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.     

Kin selection under blending inheritance

Why did Darwin fail to develop his insights on kin selection into a proper theory of social adaptation? One suggestion has been that his inadequate understanding of heredity kept the problem out of focus. Here, I determine whether it is possible to develop a quantitative theory of kin selection upon the assumption of blending inheritance. I find that, whilst Hamilton's rule of kin selection can be readily derived under the assumption of blending inheritance, this mechanism complicates the computation of relatedness coefficients, and can even cause them to fluctuate over generations. Nevertheless, I show that the ultimate criterion for selection to favour any social trait - i.e. a time-average of Hamilton's rule - remains the same as under particulate inheritance. By eliminating the gene from the theory of kin selection, I clarify the role that it plays in the theory of social adaptation.     

Hamilton's missing link

Hamilton's famous rule was presented in 1964 in a paper called "The genetical theory of social behaviour (I and II)", Journal of Theoretical Biology 7, 1-16, 17-32. The paper contains a mathematical genetical model from which the rule supposedly follows, but it does not provide a link between the paper's central result, which states that selection dynamics take the population to a state where mean inclusive fitness is maximized, and the rule, which states that selection will lead to maximization of individual inclusive fitness. This note provides a condition under which Hamilton's rule does follow from his central result.     

Kin Selection in Primate Groups

Altruism poses a problem for evolutionary biologists because natural selection is not expected to favor behaviors that are beneficial to recipients, but costly to actors. The theory of kin selection, first articulated by Hamilton (1964), provides a solution to the problem. Hamilton's well-known rule (br > c) provides a simple algorithm for the evolution of altruism via kin selection. Because kin recognition is a crucial requirement of kin selection, it is important to know whether and how primates can recognize their relatives. While conventional wisdom has been that primates can recognize maternal kin, but not paternal kin, this view is being challenged by new findings. The ability to recognize kin implies that kin selection may shape altruistic behavior in primate groups. I focus on two cases in which kin selection is tightly woven into the fabric of social life. For female baboons, macaques, and vervets maternal kinship is an important axis of social networks, coalitionary activity, and dominance relationships. Detailed studies of the patterning of altruistic interactions within these species illustrate the extent and limits of nepotism in their social lives. Carefully integrated analyses of behavior, demography, and genetics among red howlers provide an independent example of how kin selection shapes social organization and behavior. In red howlers, kin bonds shape the life histories and reproductive performance of both males and female. The two cases demonstrate that kin selection can be a powerful source of altruistic activity within primate groups. However, to fully assess the role of kin selection in primate groups, we need more information about the effects of kinship on the patterning of behavior across the Primates and accurate information about paternal kin relationships.     

Kin selection and frequency dependence: a game theoretic approach

Game theory models show that the evolution of interactions between relatives is determined by two kinds of fitness effects: Hamilton's inclusive fitness effect, and a frequency-dependent synergistic effect. The latter arises when an individual's behaviour has different effects on the fitness of interactants, depending on whether or not they perform the same behaviour. Knowing the sign of the synergistic effect is sufficient to understand most of the qualitative features of genetic models that show departures from Hamilton's rule. Since this synergistic effect does not depend on the interactants being related, it is best viewed as something distinct from kin selection. In this view, Hamilton's rule is basically correct for describing kin selection, and most deviations from it are due to the distinct process of synergistic selection.     

Hamilton goes empirical: estimation of inclusive fitness from life-history data

Hamilton's theory of kin selection is one of the most important advances in evolutionary biology since Darwin. Central to the kin-selection theory is the concept of inclusive fitness. However, despite the importance of inclusive fitness in evolutionary theory, empirical estimation of inclusive fitness has remained an elusive task. Using the concept of individual fitness, I present a method for estimating inclusive fitness and its components for diploid organisms with age-structured life histories. The method presented here: (i) allows empirical estimation of inclusive fitness from life-history data; (ii) simultaneously considers all components of fitness, including timing and magnitude of reproduction; (iii) is consistent with Hamilton's definition of inclusive fitness; and (iv) adequately addresses shortcomings of existing methods of estimating inclusive fitness. I also demonstrate the application of this new method for testing Hamilton's rule.     

Kin selection-mutation balance: a model for the origin, maintenance, and consequences of social cheating

Social conflict, in the form of intraspecific selfish "cheating," has been observed in a number of natural systems. However, a formal, evolutionary genetic theory of social cheating that provides an explanatory, predictive framework for these observations is lacking. Here we derive the kin selection-mutation balance, which provides an evolutionary null hypothesis for the statics and dynamics of cheating. When social interactions have linear fitness effects and Hamilton's rule is satisfied, selection is never strong enough to eliminate recurrent cheater mutants from a population, but cheater lineages are transient and do not invade. Instead, cheating lineages are eliminated by kin selection but are constantly reintroduced by mutation, maintaining a stable equilibrium frequency of cheaters. The presence of cheaters at equilibrium creates a "cheater load" that selects for mechanisms of cheater control, such as policing. We find that increasing relatedness reduces the cheater load more efficiently than does policing the costs and benefits of cooperation. Our results provide new insight into the effects of genetic systems, mating systems, ecology, and patterns of sex-limited expression on social evolution. We offer an explanation for the widespread cheater/altruist polymorphism found in nature and suggest that the common fear of conflict-induced social collapse is unwarranted.     

Sociobiology and the structural stability of behavior patterns

A structural stability approach to population-genetic systems and to dynamic evolutionary games is attempted in order to examine the theoretical significance of sociobiological selection models. A criterion of weak selection is derived that is not restricted to differential reproduction in polymorphic systems but describes possible directions of evolutionary change in time scales governed by genetic mutation rates. The criterion applies to the problems of how the initial mutational basis of an adaptive trait may be established and how this may happen, for analogous traits, independently in different species. Two basic sociobiological concepts are reconsidered with reference to the criterion. It is shown that W. D. Hamilton's condition of increases in inclusive fitness due to altruistic interactions among kin expresses the structural instability of populations against the evolution of altruistic behavior. Using the dynamic approach to evolutionary game theory, it is demonstrated that if a behavioral phenotype is an evolutionarily stable strategy, it is structurally stable against perturbations of the fitness payoffs, provided selection is weak. These results are applied to material problems of the evolution of animal social behavior.     

Group selection and kin selection: formally equivalent approaches

Inclusive fitness theory, summarised in Hamilton's rule, is a dominant explanation for the evolution of social behaviour. A parallel thread of evolutionary theory holds that selection between groups is also a candidate explanation for social evolution. The mathematical equivalence of these two approaches has long been known. Several recent papers, however, have objected that inclusive fitness theory is unable to deal with strong selection or with non-additive fitness effects, and concluded that the group selection framework is more general, or even that the two are not equivalent after all. Yet, these same problems have already been identified and resolved in the literature. Here, I survey these contemporary objections, and examine them in the light of current understanding of inclusive fitness theory.     

Effects of information and group structure on evolution of altruism: analysis of two-score model by covariance and contextual analyses

An altruistic individual has to gamble on cooperation to a stranger because it does not know whether the stranger is trustworthy before direct interaction. Nowak and Sigmund (Nature 393 (1998a) 573; J. Theor. Biol. 194 (1998b) 561) presented a new theoretical framework of indirect reciprocal altruism by image scoring game where all individuals are informed about a partner's behavior from its image score without direct interaction. Interestingly, in a simplified version of the image scoring game, the evolutionarily stability condition for altruism became a similar form of Hamilton's rule, i.e. inequality that the probability of getting correct information is more than the ratio of cost to benefit. Since the Hamilton's rule was derived by evolutionarily stable analysis, the evolutionary meaning of the probability of getting correct information has not been clearly examined in terms of kin and group selection. In this study, we applied covariance analysis to the two-score model for deriving the Hamilton's rule. We confirmed that the probability of getting correct information was proportional to the bias of altruistic interactions caused by using information about a partner's image score. The Hamilton's rule was dependent on the number of game bouts even though the information reduced the risk of cooperation to selfish one at the first encounter. In addition, we incorporated group structure to the two-score model to examine whether the probability of getting correct information affect selection for altruism by group selection. We calculated a Hamilton's rule of group selection by contextual analysis. Group selection is very effective when either the probability of getting correct information or that of future interaction, or both are low. The two Hamilton's rules derived by covariance and contextual analyses demonstrated the effects of information and group structure on the evolution of altruism. We inferred that information about a partner's behavior and group structure can produce flexible pathways for the evolution of altruism.     

A quantitative test of Hamilton's rule for the evolution of altruism

The evolution of altruism is a fundamental and enduring puzzle in biology. In a seminal paper Hamilton showed that altruism can be selected for when rb - c > 0, where c is the fitness cost to the altruist, b is the fitness benefit to the beneficiary, and r is their genetic relatedness. While many studies have provided qualitative support for Hamilton's rule, quantitative tests have not yet been possible due to the difficulty of quantifying the costs and benefits of helping acts. Here we use a simulated system of foraging robots to experimentally manipulate the costs and benefits of helping and determine the conditions under which altruism evolves. By conducting experimental evolution over hundreds of generations of selection in populations with different c/b ratios, we show that Hamilton's rule always accurately predicts the minimum relatedness necessary for altruism to evolve. This high accuracy is remarkable given the presence of pleiotropic and epistatic effects as well as mutations with strong effects on behavior and fitness (effects not directly taken into account in Hamilton's original 1964 rule). In addition to providing the first quantitative test of Hamilton's rule in a system with a complex mapping between genotype and phenotype, these experiments demonstrate the wide applicability of kin selection theory.     

Assortment and the analysis of natural selection on social traits

A central problem in evolutionary biology is to determine whether and how social interactions contribute to natural selection. A key method for phenotypic data is social selection analysis, in which fitness effects from social partners contribute to selection only when there is a correlation between the traits of individuals and their social partners (nonrandom phenotypic assortment). However, there are inconsistencies in the use of social selection that center around the measurement of phenotypic assortment. Here, we use data analysis and simulations to resolve these inconsistencies, showing that: (i) not all measures of assortment are suitable for social selection analysis; and (ii) the interpretation of assortment, and how to detect nonrandom assortment, will depend on the scale at which it is measured. We discuss links to kin selection theory and provide a practical guide for the social selection approach.     

Altruism via kin-selection strategies that rely on arbitrary tags with which they coevolve

Hamilton's rule explains when natural selection will favor altruism between conspecifics, given their degree of relatedness. In practice, indicators of relatedness (such as scent) coevolve with strategies based on these indicators, a fact not included in previous theories of kin recognition. Using a combination of simulation modeling and mathematical extension of Hamilton's rule, we demonstrate how altruism can emerge and be sustained in a coevolutionary setting where relatedness depends on an individual's social environment and varies from one locus to another. The results support a very general expectation of widespread, and not necessarily weak, conditional altruism in nature.     

Toward evolutionary graphs with two sexes: a kin selection analysis of a sex allocation problem

Evolutionary graphs are used to model the effects of spatial and social structure in social evolutionary problems (e.g. evolutionary games). Recent work has highlighted the fact that evolution on graphs can be understood using kin selection theory. This paper shows how one can use kin selection to study evolutionary graphs inhabited by a diploid sexual organism by means of a simple example. Specifically, we study the well-known sex allocation problem of how best to divide a fixed amount of effort between the production of sons on the one hand and the production of daughters on the other. Like many previous studies, we identify equal investment in sons and daughters as the only phenotype favoured by selection. Our analysis also highlights the advantages and disadvantages of applying kin selection to the study of evolutionary graphs.     

The validity and value of inclusive fitness theory

Social evolution is a central topic in evolutionary biology, with the evolution of eusociality (societies with altruistic, non-reproductive helpers) representing a long-standing evolutionary conundrum. Recent critiques have questioned the validity of the leading theory for explaining social evolution and eusociality, namely inclusive fitness (kin selection) theory. I review recent and past literature to argue that these critiques do not succeed. Inclusive fitness theory has added fundamental insights to natural selection theory. These are the realization that selection on a gene for social behaviour depends on its effects on co-bearers, the explanation of social behaviours as unalike as altruism and selfishness using the same underlying parameters, and the explanation of within-group conflict in terms of non-coinciding inclusive fitness optima. A proposed alternative theory for eusocial evolution assumes mistakenly that workers' interests are subordinate to the queen's, contains no new elements and fails to make novel predictions. The haplodiploidy hypothesis has yet to be rigorously tested and positive relatedness within diploid eusocial societies supports inclusive fitness theory. The theory has made unique, falsifiable predictions that have been confirmed, and its evidence base is extensive and robust. Hence, inclusive fitness theory deserves to keep its position as the leading theory for social evolution.     

Budding dispersal and the sex ratio

There is much interest in understanding how population demography impacts upon social evolution. Here, we consider the impact of rate and pattern of dispersal upon a classic social evolutionary trait--the sex ratio. We recover existing analytical results for individual dispersal, and we extend these to allow for budding dispersal. In particular, while a cancelling of relatedness and kin competition effects means that the sex ratio is unaffected by the rate of individual dispersal, we find that a decoupling of relatedness and kin competition means that budding dispersal favours increasingly female-biased sex ratios. More generally, our analysis illustrates the relative ease with which biological problems involving class structure can be solved using a kin selection approach to social evolution theory.     

Kin selection and the Evolution of Mutualisms between Species

Hamilton's theory of kin selection has revolutionized and inspired fifty years of additional theories and experiments on social evolution. Whereas Hamilton's broader intent was to explain the evolutionary stability of cooperation, his focus on shared genetic history appears to have limited the application of his theory to populations within a single species rather than across interacting species. The evolutionary mechanisms for cooperation between species require both spatial and temporal correlations among interacting partners for the benefits to be not only predictable but of sufficient duration to be reliably delivered. As a consequence when the benefits returned by mutualistic partners are redirected to individuals other than the original donor, cooperation usually becomes unstable and parasitism may evolve. However, theoretically, such redirection of mutualistic benefits may actually reinforce, rather than undermine, mutualisms between species when the recipients of these redirected benefits are genetically related to the original donor. Here, I review the few mathematical models that have used Hamilton's theory of kin selection to predict the evolution of mutualisms between species. I go on to examine the applicability of these models to the most well‐studied case of mutualism, pollinating seed predators, where the role of kin selection may have been previously overlooked. Future detailed studies of the direct, and indirect, benefits of mutualism are likely to reveal additional possibilities for applying Hamilton's theory of kin selection to mutualisms between species.     

INTERACTING PHENOTYPES AND THE EVOLUTIONARY PROCESS. III. SOCIAL EVOLUTION

Interactions among conspecifics influence social evolution through two distinct but intimately related paths. First, they provide the opportunity for indirect genetic effects (IGEs), where genes expressed in one individual influence the expression of traits in others. Second, interactions can generate social selection when traits expressed in one individual influence the fitness of others. Here, we present a quantitative genetic model of multivariate trait evolution that integrates the effects of both IGEs and social selection, which have previously been modeled independently. We show that social selection affects evolutionary change whenever the breeding value of one individual covaries with the phenotype of its social partners. This covariance can be created by both relatedness and IGEs, which are shown to have parallel roles in determining evolutionary response. We show that social selection is central to the estimation of inclusive fitness and derive a version of Hamilton's rule showing the symmetrical effects of relatedness and IGEs on the evolution of altruism. We illustrate the utility of our approach using altruism, greenbeards, aggression, and weapons as examples. Our model provides a general predictive equation for the evolution of social phenotypes that encompasses specific cases such as kin selection and reciprocity. The parameters can be measured empirically, and we emphasize the importance of considering both IGEs and social selection, in addition to relatedness, when testing hypotheses about social evolution.     

Demography, altruism, and the benefits of budding

It is now widely appreciated that competition between kin inhibits the evolution of altruism. In standard population genetics models, it is difficult for indiscriminate altruism towards social partners to be favoured at all. The reason is that while limited dispersal increases the kinship of social partners it also intensifies local competition. One solution that has received very little attention is if individuals disperse as groups (budding dispersal), as this relaxes local competition without reducing kinship. Budding behaviour is widespread through all levels of biological organization, from early protocellular life to cooperatively breeding vertebrates. We model the effects of individual dispersal, budding dispersal, soft selection and hard selection to examine the conditions under which altruism is favoured. More generally, we examine how these various demographic details feed into relatedness and scale of competition parameters that can be included into Hamilton's rule.     

Hamilton's forces of natural selection after forty years

In 1966, William D. Hamilton published a landmark paper in evolutionary biology: "The Moulding of Senescence by Natural Selection." It is now apparent that this article is as important as his better-known 1964 articles on kin selection. Not only did the 1966 article explain aging, it also supplied the basic scaling forces for natural selection over the entire life history. Like the Lorentz transformations of relativistic physics, Hamilton's Forces of Natural Selection provide an overarching framework for understanding the power of natural selection at early ages, the existence of aging, the timing of aging, the cessation of aging, and the timing of the cessation of aging. His twin Forces show that natural selection shapes survival and fecundity in different ways, so their evolution can be somewhat distinct. Hamilton's Forces also define the context in which genetic variation is shaped. The Forces of Natural Selection are readily manipulable using experimental evolution, allowing the deceleration or acceleration of aging, and the shifting of the transition ages between development, aging, and late life. For these reasons, evolutionary research on the demographic features of life history should be referred to as "Hamiltonian."