatedness - and also on the extent to which they are able to transmit their own genes to future generations - reproductive value. However, although relatedness has received a great deal of attention with regard to altruism, reproductive value has been surprisingly neglected. We review how reproductive value modulates patterns of altruism in relation to individual differences in age, sex, and general condition, and discuss how social partners may manipulate each other's reproductive value to incentivize altruism. This topic presents opportunities for tight interplay between theoretical and empirical research.

Sex-biased demography modulates male harm across the genome.

Recent years have seen an explosion of theoretical and empirical interest in the role that kin selection plays in shaping patterns of sexual conflict, with a particular focus on male harming traits. However, this work has focused solely on autosomal genes, and as such it remains unclear how demography modulates the evolution of male harm loci occurring in other portions of the genome, such as sex chromosomes and cytoplasmic elements. To investigate this, we extend existing models of sexual conflict for application to these different modes of inheritance. We first analyse the general case, revealing how sex-specific relatedness, reproductive value and the intensity of local competition combine to determine the potential for male harm. We then analyse a series of demographically explicit models, to assess how dispersal, overlapping generations, reproductive skew and the mechanism of population regulation affect sexual conflict across the genome, and drive conflict between nuclear and cytoplasmic genes. We then explore the effects of sex biases in these demographic parameters, showing how they may drive further conflicts between autosomes and sex chromosomes. Finally, we outline how different crossing schemes may be used to identify signatures of these intragenomic conflicts.

Sex, males, and hermaphrodites in the scale insect Icerya purchasi.

Androdioecy (the coexistence of males and hermaphrodites) is a rare mating system for which the evolutionary dynamics are poorly understood. Here, we investigate the cottony cushion scale, Icerya purchasi, one of only three reported cases of androdioecy in insects. In this species, female-like hermaphrodites have been shown to produce sperm and self-fertilize. However, males are ocassionally observed as well. In a large genetic analysis, we show for the first time that, although self-fertilization appears to be the primary mode of reproduction, rare outbreeding events do occur in natural populations, supporting the hypothesis that hermaphrodites mate with males and hence androdioecy is the mating system of I. purchasi. Thus, this globally invasive pest insect appears to enjoy the colonization advantages of a selfing organism while also benefitting from periodic reintroduction of genetic variation through outbreeding with males.

Adjustment of sex allocation to co-foundress number and kinship under local mate competition: An inclusive-fitness analysis.

Hamilton's theory of local mate competition (LMC) describes how competition between male relatives for mating opportunities favours a female-biased parental investment. LMC theory has been extended in many ways to explore a range of genetic and life-history influences on sex allocation strategies, including showing that increasing genetic homogeneity within mating groups should favour greater female bias. However, there has been no quantitative theoretical prediction as to how females should facultatively adjust their sex allocation in response to co-foundress number and kinship. This shortfall has been highlighted recently by the finding that sex ratios produced by sub-social parasitoid wasps in the family Bethylidae are affected by the number of co-foundresses and by whether these are sisters or unrelated females. Here we close this gap in LMC theory by taking an inclusive-fitness approach to derive explicit theoretical predictions for this scenario. We find that, in line with the recent empirical results, females should adopt a more female-biased sex allocation when their co-foundresses are less numerous and are their sisters. Our model appears to predict somewhat more female bias than is observed empirically; we discuss a number of possible model extensions that would improve realism and that would be expected to result in a closer quantitative fit with experimental data.

A gene's-eye view of sexual antagonism.

Females and males may face different selection pressures. Accordingly, alleles that confer a benefit for one sex often incur a cost for the other. Classic evolutionary theory holds that the X chromosome, whose sex-biased transmission sees it spending more time in females, should value females more than males, whereas autosomes, whose transmission is unbiased, should value both sexes equally. However, recent mathematical and empirical studies indicate that male-beneficial alleles may be more favoured by the X chromosome than by autosomes. Here we develop a gene's-eye-view approach that reconciles the classic view with these recent discordant results, by separating a gene's valuation of female versus male fitness from its ability to induce fitness effects in either sex. We use this framework to generate new comparative predictions for sexually antagonistic evolution in relation to dosage compensation, sex-specific mortality and assortative mating, revealing how molecular mechanisms, ecology and demography drive variation in masculinization versus feminization across the genome.

Kin discrimination and demography modulate patterns of sexual conflict.

Recent years have seen an explosion of interest in the overlap between kin selection and sexual selection, particularly concerning how kin selection can put the brakes on harmful sexual conflict. However, there remains a significant disconnect between theory and empirical research. Whilst empirical work has focused on kin-discriminating behaviour, theoretical models have assumed indiscriminating behaviour. Additionally, theoretical work makes particular demographic assumptions that constrain the relationship between genetic relatedness and the scale of competition, and it is not clear that these assumptions reflect the natural setting in which sexual conflict has been empirically studied. Here, we plug this gap between current theoretical and empirical understanding by developing a mathematical model of sexual conflict that incorporates kin discrimination and different patterns of dispersal. We find that kin discrimination and group dispersal inhibit harmful male behaviours at an individual level, but kin discrimination intensifies sexual conflict at the population level.

Resource heterogeneity and the evolution of public goods cooperation.

Heterogeneity in resources is a ubiquitous feature of natural landscapes affecting many aspects of biology. However, the effect of environmental heterogeneity on the evolution of cooperation has been less well studied. Here, using a mixture of theory and experiments measuring siderophore production by the bacterium Pseudomonas aeruginosa as a model for public goods based cooperation, we explore the effect of heterogeneity in resource availability. We show that cooperation in metapopulations that were spatially heterogeneous in terms of resources can be maintained at a higher level than in homogeneous metapopulations of the same average resource value. The results can be explained by a positive covariance between fitness of cooperators, population size, and local resource availability, which allowed cooperators to have a disproportionate advantage within the heterogeneous metapopulations. These results suggest that natural environmental variation may help to maintain cooperation.

Does kin discrimination promote cooperation?

Genetic relatedness is a key driver of the evolution of cooperation. One mechanism that may ensure social partners are genetically related is kin discrimination, in which individuals are able to distinguish kin from non-kin and adjust their behaviour accordingly. However, the impact of kin discrimination upon the overall level of cooperation remains obscure. Specifically, while kin discrimination allows an individual to help more-related social partners over less-related social partners, it is unclear whether and how the population average level of cooperation that is evolutionarily favoured should differ under kin discrimination versus indiscriminate social behaviour. Here, we perform a general mathematical analysis in order to assess whether, when and in which direction kin discrimination changes the average level of cooperation in an evolving population. We find that kin discrimination may increase, decrease or leave unchanged the average level of cooperation, depending upon whether the optimal level of cooperation is a convex, concave or linear function of genetic relatedness. We develop an extension of the classic 'tragedy of the commons' model of cooperation in order to provide an illustration of these results. Our analysis provides a method to guide future research on the evolutionary consequences of kin discrimination.