EVOLUTIONARY GAMES IN WRIGHT'S ISLAND MODEL: KIN SELECTION MEETS EVOLUTIONARY GAME THEORY

This article studies evolutionary game dynamics in Wright's infinite island model. I study a general n×n matrix game and derive a basic equation that describes the change in frequency of strategies. A close observation of this equation reveals that three distinct effects are at work: direct benefit to a focal individual, kin‐selected indirect benefit to the focal individual via its relatives, and the cost caused by increased kin competition in the focal individual's natal deme. Crucial parameters are the coefficient of relatedness between two individuals and its analogue for three individuals. I provide a number of examples and show when the traditional inclusive fitness measure is recovered and when not. Results demonstrate how evolutionary game theory fits into the framework of kin selection.     

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.     

Replicator Selection and the Extended Phenotype3

Adaptations are often spoken of as ‘for the good of’ some entity, but what is that entity? Groups and species are now rightly unfashionable, so what are we left with? The prevailing answer is Darwin's: ‘the individual’. Individuals clearly do not maximise their own survival so the concept of fitness had to be invented. If fitness is correctly defined in Hamilton's way as ‘inclusive fitness’ it ceases to matter whether we speak of individuals maximising their inclusive fitness or of genes maximising their survival. The two formulations are mutually inter-translatable. Yet some serious mistranslations are quoted from the literature, which have led their authors into actual biological error. The present paper blames the prevailing concentration on the individual for these errors, and advocates a reversion to the replicator as the proper focus of evolutionary attention. A gene is an obvious replicator, but there are others, and the general properties of replicators are discussed. Defenders of the individual as the unit of selection often point to the unity and integration of the genome as expressed phenotypically. This paper ends by attacking even this assumption, not by a reductionist fragmentation of the phenotype, but, on the contrary, by extending it to include more than one individual. Replicators survive by virtue of their effects on the world, and these effects are not restricted to one individual body but constitute a wider ‘extended phenotype’.     

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.     

Phenotypic and Evolutionary Consequences of Social Behaviours: Interactions among Individuals Affect Direct Genetic Effects

Traditional quantitative genetics assumes that an individual''s phenotype is determined by both genetic and environmental factors. For many animals, part of the environment is social and provided by parents and other interacting partners. When expression of genes in social partners affects trait expression in a focal individual, indirect genetic effects occur. In this study, we explore the effects of indirect genetic effects on the magnitude and range of phenotypic values in a focal individual in a multi-member model analyzing three possible classes of interactions between individuals. We show that social interactions may not only cause indirect genetic effects but can also modify direct genetic effects. Furthermore, we demonstrate that both direct and indirect genetic effects substantially alter the range of phenotypic values, particularly when a focal trait can influence its own expression via interactions with traits in other individuals. We derive a function predicting the relative importance of direct versus indirect genetic effects. Our model reveals that both direct and indirect genetic effects can depend to a large extent on both group size and interaction strength, altering group mean phenotype and variance. This may lead to scenarios where between group variation is much higher than within group variation despite similar underlying genetic properties, potentially affecting the level of selection. Our analysis highlights key properties of indirect genetic effects with important consequences for trait evolution, the level of selection and potentially speciation.     

MULTI‐LEVEL SEXUAL SELECTION: INDIVIDUAL AND FAMILY‐LEVEL SELECTION FOR MATING SUCCESS IN A HISTORICAL HUMAN POPULATION

Precopulatory sexual selection is the association between fitness and traits associated with mate acquisition. Although sexual selection is generally recognized to be a powerful evolutionary force, most investigations are limited to characters belonging to individuals. A broader multilevel perspective acknowledges that individual fitness can be affected by aspects of mating success that are characters of groups, such as families. Parental mating success in polygynous or polyandrous human societies may exemplify traits under group‐level sexual selection. Using fitness measures that account for age‐structure, I measure multilevel selection for mate number over 55 years in a human population with declining rates of polygyny. Sexual selection had three components: individual‐level selection for ever‐mating (whether an individual mated) and individual‐ and family‐level selection for polyandry and polygyny. Family‐ and individual‐level selection for polygyny was equally strong, three times stronger than family‐level selection for polyandry and more than an order of magnitude stronger than individual‐level selection for polyandry. However, individual‐level selection for polyandry and polygyny was more effective at explaining relative fitness variance than family‐level selection. Selection for ever‐mating was the most important source of sexual selection for fitness; variation for ever‐mating explained 23% of relative fitness variance.     

Partitioning of covariance as a method for studying kin selection

Covariance models of selection predict gene frequency change in terms of the relationship between the fitness of an individual and its phenotype, and therefore provide a convenient method for studying evolution in natural systems. When these models are partitioned into effects acting within and between hierarchical levels of selection, they can be directly applied to questions of kin selection. In many cases, the partitioning of covariance approach to the study of kin selection is a more useful alternative to the traditional hamiltonian or inclusive fitness approach.     

REGRESSION ANALYSIS OF NATURAL SELECTION: STATISTICAL INFERENCE AND BIOLOGICAL INTERPRETATION

Recent theoretical work in quantitative genetics has fueled interest in measuring natural selection in the wild. We discuss statistical and biological issues that may arise in applications of Lande and Arnold's (1983) multiple-regression approach to measuring selection. We review assumptions involved in estimation and hypothesis testing in regression problems, and we note difficulties that frequently arise as a result of violation of these assumptions. In particular, multicollinearity (extreme intercorrelation of characters) and extrinsic, unmeasured factors affecting fitness may seriously complicate inference regarding selection. Further, violation of the assumption that residuals are normally distributed vitiates tests of significance. For this situation, we suggest applications of recently developed jackknife tests of significance. While fitness regression permits direct assessment of selection in a form suitable for predicting selection response, we suggest that the aim of inferring causal relationships about the effects of phenotypic characters on fitness is greatly facilitated by manipulative experiments. Finally, we discuss alternative definitions of stabilizing and disruptive selection.     

Kinship reinforces cooperative predator inspection in a cichlid fish

Kin selection theory predicts that cooperation is facilitated between genetic relatives, as by cooperating with kin an individual might increase its inclusive fitness. Although numerous theoretical papers support Hamilton's inclusive fitness theory, experimental evidence is still underrepresented, in particular in noncooperative breeders. Cooperative predator inspection is one of the most intriguing antipredator strategies, as it implies high costs on inspectors. During an inspection event, one or more individuals leave the safety of a group and approach a potential predator to gather information about the current predation risk. We investigated the effect of genetic relatedness on cooperative predator inspection in juveniles of the cichlid fish Pelvicachromis taeniatus, a species in which juveniles live in shoals under natural conditions. We show that relatedness significantly influenced predator inspection behaviour with kin dyads being significantly more cooperative. Thus, our results indicate a higher disposition for cooperative antipredator behaviour among kin as predicted by kin selection theory.     

SELECTION AND EVOLUTION OF CAUSALLY COVARYING TRAITS

When traits cause variation in fitness, the distribution of phenotype, weighted by fitness, necessarily changes. The degree to which traits cause fitness variation is therefore of central importance to evolutionary biology. Multivariate selection gradients are the main quantity used to describe components of trait‐fitness covariation, but they quantify the direct effects of traits on (relative) fitness, which are not necessarily the total effects of traits on fitness. Despite considerable use in evolutionary ecology, path analytic characterizations of the total effects of traits on fitness have not been formally incorporated into quantitative genetic theory. By formally defining “extended” selection gradients, which are the total effects of traits on fitness, as opposed to the existing definition of selection gradients, a more intuitive scheme for characterizing selection is obtained. Extended selection gradients are distinct quantities, differing from the standard definition of selection gradients not only in the statistical means by which they may be assessed and the assumptions required for their estimation from observational data, but also in their fundamental biological meaning. Like direct selection gradients, extended selection gradients can be combined with genetic inference of multivariate phenotypic variation to provide quantitative prediction of microevolutionary trajectories.     

Social Selection and Indirect Genetic Effects in Structured populations

Social selection and indirect genetic effects (IGEs) are established concepts in both behavioural ecology and evolutionary genetics. While IGEs describe effects of an individual’s genotype on phenotypes of social partners (and may thus affect their fitness indirectly), the concept of social selection assumes that a given phenotype in one individual affects the fitness of other individuals directly. Although different frameworks, both have been used to investigate the evolution of social traits, such as cooperative behaviour. Despite their similarities (both concepts consider interactions among individuals), they differ in the type of interaction. It remains unclear whether the two concepts make the same predictions about evolutionary trajectories or not. To address this question, we investigate four possible scenarios of social interactions and compare the effects of IGEs and social selection for trait evolution in a multi-trait multi-member model. We show that the two mechanisms can yield similar evolutionary outcomes and that both can create selection pressure at the group level. However, the effect of IGEs can be stronger due to the possibility of feedback loops. Finally, we demonstrate that IGEs, but not social selection gradients, may lead to differences in the direction of evolutionary response between genotypes and phenotypes.     

Social dynamics of mammals: Reproductive success, kinship and individual fitness

Apparent altruism, in which an individual seemingly decreases its evolutionary fitness by assisting others, can confer benefits if the individual assists kin. Thus, an animal can increase its total or inclusive fitness by producing offspring (direct fitness) and/or helping kin to reproduce (indirect fitness). Although kin selection has been suggested as the mechanism underlying the formation of mammalian societies, many species act as if they attempt to maximize the direct fitness component of their inclusive fitness.     

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.     

Antagonistic multilevel selection on size and architecture in variable density settings

In some ecological settings, an individual's fitness depends on both its own phenotype (individual-level selection) as well as the phenotype of the individuals with which it interacts (group-level selection). Using contextual analysis to measure multilevel selection in experimental stands of Arabidopsis thaliana, we detected significant linear selection that reversed across individual versus group levels for two composite phenotypic traits, "size" and "elongation." In both cases, selection at the individual level acted to increase values of these traits, presumably due to their positive effect on resource acquisition. Group selection favored decreased values of the same traits. Nonlinear selection was weak but significant in several cases, including stabilizing selection on developmental rate; individuals with very rapid development likely had lower than average fitness due to their reduced resource level at reproduction, while very delayed reproduction may have resulted in lower fitness if prolonged competition for resources reduced overall environmental quality and fitness of all individuals in a group. Under this scenario, stabilizing selection on individual traits is evidence of selection at the group level. Significant density-dependent selection suggests that a threshold density must be reached before group selection acts. Below this threshold, selection at the individual level affects phenotypic evolution more strongly than group selection. A second experiment measured multilevel selection in progeny stands of the original experimental plants. Multilevel selection again acted antagonistically on a composite trait that included size and elongation as well as on an architectural trait, branch production. The magnitude of individual versus group selection was relatively similar in the progeny generation, and the observed balance of individual versus group selection across densities is generally consistent with the hypotheses that multilevel selection can contribute to phenotypic evolution and to important demographic phenomena, including soft selection and the "law of constant yield."     

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.     

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.     

THE CAUSES OF NATURAL SELECTION

We discuss the necessary and sufficient conditions for identifying the cause of natural selection on a phenotypic trait. We reexamine the observational methods recently proposed for measuring selection in natural populations and illustrate why the multivariate analysis of selection is insufficient for identifying the causal agents of selection. We discuss how the observational approach of multivariate selection analysis can be complemented by experimental manipulations of the phenotypic distribution and the environment to identify not only how selection is operating on the phenotypic distribution but also why it operates in the observed manner. A significant point of departure of our work from recent discussions is in regard to the role of the environment in the study of natural selection. Instead of viewing the environment as a source of unwanted variation that obscures the relationship between phenotype and fitness, we view fitness as arising from the interaction of the phenotype with the environment. The biotic and abiotic environment is the context that gives rise to the relationship between phenotype and fitness (selection). The analysis of the causes of selection is in essence a problem in ecology. The experimental study of the association between selection gradients and environmental characteristics is necessary to identify the agents of natural selection. We recommend research methods for identifying the agency of selection that depend upon a reciprocity between the observational approach of multivariate selection analysis and the manipulative approach of field experiments in evolutionary ecology.     

EVOLUTION IN FLUCTUATING ENVIRONMENTS: DECOMPOSING SELECTION INTO ADDITIVE COMPONENTS OF THE ROBERTSON–PRICE EQUATION

We analyze the stochastic components of the Robertson–Price equation for the evolution of quantitative characters that enables decomposition of the selection differential into components due to demographic and environmental stochasticity. We show how these two types of stochasticity affect the evolution of multivariate quantitative characters by defining demographic and environmental variances as components of individual fitness. The exact covariance formula for selection is decomposed into three components, the deterministic mean value, as well as stochastic demographic and environmental components. We show that demographic and environmental stochasticity generate random genetic drift and fluctuating selection, respectively. This provides a common theoretical framework for linking ecological and evolutionary processes. Demographic stochasticity can cause random variation in selection differentials independent of fluctuating selection caused by environmental variation. We use this model of selection to illustrate that the effect on the expected selection differential of random variation in individual fitness is dependent on population size, and that the strength of fluctuating selection is affected by how environmental variation affects the covariance in Malthusian fitness between individuals with different phenotypes. Thus, our approach enables us to partition out the effects of fluctuating selection from the effects of selection due to random variation in individual fitness caused by demographic stochasticity.     

Distinctions among reciprocal altruism,kin selection,and cooperation and a model for the initial evolution of beneficent behavior

Reciprocal altruism is usually regarded as distinct from kin selection. However, because reciprocators are likely to establish long-term relations and to deliver most of their aid to other individuals genetically predisposed to reciprocation, most acts of reciprocal altruism should involve indirect increments to inclusive fitness, at least as regards alleles for reciprocation. Thus, as usually defined, reciprocal altruism is not clearly distinct from kin selection because both involve indirect increments to inclusive fitness. We propose a new definition for reciprocal altruism that makes the phenomenon distinct from kin selection and allows for reciprocation between nonrelatives in which current costs exceed future benefits returned to the reciprocal altruist. Cooperation and reciprocal altruism are often considered synonymous or different only in the timing of donating and receiving aid. We show, however, that there are other critical differences between reciprocal altruism and other forms of cooperation, most importantly, the latter often involve no clearly identifiable aid. We propose a four-category system to encompass the range of cooperative and beneficent behaviors that occur in nature (reciprocal altruism, pseudoreciprocity, simultaneous cooperation and by-product beneficence). Reciprocal altruism must involve aid that is returned to an original donor as a result of behavior that has a net cost to an original recipient. Our simplest category of cooperative/beneficent behavior, “by-product beneficence,” occurs when a selfish act also benefits another individual and requires no prior or subsequent interactions between the individuals involved. By-product beneficence may be the primitive state from which more complicated types of cooperative/beneficent behavior evolved. We show via simple models that by-product beneficence can allow for the initial increase of helping behavior in a completely unstructured population although the individuals showing such behavior pay all the costs while sharing the benefits with other individuals. Previous models that attempted to explain the initial increase of cooperative/beneficent behavior were much more complex and were based on the prisoner's dilemma, which does not accurately reflect most forms of cooperation and beneficence that occur in nature.     

REDUCED GENETIC VARIANCE AMONG HIGH FITNESS INDIVIDUALS: INFERRING STABILIZING SELECTION ON MALE SEXUAL DISPLAYS IN DROSOPHILA SERRATA

Directional selection is prevalent in nature, yet phenotypes tend to remain relatively constant, suggesting a limit to trait evolution. However, the genetic basis of this limit is unresolved. Given widespread pleiotropy, opposing selection on a trait may arise from the effects of the underlying alleles on other traits under selection, generating net stabilizing selection on trait genetic variance. These pleiotropic costs of trait exaggeration may arise through any number of other traits, making them hard to detect in phenotypic analyses. Stabilizing selection can be inferred, however, if genetic variance is greater among low‐ compared to high‐fitness individuals. We extend a recently suggested approach to provide a direct test of a difference in genetic variance for a suite of cuticular hydrocarbons (CHCs) in Drosophila serrata. Despite strong directional sexual selection on these traits, genetic variance differed between high‐ and low‐fitness individuals and was greater among the low‐fitness males for seven of eight CHCs, significantly more than expected by chance. Univariate tests of a difference in genetic variance were nonsignificant but likely have low power. Our results suggest that further CHC exaggeration in D. serrata in response to sexual selection is limited by pleiotropic costs mediated through other traits.