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.

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). 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.

Organismal duplication, inclusive fitness theory, and altruism: understanding the evolution of endosperm and the angiosperm reproductive syndrome.

For almost a century, events relating to the evolutionary origin of endosperm, a unique embryo-nourishing tissue that is essential to the reproductive process in flowering plants, have remained a mystery. Integration of recent advances in phylogenetic reconstruction, comparative reproductive biology, and genetic theory can be used to elucidate the evolutionary events and forces associated with the establishment of endosperm. Endosperm is shown to be derived from one of two embryos formed during a rudimentary process of "double fertilization" that evolved in the ancestors of angiosperms. Acquisition of embryo-nourishing behavior (with accompanying loss of individual fitness) by this supernumerary fertilization product was dependent upon compensatory gains in the inclusive fitness of related embryos. The result of the loss of individual fitness by one of the two original products of double fertilization was the establishment of endosperm, a highly modified embryo/organism that reproduces cryptically through behavior that enhances the fitness of its associated embryo within a seed. Finally, although triploid endosperm remains a synapomorphy of angiosperms, inclusive fitness analysis demonstrates that the embryo-nourishing properties of endosperm initially evolved in a diploid condition.

Kin-bias, breeding site selection and female fitness in a cannibalistic Neotropical frog

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The number of reproductive workers in highly eusocial Hymenoptera: monogyny and monandry

Haplodiploidy results in relatedness asymmetries between colony members of highly eusocial Hymenoptera. As a consequence, queen and reproductive workers are more related to their own sons than to each other's male offspring. Kin selection theory predicts multiple optima in male parentage: either the queen or the workers should produce all the males. Nevertheless, shared male parentage is common in highly eusocial hymenopterans. An inclusive fitness model was used to analyze the effect of the number of reproductive workers on male parentage shared by the queen and laying workers by isolating the male component from an inclusive fitness equation using the equal fitness through male condition for each pairwise combination of the three female classes comprised of the queen, laying workers and non-laying workers. The main result of the theoretical analyses showed that the fraction of males produced by workers increases asymptotically with the number of laying workers at an increasingly diminishing rate, tending to an asymptotic value of 0.67. In addition, as the number of laying workers increases, the share of male parentage converges to that of non-laying workers. The diminishing return effect on male parentage share depending on the number of reproductive workers leads us to expect the number of reproductive workers to be relatively small in a stingless bee colony, even in the absence of productivity costs. The available data confirms this hypothesis, as there is an unusually small number of reproductive workers in stingless bee colonies.

Co-occurrence of three types of egg policing in the Norwegian wasp Dolichovespula norwegica

In insect societies, workers often try to challenge the reproductive monopoly of the queen by laying their own eggs. Successful worker reproduction, however, is frequently prevented by queen policing or worker policing, whereby either the mother queen or non-reproductive workers selectively kill worker-laid eggs. Recently, a third mechanism-""selfish"" worker policing-has also been described in which the workers selectively police worker-laid eggs but also lay eggs themselves. Here, we present results from the monogynous wasp Dolichovespula norwegica, which show that all three kinds of policing-queen policing, worker policing and ""selfish"" worker policing-co-occur. The net effect of these three kinds of policing collectively favoured the queen`s reproduction, as within 1 day 44% of the worker-laid eggs versus only 8% of the queen-laid eggs were eaten. Of the worker-laid eggs that were killed by workers, approximately two thirds were eaten by the reproductive workers even though these made up only a small proportion, 8%, of the work force. This means that policing workers obtained both direct fitness benefits as well as indirect (inclusive) fitness. In addition, we show that worker policing was carried out by a limited, specialised set of workers that was estimated to constitute approximately one quarter of the whole colony and of which 66% were non-reproductive.

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.