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.     

The sociobiology of sex: inclusive fitness consequences of inter-sexual interactions

The diversity of social interactions between sexual partners has long captivated biologists, and its evolution has been interpreted largely in terms of 'direct fitness' pay-offs to partners and their descendants. Inter-sexual interactions also have 'indirect effects' by affecting the fitness of relatives, with important consequences for inclusive fitness. However, inclusive fitness arguments have received limited consideration in this context, and definitions of 'direct' and 'indirect' fitness effects in this field are often inconsistent with those of inclusive fitness theory. Here, we use a sociobiology approach based on inclusive fitness theory to distinguish between direct and indirect fitness effects. We first consider direct effects: we review how competition leads to sexual conflict, and discuss the conditions under which repression of competition fosters sexual mutualism. We then clarify indirect effects, and show that greenbeard effects, kin recognition and population viscosity can all lead to episodes of indirect selection on sexual interactions creating potential for sexual altruism and spite. We argue that the integration of direct and indirect fitness effects within a sociobiology approach enables us to consider a more diverse spectrum of evolutionary outcomes of sexual interactions, and may help resolving current debates over sexual selection and sexual conflict.     

Fitness,inclusive fitness,and optimization

Individual-as-maximizing agent analogies result in a simple understanding of the functioning of the biological world. Identifying the conditions under which individuals can be regarded as fitness maximizing agents is thus of considerable interest to biologists. Here, we compare different concepts of fitness maximization, and discuss within a single framework the relationship between Hamilton’s (J Theor Biol 7:1–16, 1964) model of social interactions, Grafen’s (J Evol Biol 20:1243–1254, 2007a) formal Darwinism project, and the idea of evolutionary stable strategies. We distinguish cases where phenotypic effects are additive separable or not, the latter not being covered by Grafen’s analysis. In both cases it is possible to define a maximand, in the form of an objective function ?(z), whose argument is the phenotype of an individual and whose derivative is proportional to Hamilton’s inclusive fitness effect. However, this maximand can be identified with the expression for fecundity or fitness only in the case of additive separable phenotypic effects, making individual-as-maximizing agent analogies unattractive (although formally correct) under general situations of social interactions. We also feel that there is an inconsistency in Grafen’s characterization of the solution of his maximization program by use of inclusive fitness arguments. His results are in conflict with those on evolutionary stable strategies obtained by applying inclusive fitness theory, and can be repaired only by changing the definition of the problem.     

Policing and punishment across the domains of social evolution

Several decades of research in humans, other vertebrates, and social insects have offered fascinating insights into the dynamics of punishment (and its subset, policing), but authors have only rarely addressed whether there are fundamental joint principles underlying the maintenance of these behaviors. Here we present a punisher/bystander approach rooted in inclusive fitness logic to predict which individuals should take on punishing roles in animal societies. We apply our scheme to societies of eusocial Hymenoptera and nonhuman vertebrate social breeders, and we outline potential extensions for understanding conflict regulation among cells in metazoan bodies and unrelated individuals in human societies. We highlight that: 1) no social unit is expected to express punishment behavior unless it collects positive inclusive fitness benefits that surpass alternative benefits of bystanding; 2) punishment with public good benefits can be maintained through either direct fitness benefits (coercion) or indirect fitness benefits (correction) or both; 3) differences across social systems in the distributions of power, relatedness, and reproductive options drive variation in the extent to which individuals actively punish; and 4) inclusive fitness logic captures many punishment‐relevant evolutionary and ecological variables in a single framework that appears to apply across very different types of social arrangements. Synthesis Researchers have long observed that individuals in animal societies punish (and by extension, police) each other, but they have rarely investigated whether general principles underlie this behavior across social arrangements. In this paper, we present a punisher/bystander approach rooted in inclusive fitness logic to predict which individuals should take on punisher roles in animal societies. We apply the approach to eusocial insects and cooperatively breeding vertebrates and outline extensions towards the control of cancer cell lineages and punishment in human groups. We highlight how variation in specific social variables may drive differences in punishing/policing across the social domains.     

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.     

Inclusive Fitness from Multitype Branching Processes

I use multitype branching processes to study genetic models for the evolution of social behaviour, i.e. behaviours that, when acted out, affect the success of the actor’s neighbours. Here, I suppose an individual bearing a mutant copy of a gene influences the reproductive success of a neighbour by altering its own competitive ability. Approximations based on assumptions about the rareness of the mutant allele and the strength of selection allow me to formulate statements concerning the probability of mutant extinction in terms of inclusive fitness. Inclusive fitness is an idea well known to biologists and can be thought of as a sum of an individual’s fitness and the fitness of each of its relatives, weighted by some measure of genetic relatedness. Previous work has led to some confusion surrounding the definition of the inclusive-fitness effect of a mutant allele when individuals carrying that allele experience demographic conditions that fluctuate randomly. In this paper, I emphasise the link between inclusive fitness and the probability of mutant extinction. I recover standard results for populations of constant size, and I show that inclusive fitness can be used to determine the short-term fate of mutants in the face of stochastic demographic fluctuations. Overall, then, I provide a connection between certain inclusive-fitness-based approaches routinely applied in theoretical studies of social evolution.     

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.     

The philosophy of modelling or does the philosophy of biology have any use?

Biologists in search of answers to real-world issues such as the ecological consequences of global warming, the design of species'' conservation plans, understanding landscape dynamics and understanding gene expression make decisions constantly that are based on a ‘philosophical’ stance as to how to create and test explanations of an observed phenomenon. For better or for worse, some kind of philosophy is an integral part of the doing of biology. Given this, it is more important than ever to undertake a practical assessment of what philosophy does mean and should mean to biologists. Here, I address three questions: should biologists pay any attention to ‘philosophy’; should biologists pay any attention to ‘philosophy of biology’; and should biologists pay any attention to the philosophy of biology literature on modelling? I describe why the last question is easily answered affirmatively, with the proviso that the practical benefits to be gained by biologists from this literature will be directly proportional to the extent to which biologists understand ‘philosophy’ to be a part of biology, not apart from biology.     

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.     

Grandmothering and natural selection

Humans are unique among primates in that women regularly outlive their reproductive period by decades. The grandmother hypothesis proposes that natural selection increased the length of the human post-menopausal period—and, thus, extended longevity—as a result of the inclusive fitness benefits of grandmothering. However, it has yet to be demonstrated that the inclusive fitness benefits associated with grandmothering are large enough to warrant this explanation. Here, we show that the inclusive fitness benefits are too small to affect the evolution of longevity under a wide range of conditions in simulated populations. This is due in large part to the relatively weak selection that applies to women near or beyond the end of their reproductive period. However, we find that grandmothers can facilitate the evolution of a shorter reproductive period when their help decreases the weaning age of their matrilineal grandchildren. Because selection favours a shorter reproductive period in the presence of shorter interbirth intervals, this finding holds true for any form of allocare that helps mothers resume cycling more quickly. We conclude that while grandmothering is unlikely to explain human-like longevity, allocare could have played an important role in shaping other unique aspects of human life history, such as a later age at first birth and a shorter female reproductive period.     

Assortative mating for relatedness in a large naturally occurring population of Drosophila melanogaster

New theoretical work on kin selection and inclusive fitness benefits predicts that individuals will sometimes choose close or intermediate relatives as mates to maximize their fitness. However, empirical examples supporting such predictions are rare. In this study, we look for such evidence in a natural population of Drosophila melanogaster. We compared mating and nonmating individuals to test whether mating was nonrandom with respect to relatedness. Consistent with optimal inbreeding, males were more closely related to their mate than to randomly sampled females. However, all individuals collected mating showed higher relatedness and males were not significantly more related to their mate than to other mating females. We also found a negative relationship between relatedness and fecundity. Our results are consistent with the hypothesis that inclusive fitness benefits may drive inbreeding tolerance despite direct costs to fitness; however, an experimental approach is needed to investigate the link between mate preference and relatedness.     

MATHEMATICS OF KIN‐ AND GROUP‐SELECTION: FORMALLY EQUIVALENT?

Evolutionary game theory is a general mathematical framework that describes the evolution of social traits. This framework forms the basis of many multilevel selection models and is also frequently used to model evolutionary dynamics on networks. Kin selection, which was initially restricted to describe social interactions between relatives, has also led to a broader mathematical approach, inclusive fitness, that can not only describe social evolution among relatives, but also in group structured populations or on social networks. It turns out that the underlying mathematics of game theory is fundamentally different from the approach of inclusive fitness. Thus, both approaches—evolutionary game theory and inclusive fitness—can be helpful to understand the evolution of social traits in group structured or spatially extended populations.     

The replicator dynamics with n players and population structure

The well-known replicator dynamics is usually applied to 2-player games and random matching. Here we allow for games with n players, and for population structures other than random matching. This more general application leads to a version of the replicator dynamics of which the standard 2-player, well-mixed version is a special case, and which allows us to explore the dynamic implications of population structure. The replicator dynamics also allows for a reformulation of the central theorem in Van Veelen (2009), which claims that inclusive fitness gives the correct prediction for games with generalized equal gains from switching (or, in other words, when fitness effects are additive). If we furthermore also assume that relatedness is constant during selection - which is a reasonable assumption in a setting with kin recognition - then inclusive fitness even becomes a parameter that determines the speed as well as the direction of selection. For games with unequal gains from switching, inclusive fitness can give the wrong prediction. With equal gains however, not only the sign, but also even the value of inclusive fitness becomes meaningful.     

Collective action in the fraternal transitions

Inclusive fitness theory was not originally designed to explain the major transitions in evolution, but there is a growing consensus that it has the resources to do so. My aim in this paper is to highlight, in a constructive spirit, the puzzles and challenges that remain. I first consider the distinctive aspects of the cooperative interactions we see within the most complex social groups in nature: multicellular organisms and eusocial insect colonies. I then focus on one aspect in particular: the extreme redundancy these societies exhibit. I argue that extreme redundancy poses a distinctive explanatory puzzle for inclusive fitness theory, and I offer a potential solution which casts coercion as the key enabler. I suggest that the general moral to draw from the case is one of guarded optimism: while inclusive fitness is a powerful tool for understanding evolutionary transitions, it must be integrated within a broader framework that recognizes the distinctive problems such transitions present and the distinctive mechanisms by which these problems may be overcome.     

Much ado about nothing: Nowak et al.'s charge against inclusive fitness theory

In a recent article, Nowak et al. claim that the mathematical basis of inclusive fitness theory does not stand to scrunity and to have found an alternative explanation for eusociality. We show that these claims are based on false premises, many of which have been exposed more than 25 years ago, such as misrepresentations of the basic components of inclusive fitness and fallacious distinctions between individual fitness and inclusive fitness. Moreover, some limitations ascribed to inclusive fitness are actually limitations of current evolutionary theory, for which Nowak et al. propose no new solution. Likewise, their assertedly 'common sense' empirical alternative to estimating inclusive fitness is not applicable in cases of interest. Finally, their eusociality model merely confirms the importance of all the components of inclusive fitness. We conclude by discussing how rhetorical devices and editorial practices can impede scientific endeavours.     

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.     

Policing effectiveness depends on relatedness and group size

Cohesion of social groups requires the suppression of individual selfishness. Indeed, worker egg laying in insect societies is usually suppressed or punished through aggression and egg removal. The effectiveness of such "policing" is expected to increase with decreasing relatedness, as inclusive fitness of group members is more strongly affected by selfish worker reproduction when group members are less closely related to each other. As inclusive fitness is also influenced by the costs and benefits of helping, the effectiveness of policing should decrease with increasing colony size, because the costs for the whole colony from selfish worker reproduction are proportionally reduced in large groups. Here, we show that policing effectiveness in colonies of the ant Temnothorax unifasciatus is low in large groups and high in small groups when relatedness is high. When we experimentally decreased the relatedness in groups, the policing effectiveness reached the same high level as in small, highly related groups, irrespective of group size. Therefore, our results indicate that policing effectiveness is simultaneously shaped by relatedness and group size, that is, an ecological factor. This may have major implications for testing policing across species of animals.     

A comparative study of egg recognition signature mixtures in Formica ants

Processing of information from the environment, such as assessing group membership in social contexts, is a major determinant of inclusive fitness. For social insects, recognizing brood origin is crucial for inclusive fitness in many contexts, such as social parasitism and kin conflicts within colonies. Whether a recognition signature is informative in kin conflicts depends on the extent of a genetic contribution into the cues. We investigated colony‐ and matriline‐specific variation in egg surface hydrocarbons in seven species of Formica ants. We show that chemical variance is distributed similarly to genetic variation, suggesting a significant genetic contribution to eggs odors in the genus. Significant among matriline components, and significant correlations between chemical and genetic similarity among individuals also indicate kin informative egg odors in several species. We suggest that egg odor surface variation could play a large role in within colony conflicts, and that a comparative method can reveal novel insight into communication of identity.     

The danger of applying the breeder's equation in observational studies of natural populations

The breeder's equation, which predicts evolutionary change when a phenotypic covariance exists between a heritable trait and fitness, has provided a key conceptual framework for studies of adaptive microevolution in nature. However, its application requires strong assumptions to be made about the causation of fitness variation. In its univariate form, the breeder's equation assumes that the trait of interest is not correlated with other traits having causal effects on fitness. In its multivariate form, the validity of predicted change rests on the assumption that all such correlated traits have been measured and incorporated into the analysis. Here, we (i) highlight why these assumptions are likely to be seriously violated in studies of natural, rather than artificial, selection and (ii) advocate wider use of the Robertson–Price identity as a more robust, and less assumption‐laden, alternative to the breeder's equation for applications in evolutionary ecology.     

Cooperation between non-relatives in a primitively eusocial paper wasp,Polistes dominula

In cooperatively breeding vertebrates, the existence of individuals that help to raise the offspring of non-relatives is well established, but unrelated helpers are less well known in the social insects. Eusocial insect groups overwhelmingly consist of close relatives, so populations where unrelated helpers are common are intriguing. Here, we focus on Polistes dominula—the best-studied primitively eusocial wasp, and a species in which nesting with non-relatives is not only present but frequent. We address two major questions: why individuals should choose to nest with non-relatives, and why such individuals participate in the costly rearing of unrelated offspring. Polistes dominula foundresses produce more offspring of their own as subordinates than when they nest independently, providing a potential explanation for co-founding by non-relatives. There is some evidence that unrelated subordinates tailor their behaviour towards direct fitness, while the role of recognition errors in generating unrelated co-foundresses is less clear. Remarkably, the remote but potentially highly rewarding chance of inheriting the dominant position appears to strongly influence behaviour, suggesting that primitively eusocial insects may have much more in common with their social vertebrate counterparts than has commonly been thought.