Helping in cooperatively breeding long-tailed tits: a test of Hamilton's rule

Inclusive fitness theory provides the conceptual framework for our current understanding of social evolution, and empirical studies suggest that kin selection is a critical process in the evolution of animal sociality. A key prediction of inclusive fitness theory is that altruistic behaviour evolves when the costs incurred by an altruist (c) are outweighed by the benefit to the recipient (b), weighted by the relatedness of altruist to recipient (r), i.e. Hamilton''s rule rb > c. Despite its central importance in social evolution theory, there have been relatively few empirical tests of Hamilton''s rule, and hardly any among cooperatively breeding vertebrates, leading some authors to question its utility. Here, we use data from a long-term study of cooperatively breeding long-tailed tits Aegithalos caudatus to examine whether helping behaviour satisfies Hamilton''s condition for the evolution of altruism. We show that helpers are altruistic because they incur survival costs through the provision of alloparental care for offspring. However, they also accrue substantial benefits through increased survival of related breeders and offspring, and despite the low average relatedness of helpers to recipients, these benefits of helping outweigh the costs incurred. We conclude that Hamilton''s rule for the evolution of altruistic helping behaviour is satisfied in this species.     

Quantitative genetic versions of Hamilton's rule with empirical applications

Hamilton''s theory of inclusive fitness revolutionized our understanding of the evolution of social interactions. Surprisingly, an incorporation of Hamilton''s perspective into the quantitative genetic theory of phenotypic evolution has been slow, despite the popularity of quantitative genetics in evolutionary studies. Here, we discuss several versions of Hamilton''s rule for social evolution from a quantitative genetic perspective, emphasizing its utility in empirical applications. Although evolutionary quantitative genetics offers methods to measure each of the critical parameters of Hamilton''s rule, empirical work has lagged behind theory. In particular, we lack studies of selection on altruistic traits in the wild. Fitness costs and benefits of altruism can be estimated using a simple extension of phenotypic selection analysis that incorporates the traits of social interactants. We also discuss the importance of considering the genetic influence of the social environment, or indirect genetic effects (IGEs), in the context of Hamilton''s rule. Research in social evolution has generated an extensive body of empirical work focusing—with good reason—almost solely on relatedness. We argue that quantifying the roles of social and non-social components of selection and IGEs, in addition to relatedness, is now timely and should provide unique additional insights into social evolution.     

Hamilton's rule and the causes of social evolution

Hamilton''s rule is a central theorem of inclusive fitness (kin selection) theory and predicts that social behaviour evolves under specific combinations of relatedness, benefit and cost. This review provides evidence for Hamilton''s rule by presenting novel syntheses of results from two kinds of study in diverse taxa, including cooperatively breeding birds and mammals and eusocial insects. These are, first, studies that empirically parametrize Hamilton''s rule in natural populations and, second, comparative phylogenetic analyses of the genetic, life-history and ecological correlates of sociality. Studies parametrizing Hamilton''s rule are not rare and demonstrate quantitatively that (i) altruism (net loss of direct fitness) occurs even when sociality is facultative, (ii) in most cases, altruism is under positive selection via indirect fitness benefits that exceed direct fitness costs and (iii) social behaviour commonly generates indirect benefits by enhancing the productivity or survivorship of kin. Comparative phylogenetic analyses show that cooperative breeding and eusociality are promoted by (i) high relatedness and monogamy and, potentially, by (ii) life-history factors facilitating family structure and high benefits of helping and (iii) ecological factors generating low costs of social behaviour. Overall, the focal studies strongly confirm the predictions of Hamilton''s rule regarding conditions for social evolution and their causes.     

Extending the range of additivity in using inclusive fitness

Inclusive fitness is a concept widely utilized by social biologists as the quantity organisms appear designed to maximize. However, inclusive fitness theory has long been criticized on the (uncontested) grounds that other quantities, such as offspring number, predict gene frequency changes accurately in a wider range of mathematical models. Here, we articulate a set of modeling assumptions that extend the range of scenarios in which inclusive fitness can be applied. We reanalyze recent formal analyses that searched for, but did not find, inclusive fitness maximization. We show (a) that previous models have not used Hamilton''s definition of inclusive fitness, (b) a reinterpretation of Hamilton''s definition that makes it usable in this context, and (c) that under the assumption of probabilistic mixing of phenotypes, inclusive fitness is indeed maximized in these models. We also show how to understand mathematically, and at an individual level, the definition of inclusive fitness, in an explicit population genetic model in which exact additivity is not assumed. We hope that in articulating these modeling assumptions and providing formal support for inclusive fitness maximization, we help bridge the gap between empiricists and theoreticians, which in some ways has been widening, demonstrating to mathematicians why biologists are content to use inclusive fitness, and offering one way to utilize inclusive fitness in general models of social behavior.     

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.     

Hamilton's rule,inclusive fitness maximization,and the goal of individual behaviour in symmetric two‐player games

Hamilton's original work on inclusive fitness theory assumed additivity of costs and benefits. Recently, it has been argued that an exact version of Hamilton's rule for the spread of a pro‐social allele (rb > c) holds under nonadditive pay‐offs, so long as the cost and benefit terms are defined as partial regression coefficients rather than pay‐off parameters. This article examines whether one of the key components of Hamilton's original theory can be preserved when the rule is generalized to the nonadditive case in this way, namely that evolved organisms will behave as if trying to maximize their inclusive fitness in social encounters.     

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.     

Lower group productivity under kin-selected reproductive altruism

Abstract Hamilton's rule provides the foundation for understanding the genetic evolution of social behavior, showing that altruism is favored by increased relatedness and increased productivity of altruists. But how likely is it that a new altruistic mutation will satisfy Hamilton's rule by increasing the reproductive efficiency of the group? Altruism per se does not improve efficiency, and hence we would not expect a typical altruistic mutation to increase the mean productivity of the population. We examined the conditions under which a mutation causing reproductive altruism can spread when it does not increase productivity. We considered a population divided into temporary groups of genetically similar individuals (typically family groups). We show that the spread of altruism requires a pleiotropic link between altruism and enhanced productivity in diploid organisms, but not in haplodiploid organisms such as Hymenoptera. This result provides a novel biological understanding of the barrier to the spread of reproductive altruism in diploids. In haplodiploid organisms, altruism within families that lowers productivity may spread, provided daughters sacrifice their own reproduction to raise full‐sisters. We verified our results using three single‐locus genetic models that explore a range of the possible reproductive costs of helping. The advantage of female‐to‐female altruism in haplodiploids is a well‐known prediction of Hamilton's rule, but its importance in relaxing the linkage between altruism and efficiency has not been explored. We discuss the possible role of such unproductive altruism in the origins of sociality. We also note that each model predicts a large region of parameter space were polymorphism between altruism and selfishness is maintained, a pattern independent of dominance.     

Resolving the evolution of sterile worker castes: a window on the advantages and disadvantages of monogamy

Many social Hymenoptera species have morphologically sterile worker castes. It is proposed that the evolutionary routes to this obligate sterility must pass through a ‘monogamy window’, because inclusive fitness favours individuals retaining their reproductive totipotency unless they can rear full siblings. Simulated evolution of sterility, however, finds that ‘point of view’ is critically important. Monogamy is facilitating if sterility is expressed altruistically (i.e. workers defer reproduction to queens), but if sterility results from manipulation by mothers or siblings, monogamy may have no effect or lessen the likelihood of sterility. Overall, the model and data from facultatively eusocial bees suggest that eusociality and sterility are more likely to originate through manipulation than by altruism, casting doubt on a mandatory role for monogamy. Simple kin selection paradigms, such as Hamilton''s rule, can also fail to account for significant evolutionary dynamics created by factors, such as population structure, group-level effects or non-random mating patterns. The easy remedy is to always validate apparently insightful predictions from Hamiltonian equations with life-history appropriate genetic models.     

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.     

Lifetime monogamy and the evolution of eusociality

All evidence currently available indicates that obligatory sterile eusocial castes only arose via the association of lifetime monogamous parents and offspring. This is consistent with Hamilton''s rule (br_s > r_oc), but implies that relatedness cancels out of the equation because average relatedness to siblings (r_s) and offspring (r_o) are both predictably 0.5. This equality implies that any infinitesimally small benefit of helping at the maternal nest (b), relative to the cost in personal reproduction (c) that persists throughout the lifespan of entire cohorts of helpers suffices to establish permanent eusociality, so that group benefits can increase gradually during, but mostly after the transition. The monogamy window can be conceptualized as a singularity comparable with the single zygote commitment of gametes in eukaryotes. The increase of colony size in ants, bees, wasps and termites is thus analogous to the evolution of multicellularity. Focusing on lifetime monogamy as a universal precondition for the evolution of obligate eusociality simplifies the theory and may help to resolve controversies about levels of selection and targets of adaptation. The monogamy window underlines that cooperative breeding and eusociality are different domains of social evolution, characterized by different sectors of parameter space for Hamilton''s rule.     

Hamilton's rule meets the Hamiltonian: kin selection on dynamic characters

Many biological characters of interest are temporal sequences of decisions. The evolution of such characters is often modelled using dynamic optimization methods such as the maximum principle. A quantity central to these analyses is the ''Hamiltonian'' function, named after the mathematician William R. Hamilton. On the other hand, evolutionary models in which individuals interact with relatives are usually based on Hamilton''s rule, named after the evolutionary biologist William D. Hamilton. In this article we present a generalized maximum principle that includes the effects of interactions among relatives and we show that a time-dependent (dynamic) version of Hamilton''s rule holds involving the Hamiltonian. This result brings together the power and generality of both the maximum principle and Hamilton''s rule thereby providing a natural framework for understanding the evolution of ''dynamic'' characters under kin selection.     

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.     

NONADAPTIVE PROCESSES CAN CREATE THE APPEARANCE OF FACULTATIVE CHEATING IN MICROBES

Adaptations to social life may take the form of facultative cheating, in which organisms cooperate with genetically similar individuals but exploit others. Consistent with this possibility, many strains of social microbes like Myxococcus bacteria and Dictyostelium amoebae have equal fitness in single‐genotype social groups but outcompete other strains in mixed‐genotype groups. Here we show that these observations are also consistent with an alternative, nonadaptive scenario: kin selection‐mutation balance under local competition. Using simple mathematical models, we show that deleterious mutations that reduce competitiveness within social groups (growth rate, e.g.) without affecting group productivity can create fitness effects that are only expressed in the presence of other strains. In Myxococcus, mutations that delay sporulation may strongly reduce developmental competitiveness. Deleterious mutations are expected to accumulate when high levels of kin selection relatedness relax selection within groups. Interestingly, local resource competition can create nonzero “cost” and “benefit” terms in Hamilton's rule even in the absence of any cooperative trait. Our results show how deleterious mutations can play a significant role even in organisms with large populations and highlight the need to test evolutionary causes of social competition among microbes.     

Parent—offspring conflict: the full-sib—half-sib fallacy

R. L. Trivers used Hamilton''s rule regarding the evolution of altruistic behaviour to demonstrate the occurrence of parent–offspring conflict and concluded that this would be more severe when future offspring were half siblings rather than full siblings of the offspring currently receiving investment. Here we show that Trivers'' formulation applies in a limited range of circumstances and offer an alternative formulation that is universally applicable. Under this formulation the optimal investment from the offspring''s point of view in species with uniparental care and, hence, the extent of parent–offspring conflict depends on the cost of the caring parent''s investment to the future fitness of the non-caring parent.     

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.     

Inclusive fitness and the sociobiology of the genome

Inclusive fitness theory provides conditions for the evolutionary success of a gene. These conditions ensure that the gene is selfish in the sense of Dawkins (The selfish gene, Oxford University Press, Oxford, 1976): genes do not and cannot sacrifice their own fitness on behalf of the reproductive population. Therefore, while natural selection explains the appearance of design in the living world (Dawkins in The blind watchmaker: why the evidence of evolution reveals a universe without design, W. W. Norton, New York, 1996), inclusive fitness theory does not explain how. Indeed, Hamilton’s rule is equally compatible with the evolutionary success of prosocial altruistic genes and antisocial predatory genes, whereas only the former, which account for the appearance of design, predominate in successful organisms. Inclusive fitness theory, however, permits a formulation of the central problem of sociobiology in a particularly poignant form: how do interactions among loci induce utterly selfish genes to collaborate, or to predispose their carriers to collaborate, in promoting the fitness of their carriers? Inclusive fitness theory, because it abstracts from synergistic interactions among loci, does not answer this question. Fitness-enhancing collaboration among loci in the genome of a reproductive population requires suppressing alleles that decrease, and promoting alleles that increase the fitness of its carriers. Suppression and promotion are effected by regulatory networks of genes, each of which is itself utterly selfish. This implies that genes, and a fortiori individuals in a social species, do not maximize inclusive fitness but rather interact strategically in complex ways. It is the task of sociobiology to model these complex interactions.     

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.     

THE COMPONENTS OF KIN COMPETITION

It is well known that competition among kin alters the rate and often the direction of evolution in subdivided populations. Yet much remains unclear about the ecological and demographic causes of kin competition, or what role life cycle plays in promoting or ameliorating its effects. Using the multilevel Price equation, I derive a general equation for evolution in structured populations under an arbitrary intensity of kin competition. This equation partitions the effects of selection and demography, and recovers numerous previous models as special cases. I quantify the degree of kin competition, α, which explicitly depends on life cycle. I show how life cycle and demographic assumptions can be incorporated into kin selection models via α, revealing life cycles that are more or less permissive of altruism. As an example, I give closed‐form results for Hamilton's rule in a three‐stage life cycle. Although results are sensitive to life cycle in general, I identify three demographic conditions that give life cycle invariant results. Under the infinite island model, α is a function of the scale of density regulation and dispersal rate, effectively disentangling these two phenomena. Population viscosity per se does not impede kin selection.