More on the genetical theory of multilevel selection

In my article The genetical theory of multilevel selection, I provided a synthesis of the theory of multilevel selection (MLS) and the theory of natural selection in class‐structured populations. I framed this synthesis within Fisher's genetical paradigm, taking a strictly genetical approach to traits and fitness. I showed that this resolves a number of long‐standing conceptual problems that have plagued the MLS literature, including the issues of ‘aggregate’ vs. ‘emergent’ group traits, ‘collective fitness₁’ vs. ‘collective fitness₂’ and ‘MLS1’ vs. ‘MLS2 ‘. In his commentary, Goodnight suggests this theoretical and conceptual synthesis is flawed in several respects. Here, I show this is incorrect, by: reiterating the theoretical and conceptual goals of my synthesis; clarifying that my genetical approach to traits is necessary for a proper analysis of the action of MLS independently of non‐Darwinian factors; emphasizing that the Price–Hamilton approach to MLS provides a consistent, useful and conceptually superior theoretical framework; and explaining the role of reproductive value in the study of natural selection in class‐structured populations. I also show that Goodnight's contextual analysis treatment of MLS in a class‐structured population is mathematically, biologically and conceptually inadequate.     

The joint effects of kin, multilevel selection and indirect genetic effects on response to genetic selection

Kin and levels-of-selection models are common approaches for modelling social evolution. Indirect genetic effect (IGE) models represent a different approach, specifying social effects on trait values rather than fitness. We investigate the joint effect of relatedness, multilevel selection and IGEs on response to selection. We present a measure for the degree of multilevel selection, which is the natural partner of relatedness in expressions for response. Response depends on both relatedness and the degree of multilevel selection, rather than only one or the other factor. Moreover, response is symmetric in relatedness and the degree of multilevel selection, indicating that both factors have exactly the same effect. Without IGEs, the key parameter is the product of relatedness and the degree of multilevel selection. With IGEs, however, multilevel selection without relatedness can explain evolution of social traits. Thus, next to relatedness and multilevel selection, IGEs are a key element in the genetical theory of social evolution.     

Multilevel selection theory and evidence: a critique of Gardner, 2015

Gardner (2015) recently developed a model of a ‘Genetical Theory of Multilevel Selection, which is a thoughtfully developed, but flawed model. The model's flaws appear to be symptomatic of common misunderstandings of the multi level selection (MLS) literature and the recent quantitative genetic literature. I use Gardner's model as a guide for highlighting how the MLS literature can address the misconceptions found in his model, and the kin selection literature in general. I discuss research on the efficacy of group selection, the roll of indirect genetic effects in affecting the response to selection and the heritability of group‐level traits. I also discuss why the Price multilevel partition should not be used to partition MLS, and why contextual analysis and, by association, direct fitness are appropriate for partitioning MLS. Finally, I discuss conceptual issues around questions concerning the level at which fitness is measured, the units of selection, and I present a brief outline of a model of selection in class‐structured populations. I argue that the results derived from the MLS research tradition can inform kin selection research and models, and provide insights that will allow researchers to avoid conceptual flaws such as those seen in the Gardner model.     

Evolutionary stasis of a heritable morphological trait in a wild fish population despite apparent directional selection

Comparing observed versus theoretically expected evolutionary responses is important for our understanding of the evolutionary process, and for assessing how species may cope with anthropogenic change. Here, we document directional selection for larger female size in Atlantic salmon, using pedigree‐derived estimates of lifetime reproductive success as a fitness measure. We show the trait is heritable and, thus, capable of responding to selection. The Breeder's Equation, which predicts microevolution as the product of phenotypic selection and heritability, predicted evolution of larger size. This was at odds, however, with the observed lack of either phenotypic or genetic temporal trends in body size, a so‐called “paradox of stasis.” To investigate this paradox, we estimated the additive genetic covariance between trait and fitness, which provides a prediction of evolutionary change according to Robertson's secondary theorem of selection (STS) that is unbiased by missing variables. The STS prediction was consistent with the observed stasis. Decomposition of phenotypic selection gradients into genetic and environmental components revealed a potential upward bias, implying unmeasured factors that covary with trait and fitness. These results showcase the power of pedigreed, wild population studies—which have largely been limited to birds and mammals—to study evolutionary processes on contemporary timescales.     

Social phenotype extended to communities: Expanded multilevel social selection analysis reveals fitness consequences of interspecific interactions

In social species, fitness consequences are associated with both individual and social phenotypes. Social selection analysis has quantified the contribution of conspecific social traits to individual fitness. There has been no attempt, however, to apply a social selection approach to quantify the fitness implications of heterospecific social phenotypes. Here, we propose a novel social selection based approach integrating the role of all social interactions at the community level. We extended multilevel selection analysis by including a term accounting for the group phenotype of heterospecifics. We analyzed nest activity as a model social trait common to two species, the lesser kestrel (Falco naumanni) and jackdaw (Corvus monedula), nesting in either single‐ or mixed‐species colonies. By recording reproductive outcome as a measure of relative fitness, our results reveal an asymmetric system wherein only jackdaw breeding performance was affected by the activity phenotypes of both conspecific and heterospecific neighbors. Our model incorporating heterospecific social phenotypes is applicable to animal communities where interacting species share a common social trait, thus allowing an assessment of the selection pressure imposed by interspecific interactions in nature. Finally, we discuss the potential role of ecological limitations accounting for random or preferential assortments among interspecific social phenotypes, and the implications of such processes to community evolution.     

Characterizing selection in black‐throated blue warblers using a sexual network approach

Our understanding of trait evolution is built upon studies that examine the correlation between traits and fitness, most of which implicitly assume all individuals experience similar selective environments. However, accounting for differences in selective pressures, such as variation in the social environment, can advance our understanding of how selection shapes individual traits and subsequent fitness. In this study, we test whether variation in the social environment affects selection on individual phenotype. We apply a new sexual network framework to quantify each male's social environment as the mean body size of his primary competitors. We test for direct and social selection on male body size using a 10‐year data set on black‐throated blue warblers (Setophaga caerulescens), a territorial species for which body size is hypothesized to mediate competition for mates. We found that direct selection on body size was weak and nonsignificant, as was social selection via the body size of the males' competitors. Analysing both types of selection simultaneously allows us to firmly reject a role for body size in competitive interactions between males and subsequent male fitness in this population. We evaluate the application of the sexual network approach to empirical data and suggest that other phenotypic traits such as song characteristics and plumage may be more relevant than body size for male–male competition in this small passerine bird.     

Quantifying selection on standard metabolic rate and body mass in Drosophila melanogaster

Standard metabolic rate (SMR), defined as the minimal energy expenditure required for self‐maintenance, is a key physiological trait. Few studies have estimated its relationship with fitness, most notably in insects. This is presumably due to the difficulty of measuring SMR in a large number of very small individuals. Using high‐throughput flow‐through respirometry and a Drosophila melanogaster laboratory population adapted to a life cycle that facilitates fitness measures, we quantified SMR, body mass, and fitness in 515 female and 522 male adults. We used a novel multivariate approach to estimate linear and nonlinear selection differentials and gradients from the variance‐covariance matrix of fitness, SMR, and body mass, allowing traits specific covariates to be accommodated within a single model. In males, linear selection differentials for mass and SMR were positive and individually significant. Selection gradients were also positive but, despite substantial sample sizes, were nonsignificant due to increased uncertainty given strong SMR‐mass collinearity. In females, only nonlinear selection was detected and it appeared to act primarily on body size, although the individual gradients were again nonsignificant. Selection did not differ significantly between sexes although differences in the fitness surfaces suggest sex‐specific selection as an important topic for further study.     

Quantification and decomposition of environment‐selection relationships

In nature, selection varies across time in most environments, but we lack an understanding of how specific ecological changes drive this variation. Ecological factors can alter phenotypic selection coefficients through changes in trait distributions or individual mean fitness, even when the trait‐absolute fitness relationship remains constant. We apply and extend a regression‐based approach in a population of Soay sheep (Ovis aries) and suggest metrics of environment‐selection relationships that can be compared across studies. We then introduce a novel method that constructs an environmentally structured fitness function. This allows calculation of full (as in existing approaches) and partial (acting separately through the absolute fitness function slope, mean fitness, and phenotype distribution) sensitivities of selection to an ecological variable. Both approaches show positive overall effects of density on viability selection of lamb mass. However, the second approach demonstrates that this relationship is largely driven by effects of density on mean fitness, rather than on the trait‐fitness relationship slope. If such mechanisms of environmental dependence of selection are common, this could have important implications regarding the frequency of fluctuating selection, and how previous selection inferences relate to longer term evolutionary dynamics.     

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.     

Phenotypic assortment mediates the effect of social selection in a wild beetle population

Social interactions often have major fitness consequences, but little is known about how specific interacting phenotypes affect the strength of natural selection. Social influences on the evolutionary process can be assessed using a multilevel selection approach that partitions the effects of social partner phenotypes on fitness (referred to as social or group selection) from those of the traits of a focal individual (nonsocial or individual selection). To quantify the contribution of social selection to total selection affecting a trait, the patterns of phenotypic association among interactants must also be considered. We estimated selection gradients on male body size in a wild population of forked fungus beetles (Bolitotherus cornutus). We detected positive nonsocial selection and negative social selection on body size operating through differences in copulation success, indicating that large males with small social partners had highest fitness. In addition, we found that, in low-density demes, the phenotypes of focal individuals were negatively correlated with those of their social partners. This pattern reversed the negative effect of group selection on body size and led to stronger positive selection for body size. Our results demonstrate multilevel selection in nature and stress the importance of considering social selection whenever conspecific interactions occur nonrandomly.     

Social traits,social networks and evolutionary biology

The social environment is both an important agent of selection for most organisms, and an emergent property of their interactions. As an aggregation of interactions among members of a population, the social environment is a product of many sets of relationships and so can be represented as a network or matrix. Social network analysis in animals has focused on why these networks possess the structure they do, and whether individuals’ network traits, representing some aspect of their social phenotype, relate to their fitness. Meanwhile, quantitative geneticists have demonstrated that traits expressed in a social context can depend on the phenotypes and genotypes of interacting partners, leading to influences of the social environment on the traits and fitness of individuals and the evolutionary trajectories of populations. Therefore, both fields are investigating similar topics, yet have arrived at these points relatively independently. We review how these approaches are diverged, and yet how they retain clear parallelism and so strong potential for complementarity. This demonstrates that, despite separate bodies of theory, advances in one might inform the other. Techniques in network analysis for quantifying social phenotypes, and for identifying community structure, should be useful for those studying the relationship between individual behaviour and group‐level phenotypes. Entering social association matrices into quantitative genetic models may also reduce bias in heritability estimates, and allow the estimation of the influence of social connectedness on trait expression. Current methods for measuring natural selection in a social context explicitly account for the fact that a trait is not necessarily the property of a single individual, something the network approaches have not yet considered when relating network metrics to individual fitness. Harnessing evolutionary models that consider traits affected by genes in other individuals (i.e. indirect genetic effects) provides the potential to understand how entire networks of social interactions in populations influence phenotypes and predict how these traits may evolve. By theoretical integration of social network analysis and quantitative genetics, we hope to identify areas of compatibility and incompatibility and to direct research efforts towards the most promising areas. Continuing this synthesis could provide important insights into the evolution of traits expressed in a social context and the evolutionary consequences of complex and nuanced social phenotypes.     

The genetical theory of kin selection

Natural selection operates both directly, via the impact of a trait upon the individual's own fitness, and indirectly, via the impact of the trait upon the fitness of the individual's genetically related social partners. These effects are often framed in terms of Hamilton's rule, rb - c > 0, which provides the central result of social-evolution theory. However, a number of studies have questioned the generality of Hamilton's rule, suggesting that it requires restrictive assumptions. Here, we use Fisher's genetical paradigm to demonstrate the generality of Hamilton's rule and to clarify links between different studies. We show that confusion has arisen owing to researchers misidentifying model parameters with the b and c terms in Hamilton's rule, and misidentifying measures of genotypic similarity or genealogical relationship with the coefficient of genetic relatedness, r. More generally, we emphasize the need to distinguish between general kin-selection theory that forms the foundations of social evolution, and streamlined kin-selection methodology that is used to solve specific problems.     

Developmental selection and self-organization

Developmental selection is the differential survival and proliferation of developmental units, such as cellular lineages. This type of internal selection has been proposed as an explanation for diverse examples of self-organization, from the wiring of brains to the formation of pores on leaf surfaces. A general understanding of developmental selection has been slowed by failure to understand its relationship to familiar forms of genetical selection and evolution. I show the formal analogies between models of developmental selection and genetical selection. The general method I outline for the analysis of selective systems partitions self-organizing selective systems into generative rules that create variation and selective filters that move the population toward a target design. The method also emphasizes aggregate statistical measures of evolving systems, such as the covariance between particular traits and fitness. The identification of useful aggregate measures is a crucial step in the analysis of selective systems. I apply these concepts to a model of self-organization in ant colonies.     

Natural selection, evolvability and bias due to environmental covariance in the field in an annual plant

Estimates of the form and magnitude of natural selection based on phenotypic relationships between traits and fitness measures can be biased when environmental factors influence both relative fitness and phenotypic trait values. I quantified genetic variances and covariances, and estimated linear and quadratic selection coefficients, for seven traits of an annual plant grown in the field. For replicates of 50 paternal half-sib families, coefficients of selection were calculated both for individual phenotypic values of the traits and for half-sib family mean values. The potential for evolutionary response was supported by significant heritability and phenotypic directional selection for several traits but contradicted by the absence of significant genetic variation for fitness estimates and evidence of bias in phenotypic selection coefficients due to environmental covariance for at least two of the traits analysed. Only studies of a much wider range of organisms and traits will reveal the frequency and extent of such bias.     

Measurement of concurrent selection episodes

Current methods for measuring selection with longitudinal data have been developed with the assumption that episodes of selection are sequential. However, a number of empirical examinations have demonstrated that natural and sexual selection may act concurrently and in opposing directions. Other recent work has highlighted the difficulty of assigning fitness values for survival when reproduction and mortality within a population temporally overlap. I treat these as facets of a single problem; how to analyze selection where mortality and reproduction are concurrent. To address this problem, I formalize a method to estimate total fitness of individuals over a period of time utilizing longitudinal data. I then show how the fitness may be partitioned to provide two separate estimates of fitness for reproductive opportunity and reproductive success. In addition, another total fitness estimate for the period can be obtained from the two partitioned estimates. This procedure will allow calculation of total fitness where there are some missing datapoints for reproductive success of an individual. A simulation indicates that bias is generally low for the various fitness estimates. These methods should expand our ability to understand the interaction of different selection episodes.     

Exploring sub‐individual variability: role of ontogeny,abiotic environment and seed‐dispersing birds

• Within‐individual trait variation – otherwise known as sub‐individual variation – is an important component of phenotypic variation, with both a genetic and epigenetic basis. We explore its adaptive value and the effects of ontogeny and the environment on sub‐individual variability.
• We conducted a field study to analyse the effects of tree age, soil pH, soil water content and soil nutrients on sub‐individual variability in fruit size of hawthorn (Crataegus monogyna) in three sites in northwest Spain. Additionally, we examined how bird‐mediated selection influences average and sub‐individual variation in fruit size.
• Results show that average and sub‐individual variations in fruit size were related to fitness affecting seed dispersal. Older trees produced larger fruits, but tree age did not affect sub‐individual variation in fruit size. Abiotic environmental factors differently affected sub‐individual variation and average fruit size. Seed‐dispersing birds exerted correlated selection on average and variation in fruit size, favouring trees with larger and less variable fruit size at one site.
• Our work suggests that the fruit size variation within individual trees, the sub‐individual variation, is modified by abiotic environmental factors and, additionally, is an adaptive trait that responds to natural selection.

     

The effect of trait type and strength of selection on heritability and evolvability in an island bird population

The heritability (h²) of fitness traits is often low. Although this has been attributed to directional selection having eroded genetic variation in direct proportion to the strength of selection, heritability does not necessarily reflect a trait's additive genetic variance and evolutionary potential (“evolvability”). Recent studies suggest that the low h² of fitness traits in wild populations is caused not by a paucity of additive genetic variance (V_A) but by greater environmental or nonadditive genetic variance (V_R). We examined the relationship between h² and variance‐standardized selection intensities (i or β_σ), and between evolvability (I_A:V_A divided by squared phenotypic trait mean) and mean‐standardized selection gradients (β_μ). Using 24 years of data from an island population of Savannah sparrows, we show that, across diverse traits, h² declines with the strength of selection, whereas I_A and I_R (V_R divided by squared trait mean) are independent of the strength of selection. Within trait types (morphological, reproductive, life‐history), h², I_A, and I_R are all independent of the strength of selection. This indicates that certain traits have low heritability because of increased residual variance due to the age at which they are expressed or the multiple factors influencing their expression, rather than their association with fitness.     

A meta‐analysis of the agents of selection on floral traits

Floral traits are hypothesized to evolve primarily in response to selection by pollinators. However, selection can also be mediated by other environmental factors. To understand the relative importance of pollinator‐mediated selection and its variation among trait and pollinator types, we analyzed directional selection gradients on floral traits from experiments that manipulated the environment to identify agents of selection. Pollinator‐mediated selection was stronger than selection by other biotic factors (e.g., herbivores), but similar in strength to selection by abiotic factors (e.g., soil water), providing partial support for the hypothesis that floral traits evolve primarily in response to pollinators. Pollinator‐mediated selection was stronger on pollination efficiency traits than on other trait types, as expected if efficiency traits affect fitness via interactions with pollinators, but other trait types also affect fitness via other environmental factors. In addition to varying among trait types, pollinator‐mediated selection varied among pollinator taxa: selection was stronger when bees, long‐tongued flies, or birds were the primary visitors than when the primary visitors were Lepidoptera or multiple animal taxa. Finally, reducing pollinator access to flowers had a relatively small effect on selection on floral traits, suggesting that anthropogenic declines in pollinator populations would initially have modest effects on floral evolution.     

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.     

Hamilton's missing link

Hamilton's famous rule was presented in 1964 in a paper called "The genetical theory of social behaviour (I and II)", Journal of Theoretical Biology 7, 1-16, 17-32. The paper contains a mathematical genetical model from which the rule supposedly follows, but it does not provide a link between the paper's central result, which states that selection dynamics take the population to a state where mean inclusive fitness is maximized, and the rule, which states that selection will lead to maximization of individual inclusive fitness. This note provides a condition under which Hamilton's rule does follow from his central result.