Kinship,parental manipulation and evolutionary origins of eusociality

One of the hallmarks of eusociality is that workers forego their own reproduction to assist their mother in raising siblings. This seemingly altruistic behaviour may benefit workers if gains in indirect fitness from rearing siblings outweigh the loss of direct fitness. If worker presence is advantageous to mothers, however, eusociality may evolve without net benefits to workers. Indirect fitness benefits are often cited as evidence for the importance of inclusive fitness in eusociality, but have rarely been measured in natural populations. We compared inclusive fitness of alternative social strategies in the tropical sweat bee, Megalopta genalis, for which eusociality is optional. Our results show that workers have significantly lower inclusive fitness than females that found their own nests. In mathematical simulations based on M. genalis field data, eusociality cannot evolve with reduced intra-nest relatedness. The simulated distribution of alternative social strategies matched observed distributions of M. genalis social strategies when helping behaviour was simulated as the result of maternal manipulation, but not as worker altruism. Thus, eusociality in M. genalis is best explained through kin selection, but the underlying mechanism is likely maternal manipulation.     

Detecting kin selection at work using inclusive fitness

A recent model shows that altruism can evolve with limited migration and variable group sizes, and the authors claim that kin selection cannot provide a sufficient explanation of their results. It is demonstrated, using a recent reformulation of Hamilton's original arguments, that the model falls squarely within the scope of inclusive fitness theory, which furthermore shows how to calculate inclusive fitness and the relevant relatedness. A distinction is drawn between inclusive fitness, which is a method of analysing social behaviour; and kin selection, a process that operates through genetic similarity brought about by common ancestry, but not by assortation by genotype or by direct assessment of genetic similarity. The recent model is analysed, and it turns out that kin selection provides a sufficient explanation to considerable quantitative accuracy, contrary to the authors' claims. A parallel analysis is possible and would be illuminating for all models of social behaviour in which individuals' effects on each other's offspring numbers combine additively.     

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.     

Why kin and group selection models may not be enough to explain human other-regarding behaviour

Models of kin or group selection usually feature only one possible fitness transfer. The phenotypes are either to make this transfer or not to make it and for any given fitness transfer, Hamilton's rule predicts which of the two phenotypes will spread. In this article we allow for the possibility that different individuals or different generations face similar, but not necessarily identical possibilities for fitness transfers. In this setting, phenotypes are preference relations, which concisely specify behaviour for a range of possible fitness transfers (rather than being a specification for only one particular situation an animal or human can be in). For this more general set-up, we find that only preference relations that are linear in fitnesses can be explained using models of kin selection and that the same applies to a large class of group selection models. This provides a new implication of hierarchical selection models that could in principle falsify them, even if relatedness--or a parameter for assortativeness--is unknown. The empirical evidence for humans suggests that hierarchical selection models alone are not enough to explain their other-regarding or altruistic behaviour.     

Inclusive fitness,asymmetric competition and kin selection in plants

The findings that some plants alter their competitive phenotype in response to genetic relatedness of its conspecific neighbour (and presumed competitor) has spurred an increasing interest in plant kin‐interactions. This phenotypic response suggests the ability to assess the genetic relatedness of conspecific competitors, proposing kin selection as a process that can influence plant competitive interactions. Kin selection can favour restrained competitive growth towards kin, if the fitness loss from reducing own growth is compensated by increased fitness in the related neighbour. This may lead to positive frequency dependency among related conspecifics with important ecological consequences for species assemblage and coexistence. However, kin selection in plants is still controversial. First, many studies documenting a plastic response to neighbour relatedness do not estimate fitness consequences of the individual that responds, and when estimated, fitness of individuals grown in competition with kin did not necessarily exceed that of individuals grown in non‐kin groups. Although higher fitness in kin groups could be consistent with kin selection, this could also arise from mechanisms like asymmetric competition in the non‐kin groups. Here we outline the main challenges for studying kin selection in plants taking genetic variation for competitive ability into account. We emphasize the need to measure inclusive fitness in order to assess whether kin selection occurs, and show under which circumstances kin selected responses can be expected. We also illustrate why direct fitness estimates of a focal plant, and group fitness estimates are not suitable for documenting kin selection. Importantly, natural selection occurs at the individual level and it is the inclusive fitness of an individual plant – not the mean fitness of the group – that can capture if a differential response to neighbour relatedness is favoured by kin selection.     

Analysis of disruptive selection in subdivided populations

Background

Analytical methods have been proposed to determine whether there are evolutionarily stable strategies (ESS) for a trait of ecological significance, or whether there is disruptive selection in a population approaching a candidate ESS. These criteria do not take into account all consequences of small patch size in populations with limited dispersal.

Results

We derive local stability conditions which account for the consequences of small and constant patch size. All results are derived from considering R_m, the overall production of successful emigrants from a patch initially colonized by a single mutant immigrant. Further, the results are interpreted in term of concepts of inclusive fitness theory. The condition for convergence to an evolutionarily stable strategy is proportional to some previous expressions for inclusive fitness. The condition for evolutionary stability stricto sensu takes into account effects of selection on relatedness, which cannot be neglected. It is function of the relatedness between pairs of genes in a neutral model and also of a three-genes relationship. Based on these results, I analyze basic models of dispersal and of competition for resources. In the latter scenario there are cases of global instability despite local stability. The results are developed for haploid island models with constant patch size, but the techniques demonstrated here would apply to more general scenarios with an island mode of dispersal.

Conclusions

The results allow to identity and to analyze the relative importance of the different selective pressures involved. They bridge the gap between the modelling frameworks that have led to the R_m concept and to inclusive fitness.

     

Hamilton's rule confronts ideal free habitat selection

If individuals occupy habitats in a way that maximizes their fitness, if they are free to occupy the habitats they choose and if fitness declines with population density, then their abundance across habitats should follow an ideal free distribution. But, if individuals are genetically related, this simple fitness-maximization mechanism breaks down. Habitat occupation should obey Hamilton's rule (natural selection favours traits causing a loss in individual fitness as long as they result in an equal or greater gain in inclusive fitness) and depends more on inclusive fitness than it does on individual fitness. We demonstrate that the resulting inclusive-fitness distribution inflates the population density in habitats of poorer inherent quality, creating pronounced source sink dynamics. We also show that density-dependent habitat selection among relatives reinforces behaviours such as group defence and interspecific territoriality, and that it explains many anomalies in dispersal and foraging.     

A reconciliation of inclusive fitness and personal fitness approaches: a proposed correcting term for the inclusive fitness formula

Hamilton implicitly defined the inclusive fitness of an individual as the number of genomes, identical by descent to its own, but not in its own body, which owe their existence to expression of genes in said individual. Hamilton regarded inclusive fitness as the true metric of evolutionary success and the thin- maximized by selection. Williams, Stern and Orlove either claimed this property for mean reproductive success, or stated that expected reproductive success equals expected inclusive fitness. These statements are reconciled if a correcting term is added to Hamilton's inclusive fitness formula.This change completely accounts for inclusive fitness in personal fitness terminology. The use of ? in place of r renders the new formula exact. This has less numerical impact than the addition of the correcting term to begin with, but helps show inclusive fitness theory holds exactly.     

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.     

Reproductive skew in cooperative breeding: Environmental variability,antagonistic selection,choice, and control

A multitude of factors may determine reproductive skew among cooperative breeders. One explanation, derived from inclusive fitness theory, is that groups can partition reproduction such that subordinates do at least as well as noncooperative solitary individuals. The majority of recent data, however, fails to support this prediction; possibly because inclusive fitness models cannot easily incorporate multiple factors simultaneously to predict skew. Notable omissions are antagonistic selection (across generations, genes will be in both dominant and subordinate bodies), constraints on the number of sites suitable for successful reproduction, choice in which group an individual might join, and within‐group control or suppression of competition. All of these factors and more are explored through agent‐based evolutionary simulations. The results suggest the primary drivers for the initial evolution of cooperative breeding may be a combination of limited suitable sites, choice across those sites, and parental manipulation of offspring into helping roles. Antagonistic selection may be important when subordinates are more frequent than dominants. Kinship matters, but its main effect may be in offspring being available for manipulation while unrelated individuals are not. The greater flexibility of evolutionary simulations allows the incorporation of species‐specific life histories and ecological constraints to better predict sociobiology.     

Diffusion approximations for one-locus multi-allele kin selection,mutation and random drift in group-structured populations: a unifying approach to selection models in population genetics

Diffusion approximations are ascertained from a two-time-scale argument in the case of a group-structured diploid population with scaled viability parameters depending on the individual genotype and the group type at a single multi-allelic locus under recurrent mutation, and applied to the case of random pairwise interactions within groups. The main step consists in proving global and uniform convergence of the distribution of the group types in an infinite population in the absence of selection and mutation, using a coalescent approach. An inclusive fitness formulation with coefficient of relatedness between a focal individual J affecting the reproductive success of an individual I, defined as the expected fraction of genes in I that are identical by descent to one or more genes in J in a neutral infinite population, given that J is allozygous or autozygous, yields the correct selection drift functions. These are analogous to the selection drift functions obtained with pure viability selection in a population with inbreeding. They give the changes of the allele frequencies in an infinite population without mutation that correspond to the replicator equation with fitness matrix expressed as a linear combination of a symmetric matrix for allozygous individuals and a rank-one matrix for autozygous individuals. In the case of no inbreeding, the mean inclusive fitness is a strict Lyapunov function with respect to this deterministic dynamics. Connections are made between dispersal with exact replacement (proportional dispersal), uniform dispersal, and local extinction and recolonization. The timing of dispersal (before or after selection, before or after mating) is shown to have an effect on group competition and the effective population size. In memory of Sam Karlin.     

Invasion fitness,inclusive fitness,and reproductive numbers in heterogeneous populations

How should fitness be measured to determine which phenotype or “strategy” is uninvadable when evolution occurs in a group‐structured population subject to local demographic and environmental heterogeneity? Several fitness measures, such as basic reproductive number, lifetime dispersal success of a local lineage, or inclusive fitness have been proposed to address this question, but the relationships between them and their generality remains unclear. Here, we ascertain uninvadability (all mutant strategies always go extinct) in terms of the asymptotic per capita number of mutant copies produced by a mutant lineage arising as a single copy in a resident population (“invasion fitness”). We show that from invasion fitness uninvadability is equivalently characterized by at least three conceptually distinct fitness measures: (i) lineage fitness, giving the average individual fitness of a randomly sampled mutant lineage member; (ii) inclusive fitness, giving a reproductive value weighted average of the direct fitness costs and relatedness weighted indirect fitness benefits accruing to a randomly sampled mutant lineage member; and (iii) basic reproductive number (and variations thereof) giving lifetime success of a lineage in a single group, and which is an invasion fitness proxy. Our analysis connects approaches that have been deemed different, generalizes the exact version of inclusive fitness to class‐structured populations, and provides a biological interpretation of natural selection on a mutant allele under arbitrary strength of selection.     

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.     

A rule is not a rule if it changes from case to case (a reply to Marshall's comment)

This is a reply to “Queller's rule ok: Comment on van Veelen ‘when inclusive fitness is right and when it can be wrong’ ” by James Marshall in the Journal of Theoretical Biology, in this issue.In order to circumvent the disagreement about the Price equation and focus on the issue of the predictive power of inclusive fitness for group selection models, I derive Queller's and Marshall's rule without the Price equation. Both rules however need a translation step in order to be able to link them to the group selection model in van Veelen (2009). Queller's rule applies to games with 2 players and 2 strategies, and is general. Marshall's rule on the other hand applies only to a small subset of 3-player games. His rule is correct, but for other, similarly small subsets we would get other rules. This implies that if we want a rule that applies to all symmetric games with 3 players and 2 strategies, it will have to use a vector of dimension 2 that represents population structure. More in general: for group selection models with groups of size n, a correct and general prediction will need to use a vector of dimension n−1 that represents population structure.     

A note on frequency dependence and the levels/units of selection

On the basis of distinctions between those properties of entities that can be defined without reference to other entities and those that (in different ways) cannot, this note argues that non-trivial forms of frequency-dependent selection of entities should be interpreted as selection occurring at a level higher than that of those entities. It points out that, except in degenerately simple cases, evolutionary game-theoretic models of selection are not models of individual selection. Similarly, models of genotypic selection such as heterosis cannot be legitimately interpreted as models of genic selection. The analysis presented here supports the views that: (i) selection should be viewed as a multi-level process; (ii) upper-level selection is ubiquitous; (iii) kin selection should be viewed as a type of group selection rather than individual selection; and (iv) inclusive fitness is not an individual property.

Kin selection and frequency dependence: a game theoretic approach

Game theory models show that the evolution of interactions between relatives is determined by two kinds of fitness effects: Hamilton's inclusive fitness effect, and a frequency-dependent synergistic effect. The latter arises when an individual's behaviour has different effects on the fitness of interactants, depending on whether or not they perform the same behaviour. Knowing the sign of the synergistic effect is sufficient to understand most of the qualitative features of genetic models that show departures from Hamilton's rule. Since this synergistic effect does not depend on the interactants being related, it is best viewed as something distinct from kin selection. In this view, Hamilton's rule is basically correct for describing kin selection, and most deviations from it are due to the distinct process of synergistic selection.     

Models of the evolution of altruism

There are two ways of calculating the spread of a gene for altruism. One, originally proposed by Hamilton, is to allow for the effects of the gene on the survival and reproduction of collateral relatives of the individual carrying it (i.e., “inclusive fitness”); this leads to the condition k > 1/r for the spread of the gene, where k is a benefit/cost ratio. The other is to count only the direct offspring of a carrier, but to allow for the altruistic acts performed toward the carrier by its relatives (“neighbour modulated fitness” or “personal fitness”). A recent personal fitness model (L. L. Cavalli Sforza and M. W. Feldman, 1978, Theor. Pop. Biol.14, 268–280) analyses parent-offspring and sib-sib altruism and concludes that k > 1/r is applicable only when fitness components are combined additively. The present paper analyses some simple models in which the phenotypic effects are carefully specified. It is concluded that it is sometimes, but not always, appropriate to combine fitness components additively. The relative roles of inclusive and personal fitness models are compared. The former have the virtue of being easier to think about in causal terms; and the latter of incorporating the evolution of altruism into the corpus of population genetics as an example of frequency-dependent selection.     

Kin selection in Columbian ground squirrels: direct and indirect fitness benefits

Empirical and theoretical studies have supported kin selection by demonstrating nepotism or modelling its conditions and consequences. As an alternative, we previously found that female Columbian ground squirrels had greater direct fitness when more close kin were present. Extending those results, we used population matrix methods to calculate minimum estimates of individual fitness, estimated direct and indirect components of fitness, estimated inclusive fitness by adding the direct fitness (stripped of estimated influences of the social environment) and indirect fitness components together, and finally looked for inclusive fitness benefits of associations with close kin who seem to be 'genial neighbours'. We examined the estimated fitness of a sample of 35 females for which complete lifetimes were known for themselves, their mothers and their littermate sisters. Six of these females had no cosurviving adult close kin, and their direct fitness was significantly lower than 29 females with such kin (λ = 0.66 vs. λ = 1.23). The net fitness benefit of the presence of close kin was thus 0.57. The estimated indirect component of fitness through benefits to the direct fitness of close kin was 0.43. Thus, estimated inclusive fitness for females with cosurviving close kin (λ = 1.09) was significantly greater than that for females without surviving close kin (viz., λ = 0.66). The presence of closely related and philopatric female kin appeared to result in considerable fitness benefits for female ground squirrels, perhaps through the behavioural mechanisms of lowered aggression and other forms of behavioural cooperation.     

Joint phenotypes,evolutionary conflict and the fundamental theorem of natural selection

Multiple organisms can sometimes affect a common phenotype. For example, the portion of a leaf eaten by an insect is a joint phenotype of the plant and insect and the amount of food obtained by an offspring can be a joint trait with its mother. Here, I describe the evolution of joint phenotypes in quantitative genetic terms. A joint phenotype for multiple species evolves as the sum of additive genetic variances in each species, weighted by the selection on each species. Selective conflict between the interactants occurs when selection takes opposite signs on the joint phenotype. The mean fitness of a population changes not just through its own genetic variance but also through the genetic variance for its fitness that resides in other species, an update of Fisher''s fundamental theorem of natural selection. Some similar results, using inclusive fitness, apply to within-species interactions. The models provide a framework for understanding evolutionary conflicts at all levels.     

Reconciling social interaction with habitat selection in territorial species

The concept of habitat selection as the primary force in clustered distributions has been challenged by behavioral studies of conspecific attraction. This has lead to two conflicting explanations for settlement behavior, which we have integrated into one model. This model creates a range of fitness outcomes for different settlement strategies, encompassing the four combinations of positive and negative effects of the habitat selection and social interaction. It expands the ideal free distribution models (negative intra-specific interactions and positive habitat selection), to consider alternative situations where (1) beneficial social interaction increases fitness for clustered pairs in poor quality habitat, (2) neither habitat selection nor conspecific attraction can improve fitness, and (3) where both are beneficial and do not interfere with each other. The model does this by establishing an intrinsic fitness, where the effects of both habitat selection (h) and conspecific attractions (c) are neutral (h = c = 1) and do not influence settlement. Clustered distributions occur when h · c > 1 because the fitness in clusters is greater than intrinsic fitness. Dispersed distributions occur when h · c < 1 and fitness is lower than the intrinsic. The benefit of the model is that it allows conspecific attraction to be considered a positive force in fitness without rejecting the proven concept of ideal free distribution.