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.     

The relation between multilocus population genetics and social evolution theory

Evolution at multiple gene positions is complicated. Direct selection on one gene disturbs the evolutionary dynamics of associated genes. Recent years have seen the development of a multilocus methodology for modeling evolution at arbitrary numbers of gene positions with arbitrary dominance and epistatic relations, mode of inheritance, genetic linkage, and recombination. We show that the approach is conceptually analogous to social evolutionary methodology, which focuses on selection acting on associated individuals. In doing so, we (1) make explicit the links between the multilocus methodology and the foundations of social evolution theory, namely, Price's theorem and Hamilton's rule; (2) relate the multilocus approach to levels-of-selection and neighbor-modulated-fitness approaches in social evolution; (3) highlight the equivalence between genetical hitchhiking and kin selection; (4) demonstrate that the multilocus methodology allows for social evolutionary analyses involving coevolution of multiple traits and genetical associations between nonrelatives, including individuals of different species; (5) show that this methodology helps solve problems of dynamic sufficiency in social evolution theory; (6) form links between invasion criteria in multilocus systems and Hamilton's rule of kin selection; (7) illustrate the generality and exactness of Hamilton's rule, which has previously been described as an approximate, heuristic 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.     

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.     

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.     

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.     

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.     

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.     

Darwin's ‘one special difficulty’: celebrating Darwin 200

Darwin identified eusocial evolution, especially of complex insect societies, as a particular challenge to his theory of natural selection. A century later, Hamilton provided a framework for selection on inclusive fitness. Hamilton''s rule is robust and fertile, having generated multiple subdisciplines over the past 45 years. His suggestion that eusociality can be explained via kin selection, however, remains contentious. I review the continuing debate on the role of kin selection in eusocial evolution and suggest some lines of research that should resolve that debate.     

Detecting kin selection at work using inclusive fitness

A recent model shows that altruism can evolve with limited migration and variable group sizes, and the authors claim that kin selection cannot provide a sufficient explanation of their results. It is demonstrated, using a recent reformulation of Hamilton's original arguments, that the model falls squarely within the scope of inclusive fitness theory, which furthermore shows how to calculate inclusive fitness and the relevant relatedness. A distinction is drawn between inclusive fitness, which is a method of analysing social behaviour; and kin selection, a process that operates through genetic similarity brought about by common ancestry, but not by assortation by genotype or by direct assessment of genetic similarity. The recent model is analysed, and it turns out that kin selection provides a sufficient explanation to considerable quantitative accuracy, contrary to the authors' claims. A parallel analysis is possible and would be illuminating for all models of social behaviour in which individuals' effects on each other's offspring numbers combine additively.     

Social insects and selfish genes

Sometimes science advances because of a new idea. Sometimes, it's because of a new technique. When both occur together, exciting times result. In the study of social insects, DNA-based methods for measuring relatedness now allow increasingly detailed tests of Hamilton's theory of kin selection.     

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.     

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.     

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.     

Why kin and group selection models may not be enough to explain human other-regarding behaviour

Models of kin or group selection usually feature only one possible fitness transfer. The phenotypes are either to make this transfer or not to make it and for any given fitness transfer, Hamilton's rule predicts which of the two phenotypes will spread. In this article we allow for the possibility that different individuals or different generations face similar, but not necessarily identical possibilities for fitness transfers. In this setting, phenotypes are preference relations, which concisely specify behaviour for a range of possible fitness transfers (rather than being a specification for only one particular situation an animal or human can be in). For this more general set-up, we find that only preference relations that are linear in fitnesses can be explained using models of kin selection and that the same applies to a large class of group selection models. This provides a new implication of hierarchical selection models that could in principle falsify them, even if relatedness--or a parameter for assortativeness--is unknown. The empirical evidence for humans suggests that hierarchical selection models alone are not enough to explain their other-regarding or altruistic behaviour.     

The sociobiology of ethnocentrism in an Indian City

In this article, I examine whether inter- and/or intraunit variation in ethnocentrism— a trait not automatically connected with mortality/natality rates—can be correlated with differential reproductive success. As a preliminary test of general theoretical models in the literature regarding the sociobiology of ethnocentrism, it was postulated that the more ethnocentric an ethnic unit is, the more important ethnocentrism is for the members of that unit. With the use of this postulate, hypotheses were generated and tested with empirical data obtained through field research among two ethnic units—Tamils and Gujaratis—in the city of Pune, India. It was concluded that: 1) if interunit aggression and kin selection were predominant characteristics of the early hominid environments of evolutionary adaptation, then from a sociobiological perspective, ethnocentrism can be explained as an evolved human trait, intimately linked to kin selection and interunit warfare; and, 2) under what I assumed to be novel environmental conditions ethnocentrism and reproductive success appear to be uncorrelated; and, 3) because the possibility exists that novel environmental contengencies were acting to level off reproductive variance upon which natural selection could have operated in my sample, only future research in a society similar in structure to those we tend to identify with early hominid environments of evolutionary adaptation will allow researchers to rule out the possibility that ethnocentrism is an evolved human “biocultural” trait.     

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.     

A test of alternative hypotheses for kin recognition in cannibalistic tiger salamanders

The function of kin recognition is controversial. We investigatedthe adaptive significance of kin discrimination in cannibalistictiger salamander larvae, Ambystoma tigrinum. Previous laboratoryexperiments show that cannibals preferentially consume lessrelated individuals. We hypothesized that this example of kinrecognition (1) is a laboratory artifact, (2) is a by-productof sibship-specific variation in escape responses, because cannibalsfrom families with rapid responses may be more likely to cannibalize slowlyescaping non-kin, (3) is an epiphenomenon of species recognition,(4) functions in disease avoidance, because kin may be moreinfectious than non-kin, or (5) is favored by kin selection.We evaluated these five hypotheses by using laboratory and fieldexperiments to test specific predictions made by each hypothesis.We rejected hypotheses 1-4 above because (1) kin recognitionwas expressed in the wild, (2) escape responses did not reliablypredict whether a cannibal would ingest kin or non-kin, (3)kin recognition was not most pronounced in populations wheretiger salamanders co-occur with other species of salamanders,and (4) non-kin prey were more likely than kin to transmit pathogensto cannibals. However, we established that the necessary conditionfor kin selection, Hamilton's rule, was met. Thus, our resultsimplicate kin selection as the overriding reason that cannibalistictiger salamanders discriminate kin.