Social evolution in the shadow of asymmetrical relatedness.

The persistence of altruism and spite remains an enduring problem of social evolution. It is well known that selection for these actions depends on the structure of the population-that is, on actors' genetic relationships to recipients and to the 'neighbourhood' upon which the effects of their actions redound. Less appreciated, however, is that population structure can cause genetic asymmetries between partners whereby the relatedness (defined relative to the neighbourhood) of an individual i to a partner j will differ from the relatedness of j to i. Here, we introduce a widespread mechanism of kin recognition to a model of dispersal in subdivided populations. In so doing, we uncover three remarkable consequences of asymmetrical relatedness. First, altruism directed at phenotypically similar partners evolves more easily among migrant than native actors. Second, spite directed at dissimilar partners evolves more easily among native than migrant actors. Third, unlike migrants, natives can evolve to pay costs that far outstrip those they spitefully impose on others. We find that the frequency of natives relative to migrants amplifies the asymmetries between them. Taken together, our results reveal differentiated patterns of 'phenocentrism' that readily arise from asymmetries of relatedness.

Measures of relative fitness of social behaviors in finite structured population models.

How should we measure the relative selective advantage of different behavioral strategies? The various approaches to this question have fallen into one of the following categories: the fixation probability of a mutant allele in a wild type population, some measures of gene frequency and gene frequency change, and a formulation of the inclusive fitness effect. Countless theoretical studies have examined the relationship between these approaches, and it has generally been thought that, under standard simplifying assumptions, they yield equivalent results. Most of this theoretical work, however, has assumed homogeneity of the population interaction structure--that is, that all individuals are equivalent. We explore the question of selective advantage in a general (heterogeneous) population and show that, although appropriate measures of fixation probability and gene frequency change are equivalent, they are not, in general, equivalent to the inclusive fitness effect. The latter does not reflect effects of selection acting via mutation, which can arise on heterogeneous structures, even for low mutation. Our theoretical framework provides a transparent analysis of the different biological factors at work in the comparison of these fitness measures and suggests that their theoretical and empirical use needs to be revised and carefully grounded in a more general theory.

Local mate competition and transmission bottlenecks: a new model for understanding malaria parasite and other sex ratios.

The local mate competition model from sex ratio theory predicts female-biased sex ratios in populations that are highly subdivided during mating, and is thought to accord well with the population structure of malaria parasites. However, the selective advantage of female-biased sex ratios comes from the resulting increase in total reproductive output, an advantage the transmission biology of malaria parasite likely reduces. We develop a mathematical model to determine how bottlenecks in transmission that cause diminishing fitness returns from female production affect sex ratio evolution. We develop four variations of this model that incorporate whether or not parasite clones have the ability to detect others that occupy the same host and whether or not the number of clones affects the total mating population size. Our model indicates that transmission bottlenecks favor less female-biased sex ratios than those predicted under LMC. This effect is particularly pronounced if clones have no information about the presence of coexisting clones and the number of mating individuals per patch is fixed. The model could extend our understanding of malaria parasite sex ratios in three main ways. First, it identifies inconsistencies between the theoretical predictions and the data presented in a previous study, and proposes revised predictions that are more consistent with underlying biology of the parasite. Second, it may account for the positive association between parasite density and sex ratio observed within and between some species. Third, it predicts a relationship between mortality rates in the vector and sex ratios, which appears to be supported by the little existing data we have. While the inspiration for this model came from malaria parasites, it should apply to any system in which per capita dispersal success diminishes with increasing numbers of females in a patch.

Enhanced kin recognition through population estimation.

Kin recognition systems enable organisms to predict genetic relatedness. In so doing, they help to maximize the fitness consequences of social actions. Recognition based on phenotypic similarity-a process known as phenotype matching-is thought to depend upon information about one's own phenotype and the phenotypes of one's partners. We provide a simple model of genetic relatedness conditioned upon phenotypic information, however, that demonstrates that individuals additionally require estimates of the distributions of phenotypes and genotypes in the population. Following the results of our model, we develop an expanded concept of phenotype matching that brings relatedness judgments closer in line with relatedness as it is currently understood and provides a heuristic mechanism by which individuals can discriminate positive from negative relatives, thereby increasing opportunities for the evolution of altruism and spite. Finally, we propose ways in which organisms might acquire population estimates and identify research that supports their use in phenotype matching.

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.

Evolution of cooperation by phenotypic similarity.

The emergence of cooperation in populations of selfish individuals is a fascinating topic that has inspired much work in theoretical biology. Here, we study the evolution of cooperation in a model where individuals are characterized by phenotypic properties that are visible to others. The population is well mixed in the sense that everyone is equally likely to interact with everyone else, but the behavioral strategies can depend on distance in phenotype space. We study the interaction of cooperators and defectors. In our model, cooperators cooperate with those who are similar and defect otherwise. Defectors always defect. Individuals mutate to nearby phenotypes, which generates a random walk of the population in phenotype space. Our analysis brings together ideas from coalescence theory and evolutionary game dynamics. We obtain a precise condition for natural selection to favor cooperators over defectors. Cooperation is favored when the phenotypic mutation rate is large and the strategy mutation rate is small. In the optimal case for cooperators, in a one-dimensional phenotype space and for large population size, the critical benefit-to-cost ratio is given by b/c = 1 + 2/square root(3). We also derive the fundamental condition for any two-strategy symmetric game and consider high-dimensional phenotype spaces.

Joint evolution of multiple social traits: a kin selection analysis.

General models of the evolution of cooperation, altruism and other social behaviours have focused almost entirely on single traits, whereas it is clear that social traits commonly interact. We develop a general kin-selection framework for the evolution of social behaviours in multiple dimensions. We show that whenever there are interactions among social traits new behaviours can emerge that are not predicted by one-dimensional analyses. For example, a prohibitively costly cooperative trait can ultimately be favoured owing to initial evolution in other (cheaper) social traits that in turn change the cost-benefit ratio of the original trait. To understand these behaviours, we use a two-dimensional stability criterion that can be viewed as an extension of Hamilton's rule. Our principal example is the social dilemma posed by, first, the construction and, second, the exploitation of a shared public good. We find that, contrary to the separate one-dimensional analyses, evolutionary feedback between the two traits can cause an increase in the equilibrium level of selfish exploitation with increasing relatedness, while both social (production plus exploitation) and asocial (neither) strategies can be locally stable. Our results demonstrate the importance of emergent stability properties of multidimensional social dilemmas, as one-dimensional stability in all component dimensions can conceal multidimensional instability.

Relatedness with different interaction configurations.

In an inclusive fitness model of social behaviour, a key concept is that of the relatedness between two interactants. This is typically calculated with reference to a "focal" actor taken to be representative of all actors, but when there are different interaction configurations, relatedness must be constructed as an average over all such configurations. We provide an example of such a calculation in an island model with local reproduction but global mortality, leading to variable island size and hence variable numbers of individual interactions. We find that the analysis of this example significantly sharpens our understanding of relatedness. As an application, we obtain a version of Hamilton's rule for a tag-based model of altruism in a randomly mixed population. For large populations, the selective advantage of altruism is enhanced by low (but not too low) tag mutation rates and large numbers of tags. For moderate population sizes and moderate numbers of tags, we find a window of tag mutation rates with critical benefit/cost ratios of between 1 and 3.

Spiteful soldiers and sex ratio conflict in polyembryonic parasitoid wasps.

The existence of spiteful behaviors remains controversial. Spiteful behaviors are those that are harmful to both the actor and the recipient, and they represent one of the four fundamental types of social behavior (alongside selfishness, altruism, and mutual benefit). It has generally been assumed that the conditions required for spite to evolve are too restrictive, and so spite is unlikely to be important. This idea has been challenged in recent years, with the realization that localized competition can relax the conditions required for spite to evolve. Here we develop a theoretical model for a prime candidate for a spiteful behavior, the production of the sterile soldier caste in polyembryonic wasps. Our results show that (a) the biology of these soldiers is consistent with their main role being to mediate conflict over the sex ratio and not to defend against competitors and (b) greater conflict will occur in more outbred populations. We also show that the production of the sterile soldier caste can be classed as a spiteful behavior but that, to an extent, this is merely a semantic choice, and other interpretations such as altruism or indirect altruism are valid. However, the spite interpretation is useful in that it can lead to a more natural interpretation of relatedness and facilitate the classification of behaviors in a way that emphasizes biologically interesting differences that can be empirically tested.

Modelling information exchange in worker-queen conflict over sex allocation.

We investigate the conflict between queen and worker over sex allocation, specifically the allocation of the queen's eggs between workers and reproductives and the allocation of the reproductive eggs between male and female. In contrast to previous models, we allow workers to observe and use information about the strategy of the queen. We consider three conflict models: simultaneous (no information exchange), sequential (a one-way information exchange) and negotiated (an iterated two-way information exchange). We find that the first model produces sex ratios intermediate between the classic queen (1:1) and worker (1:3) optima. The second model, in which the worker has information about the queen's decisions, produces a different result and one that is somewhat counter-intuitive in that the sex ratios are less female-biased than for the other two models, and in fact are often male-biased. The third model predicts sex ratios intermediate between the first two models. We discuss how these findings may shed new light on observed sex allocation patterns in social insects and we suggest some experimental tests.

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.

Stability in negotiation games and the emergence of cooperation.

Consider a two-player game in which each player contributes a costly resource to the common good of the pair. For such contests, the Nash equilibrium contribution, x*, is one for which neither player can increase its pay-off by unilaterally altering its contribution from x*. We study an elaboration of this game, which allows the players to exchange x-offers back and forth in a negotiation phase until they converge to a final pair of contributions, x1 and x2. A significant feature of such negotiation games, hitherto unrecognized, is the existence of a set of neutrally stable equilibrium points in negotiation phase space. To explore the long-term evolutionary outcome of such games, we simulate populations containing various mixtures of negotiation strategies and, contrary to previous results, we often find convergence to a contribution that is more cooperative than the Nash equilibrium. Mathematical analysis suggests why this might be happening, and provides a novel and robust explanation for cooperation, that negotiation can facilitate the evolution of cooperative behaviour.

Hamilton's inclusive fitness in finite-structured populations.

Hamilton's formulation of inclusive fitness has been with us for 50 years. During the first 20 of those years attention was largely focused on the evolutionary trajectories of different behaviours, but over the past 20 years interest has been growing in the effect of population structure on the evolution of behaviour and that is our focus here. We discuss the evolutionary journey of the inclusive-fitness effect over this epoch, nurtured as it was in an essentially homogeneous environment (that of 'transitive' structures) having to adapt in different ways to meet the expectations of heterogeneous structures. We pay particular attention to the way in which the theory has managed to adapt the original constructs of relatedness and reproductive value to provide a formulation of inclusive fitness that captures a precise measure of allele-frequency change in finite-structured populations.

From inclusive fitness to fixation probability in homogeneous structured populations.

The methods of inclusive fitness provide a powerful analysis of the action of selection on social behaviour. The key component of this analysis is the concept of relatedness R. In infinite populations, a standard method of calculating relatedness coefficients is through coefficients of consanguinity using the notion of genetic identity by descent. In this paper, we show that this approach can also be made to work in finite populations and we assume here that the population has a homogeneous structure, such as an island model. We demonstrate that, under the assumption that genetic effects are small and additive, the resulting formulation of inclusive fitness is equivalent to other significant measures of selection in finite populations, including the change in average allele frequency and fixation probability. The results are illustrated for a model of the evolution of cooperation in a finite island population.

Sex allocation and dispersal in a heterogeneous two-patch environment.

We investigate the evolution of sex allocation and dispersal in a two-habitat environment using a game theoretic analysis. One habitat is of better quality than the other and increased habitat quality influences the competitive ability of offspring in a sex-specific manner. Unlike previous work, we allow incomplete mixing of the population during mating. We discuss three special cases involving the evolution of sex allocation under fixed levels of dispersal between habitats. In these special cases, stable sex-allocation behaviors can be both biased and unbiased. When sex-allocation behavior and dispersal rates co-evolve we identify two basic outcomes. First-when sex-specific differences in the consequences of spatial heterogeneity are large-we predict the evolution of biased sex-allocation behavior in both habitats, with dispersal by males in one direction and dispersal by females in the other direction. Second-when sex-specific differences are small-unbiased sex-allocation is predicted with no dispersal between habitats.

The evolutionary consequences of plasticity in host-pathogen interactions.

Interactions between individuals such as hosts and pathogens are often characterized by substantial phenotypic plasticity. Pathogens sometimes alter their exploitation strategies in response to defensive strategies adopted by their host and vice versa. Nevertheless, most game-theoretic models developed to explain the evolution of pathogen and host characteristics assume that no such plasticity occurs. Allowing for phenotypic plasticity in these models is difficult because one must focus on the evolution of pathogen and host reaction norms, and then allow for the potentially indefinite reciprocal changes in pathogen and host behaviour that occur during an infection as a result of their interacting reaction norms. Here, we begin to address these issues for a simple host-pathogen system in which the pathogen exhibits a level of virulence and the host exhibits a level of immune clearance. We find, quite generally, that plasticity promotes the evolution of higher levels of cooperation, in this case leading to reduced levels of both virulence and clearance.

A kin-selection approach to the resolution of sex-ratio conflict between mates.

We investigate an instance of conflict between mates over the sex ratio of their brood. We construct a kin-selection model for the evolution of the sex ratio assuming local resource competition (LRC) among females. We explore two basic scenarios: (a) the case where parents make simultaneous sex-ratio decisions (the simultaneous allocation model); and (b) the case where parental sex-ratio decisions occur one after the other (the sequential allocation model). In the simultaneous investment model, resolution of the conflict between mates depends on the extent to which relative paternal contribution influences the brood sex ratio. In the sequential allocation model, fathers determine primary sex-ratio through fertilization bias; then mothers modify the paternal sex-ratio decision by adjusting the level of investment of some resource that contributes to offspring survival. Under the sequential model, a compromise is always achieved; however this compromise favours one perspective or the other, depending on the extent to which maternal investment influences offspring survival.

SEX-RATIO BIAS WITH ASYMMETRIC EXCHANGE OF POLLEN BETWEEN DEMES.

In a patch of hermaphroditic plants, with a low level of pollen migration between patches, a prevailing wind creates a gradient, within the patch, in the strength of local competition among pollen for reproductive success. This leads to a sex ratio gradient, with a male (pollen) bias in downwind individuals, which can be quite strong even for large patches. The effect can be understood as follows: downwind individuals have relatively low reproductive value and respond by putting more resources into the gamete (pollen) with the best long-range (extra-patch) reproductive success.