Can altruism evolve in purely viscous populations?

Summary Limited dispersal is often thought to facilitate the evolution of altruism by increasing the degree of relatedness among interacting individuals. Limited dispersal can have additional effects, however, such as local population regulation, that inhibits the evolution of altruism. Many models of structured populations assume that a viscous stage of the life cycle alternates with a global mixing stage, which allows the advantages of interactions among close relatives without the disadvantages of local population regulation. Here we analyse a computer simulation model of pure population viscosity, in which offspring are always deposited close to parents and no global mixing stage exists. As expected, limited dispersal generates a high coefficient of relatedness among interacting individuals. Patches of altruists, however, are unable to export their productivity to other regions of the landscape and are easily invaded by selfish types from neighbouring patches. Unlike models of alternating viscosity, in which high relatedness and local population regulation can be decoupled, these two opposing effects are inextricably linked in purely viscous populations, which therefore are not conducive to the evolution of altruistic traits.     

Group selection in plant populations

Summary Several mechanisms have been proposed for group selection, to account for the evolution of altruistic traits. One type, Neighbourhood models, suggests that individuals react with those immediately around them, but with no recognition mechanism. The organization of plant populations seems especially favorable for this type of selection. The possibility of Neighbourhood selection was investigated by simulating a plant population. It was possible for an altruistic trait to evolve, though only under restricted conditions. The main requirement was gene flow only by very restricted pollen dispersal, and a high benefit : cost ratio in the altruistic relationship. Under conditions favourable for such evolution, the starting frequency of the allele, the initial pattern, and the population size, had little effect. Inbreeding tended to prevent the increase of the altruism allele, though this depended on the mechanism of selfing. Known ecological features of plants are discussed that could be considered altruistic and hence require some form of group selection for their evolution, and whether the benefit : cost requirements are likely to be met. Neighbourhood models of group selection are a possibility in plant populations, and we therefore cannot exclude the possibility of altruism in plants. However, Neighbourhood selection is weak force, unlikely to be effective in the face of opposing individual selection. It may be more important as reinforcement of individual selection.     

The robustness of the weak selection approximation for the evolution of altruism against strong selection

The weak selection approximation of population genetics has made possible the analysis of social evolution under a considerable variety of biological scenarios. Despite its extensive usage, the accuracy of weak selection in predicting the emergence of altruism under limited dispersal when selection intensity increases remains unclear. Here, we derive the condition for the spread of an altruistic mutant in the infinite island model of dispersal under a Moran reproductive process and arbitrary strength of selection. The simplicity of the model allows us to compare weak and strong selection regimes analytically. Our results demonstrate that the weak selection approximation is robust to moderate increases in selection intensity and therefore provides a good approximation to understand the invasion of altruism in spatially structured population. In particular, we find that the weak selection approximation is excellent even if selection is very strong, when either migration is much stronger than selection or when patches are large. Importantly, we emphasize that the weak selection approximation provides the ideal condition for the invasion of altruism, and increasing selection intensity will impede the emergence of altruism. We discuss that this should also hold for more complicated life cycles and for culturally transmitted altruism. Using the weak selection approximation is therefore unlikely to miss out on any demographic scenario that lead to the evolution of altruism under limited dispersal.     

THE COMPONENTS OF KIN COMPETITION

It is well known that competition among kin alters the rate and often the direction of evolution in subdivided populations. Yet much remains unclear about the ecological and demographic causes of kin competition, or what role life cycle plays in promoting or ameliorating its effects. Using the multilevel Price equation, I derive a general equation for evolution in structured populations under an arbitrary intensity of kin competition. This equation partitions the effects of selection and demography, and recovers numerous previous models as special cases. I quantify the degree of kin competition, α, which explicitly depends on life cycle. I show how life cycle and demographic assumptions can be incorporated into kin selection models via α, revealing life cycles that are more or less permissive of altruism. As an example, I give closed‐form results for Hamilton's rule in a three‐stage life cycle. Although results are sensitive to life cycle in general, I identify three demographic conditions that give life cycle invariant results. Under the infinite island model, α is a function of the scale of density regulation and dispersal rate, effectively disentangling these two phenomena. Population viscosity per se does not impede kin selection.     

Kin selection and coefficients of relatedness in family-structured populations with inbreeding

We consider family specific fitnesses that depend on mixed strategies of two basic phenotypes or behaviours. Pairwise interactions are assumed, but they are restricted to occur between sibs. To study the change in frequency of a rare mutant allele, we consider two different forms of weak selection, one applied through small differences in genotypic values determining individual mixed strategies, the other through small differences in viabilities according to the behaviours chosen by interacting sibs. Under these two specific forms of weak selection, we deduce conditions for initial increase in frequency of a rare mutant allele for autosomal genes in the partial selfing model as well as autosomal and sex-linked genes in the partial sib-mating model with selection before mating or selection after mating. With small differences in mixed strategies, we show that conditions for protection of a mutant allele are tantamount to conditions for initial increase in frequency obtained in additive kin selection models. With particular reference to altruism versus selfishness, we provide explicit ranges of values for the selfing or sib-mating rate based on a fixed cost-benefit ratio and the dominance scheme that allow the spreading of a rare mutant allele into the population. This study confirms that more inbreeding does not necessarily promote the evolution of altruism. Under the hypothesis of small differences in viabilities, the situation is much more intricate unless an additive model is assumed. In general however, conditions for initial increase in frequency of a mutant allele can be obtained in terms of fitness effects that depend on the genotypes of interacting individuals or their mates and generalized conditional coefficients of relatedness according to the inbreeding condition of the interacting individuals.     

Population viscosity and the evolution of altruism

The term population viscosity refers to limited dispersal, which increases the genetic relatedness of neighbors. This effect both supports the evolution of altruism by focusing the altruists' gifts on relatives of the altruist, and also limits the extent to which altruism may emerge by exposing clusters of altruists to stiffer local competition. Previous analyses have emphasized the way in which these two effects can cancel, limiting the viability of altruism. These papers were based on models in which total population density was held fixed. We present here a class of models in which population density is permitted to fluctuate, so that patches of altruists are supported at a higher density than patches of non-altruists. Under these conditions, population viscosity can support the selection of both weak and strong altruism.     

Demography, altruism, and the benefits of budding

It is now widely appreciated that competition between kin inhibits the evolution of altruism. In standard population genetics models, it is difficult for indiscriminate altruism towards social partners to be favoured at all. The reason is that while limited dispersal increases the kinship of social partners it also intensifies local competition. One solution that has received very little attention is if individuals disperse as groups (budding dispersal), as this relaxes local competition without reducing kinship. Budding behaviour is widespread through all levels of biological organization, from early protocellular life to cooperatively breeding vertebrates. We model the effects of individual dispersal, budding dispersal, soft selection and hard selection to examine the conditions under which altruism is favoured. More generally, we examine how these various demographic details feed into relatedness and scale of competition parameters that can be included into Hamilton's rule.     

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.     

Spite and the scale of competition

In recent years there has been a large body of theoretical work examining how local competition can reduce and even remove selection for altruism between relatives. However, it is less well appreciated that local competition favours selection for spite, the relatively neglected ugly sister of altruism. Here, we use extensions of social evolution theory that were formulated to deal with the consequences for altruism of competition between social partners, to illustrate several points on the evolution of spite. Specifically, we show that: (i) the conditions for the evolution of spite are less restrictive than previously assumed; (ii) previous models which have demonstrated selection for spite often implicitly assumed local competition; (iii) the scale of competition must be allowed for when distinguishing different forms of spite (Hamiltonian vs. Wilsonian); (iv) local competition can enhance the spread of spiteful greenbeards; and (v) the theory makes testable predictions for how the extent of spite should vary dependent upon population structure and average relatedness.     

Individualist and Multi-level Perspectives on Selection in Structured Populations

Recent years have seen a renewed debate over the importance of groupselection, especially as it relates to the evolution of altruism. Onefeature of this debate has been disagreement over which kinds ofprocesses should be described in terms of selection at multiple levels,within and between groups. Adapting some earlier discussions, we presenta mathematical framework that can be used to explore the exactrelationships between evolutionary models that do, and those that donot, explicitly recognize biological groups as fitness-bearing entities.We show a fundamental set of mathematical equivalences between these twokinds of models, one of which applies a form of multi-level selectiontheory and the other being a form of ``individualism.' However, we alsoargue that each type of model can have heuristic advantages over theother. Indeed, it can be positively useful to engage in a kind ofback-and-forth switching between two different perspectives on theevolutionary role of groups. So the position we defend is a``gestalt-switching pluralism.'     

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.     

Estimating Selection Coefficients in Spatially Structured Populations from Time Series Data of Allele Frequencies

Inferring the nature and magnitude of selection is an important problem in many biological contexts. Typically when estimating a selection coefficient for an allele, it is assumed that samples are drawn from a panmictic population and that selection acts uniformly across the population. However, these assumptions are rarely satisfied. Natural populations are almost always structured, and selective pressures are likely to act differentially. Inference about selection ought therefore to take account of structure. We do this by considering evolution in a simple lattice model of spatial population structure. We develop a hidden Markov model based maximum-likelihood approach for estimating the selection coefficient in a single population from time series data of allele frequencies. We then develop an approximate extension of this to the structured case to provide a joint estimate of migration rate and spatially varying selection coefficients. We illustrate our method using classical data sets of moth pigmentation morph frequencies, but it has wide applications in settings ranging from ecology to human evolution.     

The adaptive dynamics of altruism in spatially heterogeneous populations

Abstract.— We study the spatial adaptive dynamics of a continuous trait that measures individual investment in altruism. Our study is based on an ecological model of a spatially heterogeneous population from which we derive an appropriate measure of fitness. The analysis of this fitness measure uncovers three different selective processes controlling the evolution of altruism: the direct physiological cost, the indirect genetic benefits of cooperative interactions, and the indirect genetic costs of competition for space. In our model, habitat structure and a continuous life cycle makes the cost of competing for space with relatives negligible. Our study yields a classification of adaptive patterns of altruism according to the shape of the costs of altruism (with decelerating, linear, or accelerating dependence on the investment in altruism). The invasion of altruism occurs readily in species with accelerating costs, but large mutations are critical for altruism to evolve in selfish species with decelerating costs. Strict selfishness is maintained by natural selection only under very restricted conditions. In species with rapidly accelerating costs, adaptation leads to an evolutionarily stable rate of investment in altruism that decreases smoothly with the level of mobility. A rather different adaptive pattern emerges in species with slowly accelerating costs: high altruism evolves at low mobility, whereas a quasi-selfish state is promoted in more mobile species. The high adaptive level of altruism can be predicted solely from habitat connectedness and physiological parameters that characterize the pattern of cost. We also show that environmental changes that cause increased mobility in those highly altruistic species can beget selection-driven self-extinction, which may contribute to the rarity of social species.     

Maternal effect genes and the evolution of sociality in haplo-diploid organisms

Maternal care and female-biased sex ratios are considered by many to be essential prerequisites for the evolution of eusocial behaviors among the hymenoptera. Using population genetic models, I investigate the evolution of genes that have positive maternal effects but negative, direct effects on offspring fitness. I find that, under many conditions, such genes evolve more easily in haplo-diploids than in diplo-diploids. In fact, the conditions are less restrictive than those of kin selection theory, which postulate genes with negative direct effects but positive sib-social effects. For example, the conditions permitting the evolution of maternal effect genes are not affected if females mate multiply, whereas multiple mating reduces the efficacy of kin selection by reducing genetic relatedness within colonies. Inbreeding also differentially facilitates evolution of maternal effect genes in haplo-diploids relative to diplo-diploids, although it does not differentially affect the evolution of sib-altruism genes. Furthermore, when the direct, deleterious pleiotropic effect is restricted to sons, a maternal effect gene can evolve when the beneficial maternal effect is less than half (with inbreeding, much less) of the deleterious effect on sons. For kin selection, however, the sib-social benefits must always exceed the direct costs because genetic relatedness is always less than or equal to 1.0. The results suggest that haplo-diploidy facilitates (1) the evolution of maternal care, and (2) the evolution of maternal effect genes with antagonistic pleiotropic effects on sons. The latter effect may help explain the tendency toward female-biased sex ratios in haplo-diploids, especially those with inbreeding. I conclude that haplo-diploidy not only facilitates the evolution of sister-sister altruism by kin selection but also facilitates the evolution of maternal care and female-biased sex ratios, two prerequisites for eusociality.     

Suspending disbelief—of Wynne-Edwards and his reception

Critique of Wynne-Edwards' views on population regulation and sociality suppose a population of discrete, mutually exclusive groups essential to his thought. Yet both his past and present work focus on continually distributed, philopatric populations; his critics have argued the untenability of a position never his own. Wynne-Edwardsian ‘group selection’ focuses on local population productivity under philopatry. A ‘group’ is a local confluence of genotypes which need not be reified, and group selection consists of the differential replication (hence heritability) of the local social environment in which a genotype is embedded. Differential productivity contingent on social environment can eliminate some relational structures on genotypes in favor of others, creating an expanding wave of population productivity as in Wright's shifting balance metaphor. Such a process is inherent in the evolution of reciprocity, where cooperators must cluster to successfully invade a population of defectors. Regulation of resource exploitation in continuously distributed populations may be modeled as overlapping n-person Prisoner's Dilemmas, where each individual participates in several distinct commons and defection represents local over-exploitation of resources.     

A scaling law of multilevel evolution: how the balance between within- and among-collective evolution is determined

Numerous living systems are hierarchically organized, whereby replicating components are grouped into reproducing collectives—e.g., organelles are grouped into cells, and cells are grouped into multicellular organisms. In such systems, evolution can operate at two levels: evolution among collectives, which tends to promote selfless cooperation among components within collectives (called altruism), and evolution within collectives, which tends to promote cheating among components within collectives. The balance between within- and among-collective evolution thus exerts profound impacts on the fitness of these systems. Here, we investigate how this balance depends on the size of a collective (denoted by N) and the mutation rate of components (m) through mathematical analyses and computer simulations of multiple population genetics models. We first confirm a previous result that increasing N or m accelerates within-collective evolution relative to among-collective evolution, thus promoting the evolution of cheating. Moreover, we show that when within- and among-collective evolution exactly balance each other out, the following scaling relation generally holds: Nmα is a constant, where scaling exponent α depends on multiple parameters, such as the strength of selection and whether altruism is a binary or quantitative trait. This relation indicates that although N and m have quantitatively distinct impacts on the balance between within- and among-collective evolution, their impacts become identical if m is scaled with a proper exponent. Our results thus provide a novel insight into conditions under which cheating or altruism evolves in hierarchically organized replicating systems.     

Comparative analysis of population structure across environments and geographical scales at major histocompatibility complex and microsatellite loci in Atlantic salmon (Salmo salar)

Evidence of selection acting on major histocompatibility complex (MHC) genes has been illustrated with the analysis of their nucleotide sequences and allele frequency distribution. Comparing the patterns of population differentiation at neutral markers and MHC genes in the wild may provide further insights about the relative role of selection and neutrality in shaping their diversity. In this study, we combine both methods to assess the role of selection on a MHC gene in Atlantic salmon. We compare variation at a MHC class II B locus and microsatellites among 14 samples from seven different rivers and seven subpopulations within a single river system covering a variety of habitats and different geographical scales. We show that diversifying selection is acting on the sites involved in antigen presentation and that balancing selection maintains a high level of polymorphism within populations. Despite important differences in habitat type, the comparison of the population structure at MHC and microsatellites on large geographical scales reveals a correlation between patterns of differentiation, indicating that drift and migration have been more important than selection in shaping population differentiation at the MHC locus. In contrast, strong discrepancies between patterns of population differentiation at the two types of markers provides support for the role of selection in shaping population structure within rivers. Together, these results confirm that natural selection is influencing MHC gene diversity in wild Atlantic salmon although neutral forces may also be important in their evolution.     

Genetic steady-state under BLUP selection for an infinite and homogeneous population with discrete generations

A matrix derivation is proposed to analytically calculate the asymptotic genetic variance-covariance matrix under BLUP selection according to the initial genetic parameters in a large population with discrete generations. The asymptotic genetic evolution of a homogeneous population with discrete generations is calculated for a selection operating on an index including all information (pedigree and records) from a non-inbred and unselected base population (BLUP selection) or on an index restricted to records of a few ancestral generations. Under the first hypothesis, the prediction error variance of the selection index is independent of selection and is calculated from the genetic parameters of the base population. Under the second hypothesis, the prediction error variance depends on selection. Furthermore, records of several generations of ancestors of the candidates for selection must be used to maintain a constant prediction error variance over time. The number of ancestral generations needed depends on the population structure and on the occurrence of fixed effects. Without fixed effects to estimate, accounting for two generations of ancestors is sufficient to estimate the asymptotic prediction error variance. The amassing of information from an unselected base population proves to be important in order not to overestimate the asymptotic genetic gains and not to underestimate the asymptotic genetic variances.