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 phi(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.

The evolution of helping and harming on graphs: the return of the inclusive fitness effect.

Evolutionary graph theory has been proposed as providing new fundamental rules for the evolution of co-operation and altruism. But how do these results relate to those of inclusive fitness theory? Here, we carry out a retrospective analysis of the models for the evolution of helping on graphs of Ohtsuki et al. [Nature (2006) 441, 502] and Ohtsuki & Nowak [Proc. R. Soc. Lond. Ser. B Biol. Sci (2006) 273, 2249]. We show that it is possible to translate evolutionary graph theory models into classical kin selection models without disturbing at all the mathematics describing the net effect of selection on helping. Model analysis further demonstrates that costly helping evolves on graphs through limited dispersal and overlapping generations. These two factors are well known to promote relatedness between interacting individuals in spatially structured populations. By allowing more than one individual to live at each node of the graph and by allowing interactions to vary with the distance between nodes, our inclusive fitness model allows us to consider a wider range of biological scenarios leading to the evolution of both helping and harming behaviours on graphs.

Inclusive fitness theory and eusociality.

Arising from M. A. Nowak, C. E. Tarnita & E. O. Wilson 466, 1057-1062 (2010); Nowak et al. reply. Nowak et al. argue that inclusive fitness theory has been of little value in explaining the natural world, and that it has led to negligible progress in explaining the evolution of eusociality. However, we believe that their arguments are based upon a misunderstanding of evolutionary theory and a misrepresentation of the empirical literature. We will focus our comments on three general issues.

Inbreeding avoidance through kin recognition: choosy females boost male dispersal.

Inbreeding avoidance is predicted to induce sex biases in dispersal. But which sex should disperse? In polygynous species, females pay higher costs to inbreeding and thus might be expected to disperse more, but empirical evidence consistently reveals male biases. Here, we show that theoretical expectations change drastically if females are allowed to avoid inbreeding via kin recognition. At high inbreeding loads, females should prefer immigrants over residents, thereby boosting male dispersal. At lower inbreeding loads, by contrast, inclusive fitness benefits should induce females to prefer relatives, thereby promoting male philopatry. This result points to disruptive effects of sexual selection. The inbreeding load that females are ready to accept is surprisingly high. In absence of search costs, females should prefer related partners as long as delta<r/(1+r) where r is relatedness and delta is the fecundity loss relative to an outbred mating. This amounts to fitness losses up to one-fifth for a half-sib mating and one-third for a full-sib mating, which lie in the upper range of inbreeding depression values currently reported in natural populations. The observation of active inbreeding avoidance in a polygynous species thus suggests that inbreeding depression exceeds this threshold in the species under scrutiny or that inbred matings at least partly forfeit other mating opportunities for males. Our model also shows that female choosiness should decline rapidly with search costs, stemming from, for example, reproductive delays. Species under strong time constraints on reproduction should thus be tolerant of inbreeding.

Kin structure and queen execution in the Argentine ant Linepithema humile

Every spring, workers of the Argentine Ant Linepithema humile kill a large proportion of queens within their nests, Although this behaviour inflicts a high energetic cost oil the colonies, its biological significance has remained elusive so far. An earlier study showed that the probability of a queen being executed is not related to her weight, fecundity, or age. Here we test the hypothesis that workers collectively eliminate queens to which they are less related, thereby increasing their inclusive fitness. We found no evidence for this hypothesis. Workers of a nest were on average not significantly less related to executed queens than to surviving ones. Moreover, a population genetic analysis revealed that workers were not genetically differentiated between nests. This means that workers of a given nest are equally related to any queen in the population and that there can be no increase in average worker-queen relatedness by selective elimination of queens. Finally, our genetic analyses also showed that, in contrast to workers, queens were significantly genetically differentiated between nests and that there was significant isolation by distance for queens.

Stay or drift? Queen acceptance in the ant Formica paralugubris

The acceptance of new queens in ant colonies has profound effects on colony kin structure and inclusive fitness of workers. Therefore, it is important to study the recognition and discrimination behaviour of workers towards reproductive individuals entering established colonies. We examined the acceptance rate of queens in populations of the highly polygynous ant F. paralugubris, where the genetic differentiation among nests and discrimination ability among workers suggest that workers might reject foreign queens. We experimentally introduced young queens in their natal nest and in foreign nests. Surprisingly, the survival rate of mated queens did not differ significantly when introduced in a foreign male-producing nest, a foreign female-producing nest, or the natal nest. Moreover, the survival of virgin queens in their natal nest was twice the one of mated queens, suggesting that mating status plays an important role for acceptance. The results indicate that other factors than queen discrimination by workers are implicated in the limited long-distance gene flow between nests in these populations.

The role of queen pheromones in social insects: queen control or queen signal?

Queens and workers in social insect colonies can differ in reproductive goals such as colony-level sex allocation and production of males by workers. That the presence of queen(s) often seems to affect worker behaviour in situations of potential conflict has given rise to the idea of queen control over reproduction. In small colonies queen control is possible via direct aggression against workers, but in large colonies queens cannot be effectively aggressive towards all the workers. This, plus evidence that queen-produced chemicals affect worker behaviour, has led to the conclusion that physical intimidation has been replaced by pheromonal queen control, whereby queen(s) chemically manipulate workers into behaving in ways that increase the queen's fitness at the worker's expense. It is argued in this paper, however, that pheromonal queen control has never conclusively been demonstrated and is evolutionarily difficult to justify. Proposed examples of pheromonal control are more likely to be honest signals, with workers' responses increasing their own inclusive fitness. A series of experimental and field studies in which positive results would give prima facie evidence for pheromonal queen control is suggested. Finally, three terms are defined: (1) pheromonal queen control for workers or subordinate queens being chemically manipulated into acting against their own best interests; (2) pheromonal queen signal for situations where workers or subordinate queens react to queen pheromones in ways that increase their, and possibly the queens', inclusive fitness; and (3) pheromonal queen effect where changes in the workers' or subordinate queens' behaviour have an unknown consequence on their inclusive fitness.

Altruism, dispersal, and phenotype-matching kin recognition.

We investigate the coevolution between philopatry and altruism in island-model populations when kin recognition occurs through phenotype matching. In saturated environments, a good discrimination ability is a necessary prerequisite for the emergence of sociality. Discrimination decreases not only with the average phenotypic similarity between immigrants and residents (i.e., with environmental homogeneity and past gene flow) but also with the sampling variance of similarity distributions (a negative function of the number of traits sampled). Whether discrimination should rely on genetically or environmentally determined traits depends on the apportionment of phenotypic variance and, in particular, on the relative values of e (the among-group component of environmental variance) and r (the among-group component of genetic variance, which also measures relatedness among group members). If r exceeds e, highly heritable cues do better. Discrimination and altruism, however, remain low unless philopatry is enforced by ecological constraints. If e exceeds r, by contrast, nonheritable traits do better. High e values improve discrimination drastically and thus have the potential to drive sociality, even in the absence of ecological constraints. The emergence of sociality thus can be facilitated by enhancing e, which we argue is the main purpose of cue standardization within groups, as observed in many social insects, birds, and mammals, including humans.

No evidence that within-group male relatedness reduces harm to females in Drosophila.

Conflict between males and females over whether, when, and how often to mate often leads to the evolution of sexually antagonistic interactions that reduce female reproductive success. Because the offspring of relatives contribute to inclusive fitness, high relatedness between rival males might be expected to reduce competition and result in the evolution of reduced harm to females. A recent study investigated this possibility in Drosophila melanogaster and concluded that groups of brothers cause less harm to females than groups of unrelated males, attributing the effect to kin selection. That study did not control for the rearing environment of males, rendering the results impossible to interpret in the context of kin selection. Here, we conducted a similar experiment while manipulating whether males developed with kin prior to being placed with females. We found no difference between related and unrelated males in the harm caused to females when males were reared separately. In contrast, when related males developed and emerged together before the experiment, female reproductive output was higher. Our results show that relatedness among males is insufficient to reduce harm to females, while a shared rearing environment - resulting in males similar to or familiar with one another - is necessary to generate this pattern.

Sex-ratio regulation: the economics of fratricide in ants

In many insect societies, workers can manipulate the reproductive output of their colony by killing kin of lesser value to them. For instance, workers of the mound-building For mica exsecta eliminate male brood in colonies headed by a single-mated queen. By combining an inclusive fitness model and empirical data, we investigated the selective causes underlying these fratricides. Our model examines until which threshold stage in male brood development do the workers benefit from eliminating males to rear extra females instead. We then determined the minimal developmental stage reached by male larvae before elimination in F. exsecta field colonies. Surprisingly, many male larvae were kept until they were close to pupation, and only then eliminated. According to our model, part of the eliminated males were so large that workers would not benefit from replacing them with new females. Moreover, males were eliminated late in the season, so that new females could no longer be initiated, because matings take place synchronously during a short period. Together, these results indicate that workers did not replace male brood with new females, but rather reduced total brood size during late larval development. Male destruction was probably triggered by resource limitation, and the timing of brood elimination suggests that males may have been fed to females when these start to grow exponentially during the final larval stage. Hence, the evolution of fratricides in ants is best explained by a combination of ecological, demographic and genetic parameters.

The stationary distribution of a continuously varying strategy in a class-structured population under mutation-selection-drift balance.

Many traits and/or strategies expressed by organisms are quantitative phenotypes. Because populations are of finite size and genomes are subject to mutations, these continuously varying phenotypes are under the joint pressure of mutation, natural selection and random genetic drift. This article derives the stationary distribution for such a phenotype under a mutation-selection-drift balance in a class-structured population allowing for demographically varying class sizes and/or changing environmental conditions. The salient feature of the stationary distribution is that it can be entirely characterized in terms of the average size of the gene pool and Hamilton's inclusive fitness effect. The exploration of the phenotypic space varies exponentially with the cumulative inclusive fitness effect over state space, which determines an adaptive landscape. The peaks of the landscapes are those phenotypes that are candidate evolutionary stable strategies and can be determined by standard phenotypic selection gradient methods (e.g. evolutionary game theory, kin selection theory, adaptive dynamics). The curvature of the stationary distribution provides a measure of the stability by convergence of candidate evolutionary stable strategies, and it is evaluated explicitly for two biological scenarios: first, a coordination game, which illustrates that, for a multipeaked adaptive landscape, stochastically stable strategies can be singled out by letting the size of the gene pool grow large; second, a sex-allocation game for diploids and haplo-diploids, which suggests that the equilibrium sex ratio follows a Beta distribution with parameters depending on the features of the genetic system.

The adaptive dynamics of niche constructing traits in spatially subdivided populations: evolving posthumous extended phenotypes.

Niche construction, by which organisms modify the environment in which they live, has been proposed to affect the evolution of many phenotypic traits. But what about the evolution of a niche constructing trait itself, whose expression changes the pattern of natural selection to which the trait is exposed in subsequent generations? This article provides an inclusive fitness analysis of selection on niche constructing phenotypes, which can affect their environment from local to global scales in arbitrarily spatially subdivided populations. The model shows that phenotypic effects of genes extending far beyond the life span of the actor can be affected by natural selection, provided they modify the fitness of those individuals living in the future that are likely to have inherited the niche construction lineage of the actor. Present benefits of behaviors are thus traded off against future indirect costs. The future costs will generally result from a complicated interplay of phenotypic effects, population demography and environmental dynamics. To illustrate these points, I derive the adaptive dynamics of a trait involved in the consumption of an abiotic resource, where resource abundance in future generations feeds back to the evolutionary dynamics of the trait.

Sham nepotism as a result of intrinsic differences in brood viability in ants.

In animal societies, cooperation for the common wealth and latent conflicts due to the selfish interests of individuals are in delicate balance. In many ant species, colonies contain multiple breeders and workers interact with nestmates of varying degrees of relatedness. Therefore, workers could increase their inclusive fitness by preferentially caring for their closest relatives, yet evidence for nepotism in insect societies remains scarce and controversial. We experimentally demonstrate that workers of the ant Formica exsecta do not discriminate between highly related and unrelated brood, but that brood viability differs between queens. We further show that differences in brood viability are sufficient to explain a relatedness pattern that has previously been interpreted as evidence for nepotism. Hence, our findings support the view that nepotism remains elusive in social insects and emphasize the need for further controlled experiments.

Only full-sibling families evolved eusociality.

Arising from M. A. Nowak, C. E. Tarnita & E. O. Wilson 466, 1057-1062 (2010); Nowak et al. reply. The paper by Nowak et al. has the evolution of eusociality as its title, but it is mostly about something else. It argues against inclusive fitness theory and offers an alternative modelling approach that is claimed to be more fundamental and general, but which, we believe, has no practical biological meaning for the evolution of eusociality. Nowak et al. overlook the robust empirical observation that eusociality has only arisen in clades where mothers are associated with their full-sibling offspring; that is, in families where the average relatedness of offspring to siblings is as high as to their own offspring, independent of population structure or ploidy. We believe that this omission makes the paper largely irrelevant for understanding the evolution of eusociality.