The genetical theory of kin selection

The causal meaning of Hamilton's rule

Hamilton's original derivation of his rule for the spread of an altruistic gene (rb>c) assumed additivity of costs and benefits. Recently, it has been argued that an exact version of the rule holds under non-additive pay-offs, so long as the cost and benefit terms are suitably defined, as partial regression coefficients. However, critics have questioned both the biological significance and the causal meaning of the resulting rule. This paper examines the causal meaning of the generalized Hamilton's rule in a simple model, by computing the effect of a hypothetical experiment to assess the cost of a social action and comparing it to the partial regression definition. The two do not agree. A possible way of salvaging the causal meaning of Hamilton's rule is explored, by appeal to R. A. Fisher's 'average effect of a gene substitution'.

There is no fitness but fitness, and the lineage is its bearer

Inclusive fitness has been the cornerstone of social evolution theory for more than a half-century and has matured as a mathematical theory in the past 20 years. Yet surprisingly for a theory so central to an entire field, some of its connections to evolutionary theory more broadly remain contentious or underappreciated. In this paper, we aim to emphasize the connection between inclusive fitness and modern evolutionary theory through the following fact: inclusive fitness is simply classical Darwinian fitness, averaged over social, environmental and demographic states that members of a gene lineage experience. Therefore, inclusive fitness is neither a generalization of classical fitness, nor does it belong exclusively to the individual. Rather, the lineage perspective emphasizes that evolutionary success is determined by the effect of selection on all biological and environmental contexts that a lineage may experience. We argue that this understanding of inclusive fitness based on gene lineages provides the most illuminating and accurate picture and avoids pitfalls in interpretation and empirical applications of inclusive fitness theory.

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.

Asymmetry within social groups: division of labour and intergroup competition

Social animals vary in their ability to compete with group members over shared resources and also vary in their cooperative efforts to produce these resources. Competition among groups can promote within-group cooperation, but many existing models of intergroup cooperation do not explicitly account for observations that group members invest differentially in cooperation and that there are often within-group competitive or power asymmetries. We present a game theoretic model of intergroup competition that investigates how such asymmetries affect within-group cooperation. In this model, group members adopt one of two roles, with relative competitive efficiency and the number of individuals varying between roles. Players in each role make simultaneous, coevolving decisions. The model predicts that although intergroup competition increases cooperative contributions to group resources by both roles, contributions are predominantly from individuals in the less competitively efficient role, whereas individuals in the more competitively efficient role generally gain the larger share of these resources. When asymmetry in relative competitive efficiency is greater, a group's per capita cooperation (averaged across both roles) is higher, due to increased cooperation from the competitively inferior individuals. For extreme asymmetry in relative competitive efficiency, per capita cooperation is highest in groups with a single competitively superior individual and many competitively inferior individuals, because the latter acquiesce and invest in cooperation rather than within-group competition. These predictions are consistent with observed features of many societies, such as monogynous Hymenoptera with many workers and caste dimorphism.

Regression, least squares, and the general version of inclusive fitness

A general version of inclusive fitness based on regression is rederived with minimal mathematics and directly from the verbal interpretation of its terms that motivated the original formulation of the inclusive fitness concept. This verbal interpretation is here extended to provide the two relationships required to determine the two coefficients -c and b. These coefficients retain their definition as expected effects on the fitness of an individual, respectively of a change in allelic state of this individual, and of correlated change in allelic state of social partners. The known least-squares formulation of the relationships determining b and c can be immediately deduced and shown to be equivalent to this new formulation. These results make clear that criticisms of the mathematical tools (in particular least-squares regression) previously used to derive this version of inclusive fitness are misdirected.

Does microchimerism mediate kin conflicts?

Fetal microchimerism (FMc) is predicted to promote the fitness of the fetus and maternal microchimerism (MMc) to promote the fitness of the mother. Offspring and mothers benefit from each other's health. Therefore, microchimeric cells should usually not be harmful to their host. However, the evolutionary interests of mothers and offspring diverge when there is competition among siblings for maternal investment. Fetal cells in mothers' bodies could benefit their own offspring at the expense of its sibs by promoting lactogenesis or by extending the interbirth interval. Maternal cells in fetal bodies could benefit from the suppression of sibling rivalry. Non-inherited haplotypes in MMc or sibling microchimerism (SMc) gain no direct benefit from their hosts' health and could be associated with substantial detrimental effects.

Extensive fitness and human cooperation

Evolution depends on the fitness of organisms, the expected rate of reproducing. Directly getting offspring is the most basic form of fitness, but fitness can also be increased indirectly by helping genetically related individuals (such as kin) to increase their fitness. The combined effect is known as inclusive fitness. Here it is argued that a further elaboration of fitness has evolved, particularly in humans. It is called extensive fitness and it incorporates producing organisms that are merely similar in phenotype. The evolvability of this mechanism is illustrated by computations on a simple model combining heredity and behaviour. Phenotypes are driven into the direction of high fitness through a mechanism that involves an internal estimate of fitness, implicitly made within the organism itself. This mechanism has recently been conjectured to be responsible for producing agency and goals. In the model, inclusive and extensive fitness are both implemented by letting fitness increase nonlinearly with the size of subpopulations of similar heredity (for the indirect part of inclusive fitness) and of similar phenotype (for the phenotypic part of extensive fitness). Populations implementing extensive fitness outcompete populations implementing mere inclusive fitness. This occurs because groups with similar phenotype tend to be larger than groups with similar heredity, and fitness increases more when groups are larger. Extensive fitness has two components, a direct component where individuals compete in inducing others to become like them and an indirect component where individuals cooperate and help others who are already similar to them.

Sex investment ratios in eusocial Hymenoptera support inclusive fitness theory

Inclusive fitness theory predicts that sex investment ratios in eusocial Hymenoptera are a function of the relatedness asymmetry (relative relatedness to females and males) of the individuals controlling sex allocation. In monogynous ants (with one queen per colony), assuming worker control, the theory therefore predicts female-biased sex investment ratios, as found in natural populations. Recently, E.O. Wilson and M.A. Nowak criticized this explanation and presented an alternative hypothesis. The Wilson-Nowak sex ratio hypothesis proposes that, in monogynous ants, there is selection for a 1 : 1 numerical sex ratio to avoid males remaining unmated, which, given queens exceed males in size, results in a female-biased sex investment ratio. The hypothesis also asserts that, contrary to inclusive fitness theory, queens not workers control sex allocation and queen-worker conflict over sex allocation is absent. Here, I argue that the Wilson-Nowak sex ratio hypothesis is flawed because it contradicts Fisher's sex ratio theory, which shows that selection on sex ratio does not maximize the number of mated offspring and that the sex ratio proposed by the hypothesis is not an equilibrium for the queen. In addition, the hypothesis is not supported by empirical evidence, as it fails to explain 'split' (bimodal) sex ratios or data showing queen and worker control and ongoing queen-worker conflict. By contrast, these phenomena match predictions of inclusive fitness theory. Hence, the Wilson-Nowak sex ratio hypothesis fails both as an alternative hypothesis for sex investment ratios in eusocial Hymenoptera and as a critique of inclusive fitness theory.

More on the genetical theory of multilevel selection

In my article The genetical theory of multilevel selection, I provided a synthesis of the theory of multilevel selection (MLS) and the theory of natural selection in class-structured populations. I framed this synthesis within Fisher's genetical paradigm, taking a strictly genetical approach to traits and fitness. I showed that this resolves a number of long-standing conceptual problems that have plagued the MLS literature, including the issues of 'aggregate' vs. 'emergent' group traits, 'collective fitness1 ' vs. 'collective fitness2 ' and 'MLS1' vs. 'MLS2 '. In his commentary, Goodnight suggests this theoretical and conceptual synthesis is flawed in several respects. Here, I show this is incorrect, by: reiterating the theoretical and conceptual goals of my synthesis; clarifying that my genetical approach to traits is necessary for a proper analysis of the action of MLS independently of non-Darwinian factors; emphasizing that the Price-Hamilton approach to MLS provides a consistent, useful and conceptually superior theoretical framework; and explaining the role of reproductive value in the study of natural selection in class-structured populations. I also show that Goodnight's contextual analysis treatment of MLS in a class-structured population is mathematically, biologically and conceptually inadequate.

Multilevel selection theory and evidence: a critique of Gardner, 2015

Gardner (2015) recently developed a model of a 'Genetical Theory of Multilevel Selection, which is a thoughtfully developed, but flawed model. The model's flaws appear to be symptomatic of common misunderstandings of the multi level selection (MLS) literature and the recent quantitative genetic literature. I use Gardner's model as a guide for highlighting how the MLS literature can address the misconceptions found in his model, and the kin selection literature in general. I discuss research on the efficacy of group selection, the roll of indirect genetic effects in affecting the response to selection and the heritability of group-level traits. I also discuss why the Price multilevel partition should not be used to partition MLS, and why contextual analysis and, by association, direct fitness are appropriate for partitioning MLS. Finally, I discuss conceptual issues around questions concerning the level at which fitness is measured, the units of selection, and I present a brief outline of a model of selection in class-structured populations. I argue that the results derived from the MLS research tradition can inform kin selection research and models, and provide insights that will allow researchers to avoid conceptual flaws such as those seen in the Gardner model.

Games among relatives revisited

We present a simple model for the evolution of social behavior in family-structured, finite sized populations. Interactions are represented as evolutionary games describing frequency-dependent selection. Individuals interact more frequently with siblings than with members of the general population, as quantified by an assortment parameter r, which can be interpreted as "relatedness". Other models, mostly of spatially structured populations, have shown that assortment can promote the evolution of cooperation by facilitating interaction between cooperators, but this effect depends on the details of the evolutionary process. For our model, we find that sibling assortment promotes cooperation in stringent social dilemmas such as the Prisoner's Dilemma, but not necessarily in other situations. These results are obtained through straightforward calculations of changes in gene frequency. We also analyze our model using inclusive fitness. We find that the quantity of inclusive fitness does not exist for general games. For special games, where inclusive fitness exists, it provides less information than the straightforward analysis.

The interpretation of selection coefficients

Evolutionary biologists have an array of powerful theoretical techniques that can accurately predict changes in the genetic composition of populations. Changes in gene frequencies and genetic associations between loci can be tracked as they respond to a wide variety of evolutionary forces. However, it is often less clear how to decompose these various forces into components that accurately reflect the underlying biology. Here, we present several issues that arise in the definition and interpretation of selection and selection coefficients, focusing on insights gained through the examination of selection coefficients in multilocus notation. Using this notation, we discuss how its flexibility-which allows different biological units to be identified as targets of selection-is reflected in the interpretation of the coefficients that the notation generates. In many situations, it can be difficult to agree on whether loci can be considered to be under "direct" versus "indirect" selection, or to quantify this selection. We present arguments for what the terms direct and indirect selection might best encompass, considering a range of issues, from viability and sexual selection to kin selection. We show how multilocus notation can discriminate between direct and indirect selection, and describe when it can do so.

Inclusive fitness theorizing invokes phenomena that are not relevant for the evolution of eusociality

In this Formal Comment, the authors challenge the claims of a recent theoretical study that genetic relatedness is important in the evolution of eusociality.

Relatedness, conflict, and the evolution of eusociality

The evolution of sterile worker castes in eusocial insects was a major problem in evolutionary theory until Hamilton developed a method called inclusive fitness. He used it to show that sterile castes could evolve via kin selection, in which a gene for altruistic sterility is favored when the altruism sufficiently benefits relatives carrying the gene. Inclusive fitness theory is well supported empirically and has been applied to many other areas, but a recent paper argued that the general method of inclusive fitness was wrong and advocated an alternative population genetic method. The claim of these authors was bolstered by a new model of the evolution of eusociality with novel conclusions that appeared to overturn some major results from inclusive fitness. Here we report an expanded examination of this kind of model for the evolution of eusociality and show that all three of its apparently novel conclusions are essentially false. Contrary to their claims, genetic relatedness is important and causal, workers are agents that can evolve to be in conflict with the queen, and eusociality is not so difficult to evolve. The misleading conclusions all resulted not from incorrect math but from overgeneralizing from narrow assumptions or parameter values. For example, all of their models implicitly assumed high relatedness, but modifying the model to allow lower relatedness shows that relatedness is essential and causal in the evolution of eusociality. Their modeling strategy, properly applied, actually confirms major insights of inclusive fitness studies of kin selection. This broad agreement of different models shows that social evolution theory, rather than being in turmoil, is supported by multiple theoretical approaches. It also suggests that extensive prior work using inclusive fitness, from microbial interactions to human evolution, should be considered robust unless shown otherwise.

Mathematical modelling shows that the evolution of sterile castes requires genetic relatedness but also involves conflicts between kin; these results contradict recent claims but agree with inclusive fitness theory.

The evolution of sterile worker castes in social insects has fascinated biologists ever since Darwin; how can selection favor a trait that decreases reproductive fitness? W. D. Hamilton solved this dilemma in the 1960s with a theory showing that reproductive altruism could evolve if it increased the worker’s inclusive fitness, which included effects that it had on increasing the fitness of its relatives. This solution to a crucial evolutionary problem, sometimes called kin selection, was challenged in a recent paper. The paper generated much controversy, but no one has contested its new theoretical model of the evolution of eusociality, which appeared to overturn much of what was previously thought to be true from kin selection theory. Here we examine this model in greater depth, showing that its apparently novel conclusions are overgeneralized from narrow and often inappropriate assumptions. Instead, this modeling strategy yields results that confirm important insights from kin selection and inclusive fitness, such as the importance of relatedness and the existence of conflicts in social insect colonies.

The genetical theory of multilevel selection

The theory of multilevel selection (MLS) is beset with conceptual difficulties. Although it is widely agreed that covariance between group trait and group fitness may arise in the natural world and drive a response to 'group selection', ambiguity exists over the precise meaning of group trait and group fitness and as to whether group selection should be defined according to changes in frequencies of different types of individual or different types of group. Moreover, the theory of MLS has failed to properly engage with the problem of class structure, which greatly limits its empirical application to, for example, social insects whose colonies are structured into separate age, sex, caste and ploidy classes. Here, I develop a genetical theory of MLS, to address these problems. I show that taking a genetical approach facilitates a decomposition of group-level traits - including reproductive success - into the separate contributions made by each constituent individual, even in the context of so-called emergence. However, I uncover a novel problem with the group-oriented approach: in many scenarios, it may not be possible to express a meaningful covariance between trait and fitness at the level of the social group, because the group's constituents belong to separate, irreconcilable classes.

Mating ecology explains patterns of genome elimination

Genome elimination - whereby an individual discards chromosomes inherited from one parent, and transmits only those inherited from the other parent - is found across thousands of animal species. It is more common in association with inbreeding, under male heterogamety, in males, and in the form of paternal genome elimination. However, the reasons for this broad pattern remain unclear. We develop a mathematical model to determine how degree of inbreeding, sex determination, genomic location, pattern of gene expression and parental origin of the eliminated genome interact to determine the fate of genome-elimination alleles. We find that: inbreeding promotes paternal genome elimination in the heterogametic sex; this may incur population extinction under female heterogamety, owing to eradication of males; and extinction is averted under male heterogamety, owing to countervailing sex-ratio selection. Thus, we explain the observed pattern of genome elimination. Our results highlight the interaction between mating system, sex-ratio selection and intragenomic conflict.

Fluctuation driven fixation of cooperative behavior

Cooperative behaviors are defined as the production of common goods benefitting all members of the community at the producer's cost. They could seem to be in contradiction with natural selection, as non-cooperators have an increased fitness compared to cooperators. Understanding the emergence of cooperation has necessitated the development of concepts and models (inclusive fitness, multilevel selection, etc.) attributing deterministic advantages to this behavior. In contrast to these models, we show here that cooperative behaviors can emerge by taking into account only the stochastic nature of evolutionary dynamics: when cooperative behaviors increase the population size, they also increase the genetic drift against non-cooperators. Using the Wright-Fisher models of population genetics, we compute exactly this increased genetic drift and its consequences on the fixation probability of both types of individuals. This computation leads to a simple criterion: cooperative behavior dominates when the relative increase in population size caused by cooperators is higher than the selection pressure against them. This is a purely stochastic effect with no deterministic interpretation.

Site-specific group selection drives locally adapted group compositions

Group selection may be defined as selection caused by the differential extinction or proliferation of groups. The socially polymorphic spider Anelosimus studiosus exhibits a behavioural polymorphism in which females exhibit either a 'docile' or 'aggressive' behavioural phenotype. Natural colonies are composed of a mixture of related docile and aggressive individuals, and populations differ in colonies' characteristic docile:aggressive ratios. Using experimentally constructed colonies of known composition, here we demonstrate that population-level divergence in docile:aggressive ratios is driven by site-specific selection at the group level--certain ratios yield high survivorship at some sites but not others. Our data also indicate that colonies responded to the risk of extinction: perturbed colonies tended to adjust their composition over two generations to match the ratio characteristic of their native site, thus promoting their long-term survival in their natal habitat. However, colonies of displaced individuals continued to shift their compositions towards mixtures that would have promoted their survival had they remained at their home sites, regardless of their contemporary environment. Thus, the regulatory mechanisms that colonies use to adjust their composition appear to be locally adapted. Our data provide experimental evidence of group selection driving collective traits in wild populations.

A microbial model of economic trading and comparative advantage

The economic theory of comparative advantage postulates that beneficial trading relationships can be arrived at by two self-interested entities producing the same goods as long as they have opposing relative efficiencies in producing those goods. The theory predicts that upon entering trade, in order to maximize consumption both entities will specialize in producing the good they can produce at higher efficiency, that the weaker entity will specialize more completely than the stronger entity, and that both will be able to consume more goods as a result of trade than either would be able to alone. We extend this theory to the realm of unicellular organisms by developing mathematical models of genetic circuits that allow trading of a common good (specifically, signaling molecules) required for growth in bacteria in order to demonstrate comparative advantage interactions. In Conception 1, the experimenter controls production rates via exogenous inducers, allowing exploration of the parameter space of specialization. In Conception 2, the circuits self-regulate via feedback mechanisms. Our models indicate that these genetic circuits can demonstrate comparative advantage, and that cooperation in such a manner is particularly favored under stringent external conditions and when the cost of production is not overly high. Further work could involve implementing the models in living bacteria and searching for naturally occurring cooperative relationships between bacteria that conform to the principles of comparative advantage.

Queller's separation condition explained and defended

The theories of inclusive fitness and multilevel selection provide alternative perspectives on social evolution. The question of whether these perspectives are of equal generality remains a divisive issue. In an analysis based on the Price equation, Queller argued (by means of a principle he called the separation condition) that the two approaches are subject to the same limitations, arising from their fundamentally quantitative-genetical character. Recently, van Veelen et al. have challenged Queller's results, using this as the basis for a broader critique of the Price equation, the separation condition, and the very notion of inclusive fitness. Here we show that the van Veelen et al. model, when analyzed in the way Queller intended, confirms rather than refutes his original conclusions. We thereby confirm (i) that Queller's separation condition remains a legitimate theoretical principle and (ii) that the standard inclusive fitness and multilevel approaches are indeed subject to the same limitations.

Natural selection drives the evolution of ant life cycles

The genetic origin of advanced social organization has long been one of the outstanding problems of evolutionary biology. Here we present an analysis of the major steps in ant evolution, based for the first time, to our knowledge, on combined recent advances in paleontology, phylogeny, and the study of contemporary life histories. We provide evidence of the causal forces of natural selection shaping several key phenomena: (i) the relative lateness and rarity in geological time of the emergence of eusociality in ants and other animal phylads; (ii) the prevalence of monogamy at the time of evolutionary origin; and (iii) the female-biased sex allocation observed in many ant species. We argue that a clear understanding of the evolution of social insects can emerge if, in addition to relatedness-based arguments, we take into account key factors of natural history and study how natural selection acts on alleles that modify social behavior.

A simple model of group selection that cannot be analyzed with inclusive fitness

A widespread claim in evolutionary theory is that every group selection model can be recast in terms of inclusive fitness. Although there are interesting classes of group selection models for which this is possible, we show that it is not true in general. With a simple set of group selection models, we show two distinct limitations that prevent recasting in terms of inclusive fitness. The first is a limitation across models. We show that if inclusive fitness is to always give the correct prediction, the definition of relatedness needs to change, continuously, along with changes in the parameters of the model. This results in infinitely many different definitions of relatedness - one for every parameter value - which strips relatedness of its meaning. The second limitation is across time. We show that one can find the trajectory for the group selection model by solving a partial differential equation, and that it is mathematically impossible to do this using inclusive fitness.

Genetic information transfer promotes cooperation in bacteria

Many bacterial species are social, producing costly secreted "public good" molecules that enhance the growth of neighboring cells. The genes coding for these cooperative traits are often propagated via mobile genetic elements and can be virulence factors from a biomedical perspective. Here, we present an experimental framework that links genetic information exchange and the selection of cooperative traits. Using simulations and experiments based on a synthetic bacterial system to control public good secretion and plasmid conjugation, we demonstrate that horizontal gene transfer can favor cooperation. In a well-mixed environment, horizontal transfer brings a direct infectious advantage to any gene, regardless of its cooperation properties. However, in a structured population transfer selects specifically for cooperation by increasing the assortment among cooperative alleles. Conjugation allows cooperative alleles to overcome rarity thresholds and invade bacterial populations structured purely by stochastic dilution effects. Our results provide an explanation for the prevalence of cooperative genes on mobile elements, and suggest a previously unidentified benefit of horizontal gene transfer for bacteria.

A conceptual framework for organismal biology: linking theories, models, and data

Implicit or subconscious theory is especially common in the biological sciences. Yet, theory plays a variety of roles in scientific inquiry. First and foremost, it determines what does and does not count as a valid or interesting question or line of inquiry. Second, theory determines the background assumptions within which inquiries are pursued. Third, theory provides linkages among disciplines. For these reasons, it is important and useful to develop explicit theories for biology. A general theory of organisms is developed, which includes 10 fundamental principles that apply to all organisms, and 6 that apply to multicellular organisms only. The value of a general theory comes from its utility to help guide the development of more specific theories and models. That process is demonstrated by examining two domains: ecoimmunology and development. For the former, a constitutive theory of ecoimmunology is presented, and used to develop a specific model that explains energetic trade-offs that may result from an immunological response of a host to a pathogen. For the latter, some of the issues involved in trying to devise a constitutive theory that covers all of development are explored, and a more narrow theory of phenotypic novelty is presented. By its very nature, little of a theory of organisms will be new. Rather, the theory presented here is a formal expression of nearly two centuries of conceptual advances and practice in research. Any theory is dynamic and subject to debate and change. Such debate will occur as part of the present, initial formulation, as the ideas presented here are refined. The very process of debating the form of the theory acts to clarify thinking. The overarching goal is to stimulate debate about the role of theory in the study of organisms, and thereby advance our understanding of them.

Evolutionary dynamics of n-player games played by relatives

One of the core concepts in social evolution theory is kin selection. Kin selection provides a perspective to understand how natural selection operates when genetically similar individuals are likely to interact. A family-structured population is an excellent example of this, where relatives are engaged in social interactions. Consequences of such social interactions are often described in game-theoretical frameworks, but there is a growing consensus that a naive inclusive fitness accounting with dyadic relatedness coefficients are of limited use when non-additive fitness effects are essential in those situations. Here, I provide a general framework to analyse multiplayer interactions among relatives. Two important results follow from my analysis. First, it is generally necessary to know the n-tuple genetic association of family members when n individuals are engaged in social interactions. However, as a second result, I found that, for a special class of games, we need only measures of lower-order genetic association to fully describe its evolutionary dynamics. I introduce the concept of degree of the game and show how this degree is related to the degree of genetic association.

Effects of genetic similarity on the life-history strategy of co-infecting trematodes: are parasites capable of intrahost kin recognition?

For conspecific parasites sharing the same host, kin recognition can be advantageous when the fitness of one individual depends on what another does; yet, evidence of kin recognition among parasites remains limited. Some trematodes, like Coitocaecum parvum, have plastic life cycles including two alternative life-history strategies. The parasite can wait for its intermediate host to be eaten by a fish definitive host, thus completing the classical three-host life cycle, or mature precociously and produce eggs while still inside its intermediate host as a facultative shortcut. Two different amphipod species are used as intermediate hosts by C. parvum, one small and highly mobile and the other larger, sedentary, and burrow dwelling. Amphipods often harbour two or more C. parvum individuals, all capable of using one or the other developmental strategy, thus creating potential conflicts or cooperation opportunities over transmission routes. This model was used to test the kin recognition hypothesis according to which cooperation between two conspecific individuals relies on the individuals' ability to evaluate their degree of genetic similarity. First, data showed that levels of intrahost genetic similarity between co-infecting C. parvum individuals differed between host species. Second, genetic similarity between parasites sharing the same host was strongly linked to their likelihood of adopting identical developmental strategies. Two nonexclusive hypotheses that could explain this pattern are discussed: kin recognition and cooperation between genetically similar parasites and/or matching genotypes involving parasite genotype-host compatibility filters.

The genetical theory of social behaviour

We survey the population genetic basis of social evolution, using a logically consistent set of arguments to cover a wide range of biological scenarios. We start by reconsidering Hamilton's (Hamilton 1964 J. Theoret. Biol. 7, 1-16 (doi:10.1016/0022-5193(64)90038-4)) results for selection on a social trait under the assumptions of additive gene action, weak selection and constant environment and demography. This yields a prediction for the direction of allele frequency change in terms of phenotypic costs and benefits and genealogical concepts of relatedness, which holds for any frequency of the trait in the population, and provides the foundation for further developments and extensions. We then allow for any type of gene interaction within and between individuals, strong selection and fluctuating environments and demography, which may depend on the evolving trait itself. We reach three conclusions pertaining to selection on social behaviours under broad conditions. (i) Selection can be understood by focusing on a one-generation change in mean allele frequency, a computation which underpins the utility of reproductive value weights; (ii) in large populations under the assumptions of additive gene action and weak selection, this change is of constant sign for any allele frequency and is predicted by a phenotypic selection gradient; (iii) under the assumptions of trait substitution sequences, such phenotypic selection gradients suffice to characterize long-term multi-dimensional stochastic evolution, with almost no knowledge about the genetic details underlying the coevolving traits. Having such simple results about the effect of selection regardless of population structure and type of social interactions can help to delineate the common features of distinct biological processes. Finally, we clarify some persistent divergences within social evolution theory, with respect to exactness, synergies, maximization, dynamic sufficiency and the role of genetic arguments.

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.

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.

War and peace: social interactions in infections

One of the most striking facts about parasites and microbial pathogens that has emerged in the fields of social evolution and disease ecology in the past few decades is that these simple organisms have complex social lives, indulging in a variety of cooperative, communicative and coordinated behaviours. These organisms have provided elegant experimental tests of the importance of relatedness, kin discrimination, cooperation and competition, in driving the evolution of social strategies. Here, we briefly review the social behaviours of parasites and microbial pathogens, including their contributions to virulence, and outline how inclusive fitness theory has helped to explain their evolution. We then take a mechanistically inspired ‘bottom-up’ approach, discussing how key aspects of the ways in which parasites and pathogens exploit hosts, namely public goods, mobile elements, phenotypic plasticity, spatial structure and multi-species interactions, contribute to the emergent properties of virulence and transmission. We argue that unravelling the complexities of within-host ecology is interesting in its own right, and also needs to be better incorporated into theoretical evolution studies if social behaviours are to be understood and used to control the spread and severity of infectious diseases.

Inclusive fitness maximization: An axiomatic approach

Kin selection theorists argue that evolution in social contexts will lead organisms to behave as if maximizing their inclusive, as opposed to personal, fitness. The inclusive fitness concept allows biologists to treat organisms as akin to rational agents seeking to maximize a utility function. Here we develop this idea and place it on a firm footing by employing a standard decision-theoretic methodology. We show how the principle of inclusive fitness maximization and a related principle of quasi-inclusive fitness maximization can be derived from axioms on an individual׳s 'as if preferences' (binary choices) for the case in which phenotypic effects are additive. Our results help integrate evolutionary theory and rational choice theory, help draw out the behavioural implications of inclusive fitness maximization, and point to a possible way in which evolution could lead organisms to implement it.

Continuous-time models of group selection, and the dynamical insufficiency of kin selection models

Traditionally, the process of group selection has been described mathematically by discrete-time models, and analyzed using tools like the Price equation. This approach makes implicit assumptions about the process that are not valid in general, like the central role of synchronized mass-dispersion and group re-formation events. In many important examples (like hunter-gatherer tribes) there are no mass-dispersion events, and the group-level events that do occur, like fission, fusion, and extinction, occur asynchronously. Examples like these can be fully analyzed by the equations of two-level population dynamics (described here) so their models are dynamically sufficient. However, it will be shown that examples like these cannot be fully analyzed by kin selection (inclusive fitness) methods because kin selection versions of group selection models are not dynamically sufficient. This is a critical mathematical difference between group selection and kin selection models, which implies that the two theories are not mathematically equivalent.

Adaptation and inclusive fitness

Inclusive fitness theory captures how individuals can influence the transmission of their genes to future generations by influencing either their own reproductive success or that of related individuals. This framework is frequently used for studying the way in which natural selection leads to organisms being adapted to their environments. A number of recent papers have criticised this approach, suggesting that inclusive fitness is just one of many possible mathematical methods for modelling when traits will be favoured by natural selection, and that it leads to errors, such as overemphasising the role of common ancestry relative to other mechanisms that could lead to individuals being genetically related. Here, we argue that these suggested problems arise from a misunderstanding of two fundamental points: first, inclusive fitness is more than just a mathematical 'accounting method' - it is the answer to the question of what organisms should appear designed to maximise; second, there is something special about relatedness caused by common ancestry, in contrast with the other mechanisms that may lead to individuals being genetically related, because it unites the interests of genes across the genome, allowing complex, multigenic adaptations to evolve. The critiques of inclusive fitness theory have provided neither an equally valid answer to the question of what organisms should appear designed to maximise, nor an alternative process to unite the interest of genes. Consequently, inclusive fitness remains the most general theory for explaining adaptation.

The quantitative genetics of indirect genetic effects: a selective review of modelling issues

Indirect genetic effects (IGE) occur when the genotype of an individual affects the phenotypic trait value of another conspecific individual. IGEs can have profound effects on both the magnitude and the direction of response to selection. Models of inheritance and response to selection in traits subject to IGEs have been developed within two frameworks; a trait-based framework in which IGEs are specified as a direct consequence of individual trait values, and a variance-component framework in which phenotypic variance is decomposed into a direct and an indirect additive genetic component. This work is a selective review of the quantitative genetics of traits affected by IGEs, with a focus on modelling, estimation and interpretation issues. It includes a discussion on variance-component vs trait-based models of IGEs, a review of issues related to the estimation of IGEs from field data, including the estimation of the interaction coefficient Ψ (psi), and a discussion on the relevance of IGEs for response to selection in cases where the strength of interaction varies among pairs of individuals. An investigation of the trait-based model shows that the interaction coefficient Ψ may deviate considerably from the corresponding regression coefficient when feedback occurs. The increasing research effort devoted to IGEs suggests that they are a widespread phenomenon, probably particularly in natural populations and plants. Further work in this field should considerably broaden our understanding of the quantitative genetics of inheritance and response to selection in relation to the social organisation of populations.

Cultural transmission and the evolution of human behaviour: a general approach based on the Price equation

Transmitted culture can be viewed as an inheritance system somewhat independent of genes that is subject to processes of descent with modification in its own right. Although many authors have conceptualized cultural change as a Darwinian process, there is no generally agreed formal framework for defining key concepts such as natural selection, fitness, relatedness and altruism for the cultural case. Here, we present and explore such a framework using the Price equation. Assuming an isolated, independently measurable culturally transmitted trait, we show that cultural natural selection maximizes cultural fitness, a distinct quantity from genetic fitness, and also that cultural relatedness and cultural altruism are not reducible to or necessarily related to their genetic counterparts. We show that antagonistic coevolution will occur between genes and culture whenever cultural fitness is not perfectly aligned with genetic fitness, as genetic selection will shape psychological mechanisms to avoid susceptibility to cultural traits that bear a genetic fitness cost. We discuss the difficulties with conceptualizing cultural change using the framework of evolutionary theory, the degree to which cultural evolution is autonomous from genetic evolution, and the extent to which cultural change should be seen as a Darwinian process. We argue that the nonselection components of evolutionary change are much more important for culture than for genes, and that this and other important differences from the genetic case mean that different approaches and emphases are needed for cultural than genetic processes.

Biological information: why we need a good measure and the challenges ahead

Evolution can be characterized as a process that shapes and maintains information across generations. It is also widely acknowledged that information may play a pivotal role in many other ecological processes. Most of the ecologically relevant information (and some important evolutionary information too) is of a very subjective and analogue kind: individuals use cues that may carry information useful only to them but not to others. This is a problem because most information theory has been developed for objective and discrete information. Can information theory be extended to this theory to incorporate multiple forms of information, each with its own (physical) carriers and dynamics? Here, I will not review all the possible roles that information can play, but rather what conditions an appropriate theory should satisfy. The most promising starting point is provided by entropy measures of conditional probabilities (using the so-called Kullback-Leibler divergence), allowing an assessment of how acquiring information can lead to an increase in fitness. It is irrelevant (to a certain extent) where the information comes from-genes, experience or culture-but it is important to realize that information is not merely subjective but its value should be evaluated in fitness terms, and it is here that evolutionary theory has an enormous potential. A number of important stumbling points remain, however; namely, the identification of whose fitness it concerns and what role the spatio-temporal dynamics plays (which is tightly linked to the nature of the physical carriers of the information and the processes that impact on it).