Exact versus heuristic models of kin selection

This paper examines the conditions under which the classical inclusive fitness formulation of Hamilton (1964) provides an adequate approximation to the dynamics of gene frequency change and to conditions for genetic equilibrium, in the “additive” model of altruism between sibs of Uyenoyama and Feldman (1981). It is concluded that the classical formulation is adequate, provided that either the effect of the gene on the probability of behaving altruistically is low or the costs and benefits of altruism are small, unless the benefit/cost ratio k is very close to 2, the value that must be exceeded for altruism to be favoured. In addition, the gene for altruism must be underdominant, recessive or partially recessive in its effect on the probability of behaving altruistically, for the inclusive fitness predictions to break down significantly.     

Inbreeding and evolution by kin selection

Because alleles associated with altruistic behaviors can increase in frequency when altruists increase the fitness of closely related individuals, it has been assumed that inbreeding presents the most favorable conditions for the evolution of altruism. Using a family-structured model of kin selection, we varied the proportion of the population mating with sibs and the proportion mating randomly to investigate the hypothesis that inbreeding facilitates the evolution of altruistic behaviors.We partitioned total gene frequency change of the altruistic allele into two components: (1) the change in gene frequency owing to selection within families, or individual selection; this component of selection is always negative and selects against altruistic social behaviors; and (2) the change in gene frequency owing to fitness differences between families, or group selection; this component of selection favors the evolution of altruistic social behaviors. Because inbreeding increases the component of group selection at the expense of individual selection by increasing the between-group variation, it facilitates the spread of the altruistic allele. Computer simulations show that even small amounts of inbreeding (within-sibship mating) significantly increase the rate of gene frequency change.     

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.     

Bet hedging based cooperation can limit kin selection and form a basis for mutualism

Mutualism is a mechanism of cooperation in which partners that differ help each other. As such, mutualism opposes mechanisms of kin selection and tag-based selection (for example the green beard mechanism), which are based on giving exclusive help to partners that are related or carry the same tag. In contrast to kin selection, which is a basis for parochialism and intergroup warfare, mutualism can therefore be regarded as a mechanism that drives peaceful coexistence between different groups and individuals. Here the competition between mutualism and kin (tag) selection is studied. In a model where kin selection and tag-based selection are dominant, mutualism is promoted by introducing environmental fluctuations. These fluctuations cause reduction in reproductive success by the mechanism of variance discount. The best strategy to counter variance discount is to share with agents who experience the most anticorrelated fluctuations, a strategy called bet hedging. In this way, bet hedging stimulates cooperation with the most unrelated partners, which is a basis for mutualism. Analytic results and simulations reveal that, if this effect is large enough, mutualistic strategies can dominate kin selective strategies. In addition, mutants of these mutualistic strategies that experience fluctuations that are more anticorrelated to their partner, can outcompete wild type, which can lead to the evolution of specialization. In this way, the evolutionary success of mutualistic strategies can be explained by bet hedging-based cooperation.     

The evolution of altruism by kin selection: New phenomena with strong selection

The development of a theory of kin selection has proceeded along two lines. Inclusive- fitness models have implicitly assumed that selection is weak, whereas exact-population genetic models place no constraints on the strength of selection. Several examples are presented showing that qualitatively new behavior has emerged from the exact models. However, for many problems, the exact-population and inclusive-fitness models often yield identical results. Unfortunately, it is not possible to identify a priori those problems that can be handled sufficiently by the simpler inclusive-fitness models. The initial increase of cooperative behavior in a population of egoists involves difficulties similar to the initial increase of altruism. Clustering of cooperatives produces dynamics for the increase of cooperation that are formally similar to population models of inbreeding. Here, an increase in the tendency to cluster is equivalent to increasing the “relationship” among cooperatives, and therefore augments the chance for cooperation to increase.     

Group selection, kin selection, altruism and cooperation: When inclusive fitness is right and when it can be wrong

Group selection theory has a history of controversy. After a period of being in disrepute, models of group selection have regained some ground, but not without a renewed debate over their importance as a theoretical tool. In this paper I offer a simple framework for models of the evolution of altruism and cooperation that allows us to see how and to what extent both a classification with and one without group selection terminology are insightful ways of looking at the same models. Apart from this dualistic view, this paper contains a result that states that inclusive fitness correctly predicts the direction of selection for one class of models, represented by linear public goods games. Equally important is that this result has a flip side: there is a more general, but still very realistic class of models, including models with synergies, for which it is not possible to summarize their predictions on the basis of an evaluation of inclusive fitness.     

Genetical aspects of kin selection: effects of inbreeding

Hamilton's c/b < “r” rule is an important tool in sociobiological research and clearly functions as a “positive heuristic”, sensu Lakatos (1970). This paper examines the theoretical underpinnings of this rule in population genetics when inbreeding is taken into account. The model used is an extension of Charnov (1977) and assumes that the altruistic gene codes for a behavior between inbred individuals of a fixed genetic relationship. No consideration is given to the population or mating system processes which give rise to this relationship. It is shown that in inbred populations with weak selection the right-hand side of Hamilton's rule depends upon gene frequency and dominance as well as the degree of genetic relationship between the individuals involved. Because of this dependence, stable polymorphisms in altruistic and non-altruistic alleles are possible for certain ranges of c/b ratios. Another consequence is that the more dominant the altruistic gene, the easier it is for it to invade a population, but the harder it is for it to increase to high frequencies. In the special case when the individuals involved are inbred to the same extent and gene effects are additive, the RHS of the rule is independent of gene frequency and equals b_YX and r_YX: respectively Hamilton's regression coefficient of relatedness and Wright's correlation coefficient of relationship.     

Evolution of eusociality by kin selection: the effect of inbreeding between siblings

The effect of sib-sib inbreeding on the evolution of eusocial altruism in Hymenoptera by kin selection is examined by computer simulations. Inbreeding has minor effects on the ratio of relatedness to siblings: relatedness to offspring, but this ratio remains approximately one no matter what the degree of inbreeding. This implies that although inbreeding increases relatedness to siblings, relatedness to offspring increases to the same degree. Hence, inbreeding does not make the evolution of altruism more likely. If all the brothers of (non-mating) altruists outbreed, thereby increasing the frequency of altruism alleles in the outbred fraction of the population especially at low gene frequency, then altruism can be promoted by inbreeding. However, this is an indirect advantage, not attributable to inbreeding per se.     

Sexual selection for syntax and kin selection for semantics: problems and prospects

The evolution of human language, and the kind of thought the communication of which requires it, raises considerable explanatory challenges. These systems of representation constitute a radical discontinuity in the natural world. Even species closely related to our own appear incapable of either thought or talk with the recursive structure, generalized systematicity, and task-domain neutrality that characterize human talk and the thought it expresses. W. Tecumseh Fitch’s proposal (2004, in press) that human language is descended from a sexually selected, prosodic proto-language that approximated its syntactic complexity, and later acquired semantics thanks to kin selection for its use as a means of pedagogical transmission, has the promise of meeting these explanatory challenges. However, Fitch’s theory raises two problems of its own: (1) according to Boyd and Richerson (1996, Proc. Br. Acad. 88: 77–93), circumstances in which pedagogy is adaptive are inevitably rare in nature, and (2) it is unlikely that our non-discursive precursors had generally systematic, task-domain neutral thoughts to communicate to their offspring. I propose solutions to these problems. Pedagogy would be favored in a population where complex rituals dominated diverse aspects of life. Prosodic proto-language could emerge as the medium of pedagogic transmission. As this medium was used to teach a greater variety of tasks, it would become increasingly general and domain neutral. The presence and importance of such a system of communication in hominid populations could then drive, via Baldwinian mechanisms, the evolution of a kind of ‘thinking for speaking’ (Slobin 1991, Pragmatics 1: 7–25) characterized by recursive structure, generalized systematicity, and task-domain neutrality.     

Natural selection on fecundity variance in subdivided populations: kin selection meets bet hedging

In a series of seminal articles in 1974, 1975, and 1977, J. H. Gillespie challenged the notion that the "fittest" individuals are those that produce on average the highest number of offspring. He showed that in small populations, the variance in fecundity can determine fitness as much as mean fecundity. One likely reason why Gillespie's concept of within-generation bet hedging has been largely ignored is the general consensus that natural populations are of large size. As a consequence, essentially no work has investigated the role of the fecundity variance on the evolutionary stable state of life-history strategies. While typically large, natural populations also tend to be subdivided in local demes connected by migration. Here, we integrate Gillespie's measure of selection for within-generation bet hedging into the inclusive fitness and game theoretic measure of selection for structured populations. The resulting framework demonstrates that selection against high variance in offspring number is a potent force in large, but structured populations. More generally, the results highlight that variance in offspring number will directly affect various life-history strategies, especially those involving kin interaction. The selective pressures on three key traits are directly investigated here, namely within-generation bet hedging, helping behaviors, and the evolutionary stable dispersal rate. The evolutionary dynamics of all three traits are markedly affected by variance in offspring number, although to a different extent and under different demographic conditions.     

The evolution of trans-generational altruism: kin selection meets niche construction

A cornerstone result of sociobiology states that limited dispersal can induce kin competition to offset the kin selected benefits of altruism. Several mechanisms have been proposed to circumvent this dilemma but all assume that actors and recipients of altruism interact during the same time period. Here, this assumption is relaxed and a model is developed where individuals express an altruistic act, which results in posthumously helping relatives living in the future. The analysis of this model suggests that kin selected benefits can then feedback on the evolution of the trait in a way that promotes altruistic helping at high rates under limited dispersal. The decoupling of kin competition and kin selected benefits results from the fact that by helping relatives living in the future, an actor is helping individuals that are not in direct competition with itself. A direct consequence is that behaviours which actors gain by reducing the common good of present and future generations can be opposed by kin selection. The present model integrates niche-constructing traits with kin selection theory and delineates demographic and ecological conditions under which altruism can be selected for; and conditions where the 'tragedy of the commons' can be reduced.     

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.     

Distinctions among reciprocal altruism,kin selection,and cooperation and a model for the initial evolution of beneficent behavior

Reciprocal altruism is usually regarded as distinct from kin selection. However, because reciprocators are likely to establish long-term relations and to deliver most of their aid to other individuals genetically predisposed to reciprocation, most acts of reciprocal altruism should involve indirect increments to inclusive fitness, at least as regards alleles for reciprocation. Thus, as usually defined, reciprocal altruism is not clearly distinct from kin selection because both involve indirect increments to inclusive fitness. We propose a new definition for reciprocal altruism that makes the phenomenon distinct from kin selection and allows for reciprocation between nonrelatives in which current costs exceed future benefits returned to the reciprocal altruist. Cooperation and reciprocal altruism are often considered synonymous or different only in the timing of donating and receiving aid. We show, however, that there are other critical differences between reciprocal altruism and other forms of cooperation, most importantly, the latter often involve no clearly identifiable aid. We propose a four-category system to encompass the range of cooperative and beneficent behaviors that occur in nature (reciprocal altruism, pseudoreciprocity, simultaneous cooperation and by-product beneficence). Reciprocal altruism must involve aid that is returned to an original donor as a result of behavior that has a net cost to an original recipient. Our simplest category of cooperative/beneficent behavior, “by-product beneficence,” occurs when a selfish act also benefits another individual and requires no prior or subsequent interactions between the individuals involved. By-product beneficence may be the primitive state from which more complicated types of cooperative/beneficent behavior evolved. We show via simple models that by-product beneficence can allow for the initial increase of helping behavior in a completely unstructured population although the individuals showing such behavior pay all the costs while sharing the benefits with other individuals. Previous models that attempted to explain the initial increase of cooperative/beneficent behavior were much more complex and were based on the prisoner's dilemma, which does not accurately reflect most forms of cooperation and beneficence that occur in nature.     

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.     

Evolution in structured populations: beyond the kin versus group debate

Much of the literature on social evolution is pervaded by the old debate about the relative merits of kin and group selection. In this debate, the biological interpretation of processes occurring in real populations is often conflated with the mathematical methodology used to describe these processes. Here, we highlight the distinction between the two by placing this discussion within the broader context of evolution in structured populations. In this review we show that the current debate overlooks important aspects of the interplay between genetic and demographic structuring, and argue that a continued focus on the relative merits of kin versus group selection distracts attention from moving the field forward.     

Evolution of sex ratios in social hymenoptera: kin selection,local mate competition,polyandry and kin recognition

A model is constructed to study the effects of local mate competition and multiple mating on the optimum allocation of resources between the male and female reproductive brood in social hymenopteran colonies from the ‘points of view’ of the queen (parental manipulation theory) as well as the workers (kin selection theory). Competition between pairs of alleles specifying different sex investment ratios is investigated in a game theoretic frame work. All other things being equal, local mate competition shifts the sex allocation ratio in favour of females both under queen and worker control. While multiple mating has no effect on the queen’s optimum investment ratio, it leads to a relatively male biased investment ratio under worker control. Under queen control a true Evolutionarily Stable Strategy(ess) does not exist but the ‘best’ strategy is merely immune from extinction. A trueess exists under worker control in colonies with singly mated queens but there is an asymmetry between the dominant and recessive alleles so that for some values of sex ratio a recessive allele goes to fixation but a dominant allele with the same properties fails to do so. Under multiple mating, again, a trueess does not exist but a frequency dependent region emerges. The best strategy here is one that is guaranteed fixation against any competing allele with a lower relative frequency. Our results emphasize the need to determine levels of local mate competition and multiple mating before drawing any conclusions regarding the outcome of queen-worker conflict in social hymenoptera. Multiple mating followed by sperm mixing, both of which are known to occur in social hymenoptera, lower average genetic relatedness between workers and their reproductive sisters. This not only shifts the optimum sex ratio from the workers’ ‘point of view’ in favour of males but also poses problems for the kin selection theory. We show that kin recognition resulting in the ability to invest in full but not in half sisters reverts the sex ratio back to that in the case of single mating and thus completely overcomes the hurdles for the operation of kin selection.