Multilevel selection and the partitioning of covariance: a comparison of three approaches

Where the evolution of a trait is affected by selection at more than one hierarchical level, it is often useful to compare the magnitude of selection at each level by asking how much of the total evolutionary change is attributable to each level of selection. Three statistical partitioning techniques, each designed to answer this question, are compared, in relation to a simple multilevel selection model in which a trait's evolution is affected by both individual and group selection. None of the three techniques is wholly satisfactory: one implies that group selection can operate even if individual fitness is determined by individual phenotype alone, whereas the other two imply that group selection can operate even if there is no variance in group fitness. This has significant implications both for our understanding of what the term "multilevel selection" means and for the traditional concept of group selection.     

Alternative formulations of multilevel selection

Hierarchical expansions of the theory of natural selection exist in two distinct bodies of thought in evolutionary biology, the group selection and the species selection traditions. Both traditions share the point of view that the principles of natural selection apply at levels of biological organization above the level of the individual organism. This leads them both to considermultilevel selection situations, where selection is occurring simultaneously at more than one level. Impeding unification of the theoretical approaches of the multilevel selection traditions are the different goals of investigators in the different subdisciplines and the different types of data potentially available for analysis. We identify two alternative approaches to multilevel situations, which we termmultilevel selection [1] andmultilevel selection [2]. Of interest in the former case are the effects of group membership onindividual fitnesses, and in the latter the tendencies for the groups themselves to go extinct or to found new groups (i.e., group fitnesses). We argue that: neither represents the entire multilevel selection process; both are aspects of any multilevel selection situation; and both are legitimate approaches, suitable for answering different questions. Using this formalism, we show that: multilevel selection [2] does not require emergent group properties in order to provide an explanatory mechanism of evolutionary change; multilevel selection [1] is usually more appropriate for neontological group selection studies; and species selection is most fruitfully considered from the point of view of multilevel selection [2]. Finally we argue that the effect hypothesis of macroevolution, requiring, in selection among species, both the absence of group effects on organismic fitness (multilevel selection [1]), and the direct determination of species fitnesses by those of organisms, is untestable with paleontological data. Furthermore, the conditions for the effect hypothesis to hold are extremely restrictive and unlikely to apply to the vast majority of situations encountered in nature.     

An exact form of the breeder's equation for the evolution of a quantitative trait under natural selection

Starting with the Price equation, I show that the total evolutionary change in mean phenotype that occurs in the presence of fitness variation can be partitioned exactly into five components representing logically distinct processes. One component is the linear response to selection, as represented by the breeder's equation of quantitative genetics, but with heritability defined as the linear regression coefficient of mean offspring phenotype on parent phenotype. The other components are identified as constitutive transmission bias, two types of induced transmission bias, and a spurious response to selection caused by a covariance between parental fitness and offspring phenotype that cannot be predicted from parental phenotypes. The partitioning can be accomplished in two ways, one with heritability measured before (in the absence of) selection, and the other with heritability measured after (in the presence of) selection. Measuring heritability after selection, though unconventional, yields a representation for the linear response to selection that is most consistent with Darwinian evolution by natural selection because the response to selection is determined by the reproductive features of the selected group, not of the parent population as a whole. The analysis of an explicitly Mendelian model shows that the relative contributions of the five terms to the total evolutionary change depends on the level of organization (gene, individual, or mated pair) at which the parent population is divided into phenotypes, with each frame of reference providing unique insight. It is shown that all five components of phenotypic evolution will generally have nonzero values as a result of various combinations of the normal features of Mendelian populations, including biparental sex, allelic dominance, inbreeding, epistasis, linkage disequilibrium, and environmental covariances between traits. Additive genetic variance can be a poor predictor of the adaptive response to selection in these models. The narrow-sense heritability sigma2A/sigma2P should be viewed as an approximation to the offspring-parent linear regression rather than the other way around.     

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.     

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."     

A Critique of R.D. Alexander's Views on Group Selection

Group selection is increasingly being viewed as an important force in human evolution. This paper examines the views of R.D. Alexander, one of the most influential thinkers about human behavior from an evolutionary perspective, on the subject of group selection. Alexander's general conception of evolution is based on the gene-centered approach of G.C. Williams, but he has also emphasized a potential role for group selection in the evolution of individual genomes and in human evolution. Alexander's views are internally inconsistent and underestimate the importance of group selection. Specific themes that Alexander has developed in his account of human evolution are important but are best understood within the framework of multilevel selection theory. From this perspective, Alexander's views on moral systems are not the radical departure from conventional views that he claims, but remain radical in another way more compatible with conventional views.     

Multilevel selection and the social transmission of behavior

Many evolutionary models assume that behaviors are caused directly by genes. An implication is that behavioral uniformity should be found only in groups that are genetically uniform. Yet, the members of human social groups often behave in a uniform fashion, despite the fact that they are genetically diverse. Behavioral uniformity can occur through a variety of psychological mechanisms and social processes, such as imitation, consensus decision making, or the imposition of social norms. We present a series of models in which genes code for social transmission rules, which in turn govern the behaviors that are adopted. Transmission rules can evolve in randomly formed groups that concentrate phenotypic variation at the between-group level, favoring the evolution of altruistic behaviors and other group-advantageous traits. In addition, a direct bias toward adopting altruistic behaviors can evolve. Our models begin to show how group selection can be a strong force in human evolution, despite the absence of extreme genetic variation among groups.     

Multilevel and sex‐specific selection on competitive traits in North American red squirrels

Individuals often interact more closely with some members of the population (e.g., offspring, siblings, or group members) than they do with other individuals. This structuring of interactions can lead to multilevel natural selection, where traits expressed at the group‐level influence fitness alongside individual‐level traits. Such multilevel selection can alter evolutionary trajectories, yet is rarely quantified in the wild, especially for species that do not interact in clearly demarcated groups. We quantified multilevel natural selection on two traits, postnatal growth rate and birth date, in a population of North American red squirrels (Tamiasciurus hudsonicus). The strongest level of selection was typically within‐acoustic social neighborhoods (within 130 m of the nest), where growing faster and being born earlier than nearby litters was key, while selection on growth rate was also apparent both within‐litters and within‐study areas. Higher population densities increased the strength of selection for earlier breeding, but did not influence selection on growth rates. Females experienced especially strong selection on growth rate at the within‐litter level, possibly linked to the biased bequeathal of the maternal territory to daughters. Our results demonstrate the importance of considering multilevel and sex‐specific selection in wild species, including those that are territorial and sexually monomorphic.     

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.     

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.     

Experimental evidence for multivariate stabilizing sexual selection

Stabilizing selection is a fundamental concept in evolutionary biology. In the presence of a single intermediate optimum phenotype (fitness peak) on the fitness surface, stabilizing selection should cause the population to evolve toward such a peak. This prediction has seldom been tested, particularly for suites of correlated traits. The lack of tests for an evolutionary match between population means and adaptive peaks may be due, at least in part, to problems associated with empirically detecting multivariate stabilizing selection and with testing whether population means are at the peak of multivariate fitness surfaces. Here we show how canonical analysis of the fitness surface, combined with the estimation of confidence regions for stationary points on quadratic response surfaces, may be used to define multivariate stabilizing selection on a suite of traits and to establish whether natural populations reside on the multivariate peak. We manufactured artificial advertisement calls of the male cricket Teleogryllus commodus and played them back to females in laboratory phonotaxis trials to estimate the linear and nonlinear sexual selection that female phonotactic choice imposes on male call structure. Significant nonlinear selection on the major axes of the fitness surface was convex in nature and displayed an intermediate optimum, indicating multivariate stabilizing selection. The mean phenotypes of four independent samples of males, from the same population as the females used in phonotaxis trials, were within the 95% confidence region for the fitness peak. These experiments indicate that stabilizing sexual selection may play an important role in the evolution of male call properties in natural populations of T. commodus.     

Laboratory models,causal explanation and group selection

We develop an account of laboratory models, which have been central to the group selection controversy. We compare arguments for group selection in nature with Darwin's arguments for natural selection to argue that laboratory models provide important grounds for causal claims about selection. Biologists get information about causes and cause-effect relationships in the laboratory because of the special role their own causal agency plays there. They can also get information about patterns of effects and antecedent conditions in nature. But to argue that some cause is actually responsible in nature, they require an inference from knowledge of causes in the laboratory context and of effects in the natural context. This process, cause detection, forms the core of an analogical argument for group selection. We discuss the differing roles of mathematical and laboratory models in constructing selective explanations at the group level and apply our discussion to the units of selection controversy to distinguish between the related problems of cause determination and evaluation of evidence. Because laboratory models are at the intersection of the two problems, their study is crucial for framing a coherent theory of explanation for evolutionary biology.     

Multilevel selection analysis of a microbial social trait

The study of microbial communities often leads to arguments for the evolution of cooperation due to group benefits. However, multilevel selection models caution against the uncritical assumption that group benefits will lead to the evolution of cooperation. We analyze a microbial social trait to precisely define the conditions favoring cooperation. We combine the multilevel partition of the Price equation with a laboratory model system: swarming in Pseudomonas aeruginosa. We parameterize a population dynamics model using competition experiments where we manipulate expression, and therefore the cost‐to‐benefit ratio of swarming cooperation. Our analysis shows that multilevel selection can favor costly swarming cooperation because it causes population expansion. However, due to high costs and diminishing returns constitutive cooperation can only be favored by natural selection when relatedness is high. Regulated expression of cooperative genes is a more robust strategy because it provides the benefits of swarming expansion without the high cost or the diminishing returns. Our analysis supports the key prediction that strong group selection does not necessarily mean that microbial cooperation will always emerge.     

MATHEMATICS OF KIN‐ AND GROUP‐SELECTION: FORMALLY EQUIVALENT?

Evolutionary game theory is a general mathematical framework that describes the evolution of social traits. This framework forms the basis of many multilevel selection models and is also frequently used to model evolutionary dynamics on networks. Kin selection, which was initially restricted to describe social interactions between relatives, has also led to a broader mathematical approach, inclusive fitness, that can not only describe social evolution among relatives, but also in group structured populations or on social networks. It turns out that the underlying mathematics of game theory is fundamentally different from the approach of inclusive fitness. Thus, both approaches—evolutionary game theory and inclusive fitness—can be helpful to understand the evolution of social traits in group structured or spatially extended populations.     

Multilevel selection: the evolution of cooperation in non-kin groups

Hamiltons (1964a, 1964b) landmark papers are rightly recognized as the formal basis for our understanding of the evolution of altruistic traits. However, Hamiltons equation as he originally expressed it is simplistic. A genetically oriented approach to studying multilevel selection can provide insights into how the terminology and assumptions used by Hamilton can be generalized. Using contextual analysis I demonstrated that Hamiltons rule actually embodies three distinct processes, group selection, individual selection, and transmission genetics or heritability. Whether an altruistic trait will evolve depends the balance of all of these factors. The genetical approach, and particularly, contextual analysis provides a means of separating these factors and examining them one at a time. Perhaps the greatest issue with Hamiltons equation is the interpretation of r. Hamilton (1964a) interpreted this as relatedness. In this paper I show that what Hamilton called relatedness is more generally interpreted as the proportion for variance among groups, and that many processes in addition to relatedness can increase the variance among groups. I also show that the evolution of an altruistic trait is driven by the ratio of the heritability at the group level to the heritability at the individual level. Under some circumstances this ratio can be greater than 1. In this situation altruism can evolve even if selection favoring selfish behavior is stronger than selection favoring altruism.     

Organisms in evolution

Organisms constitute one of the most remarkable features of our living world. However, they have not yet received any accepted characterization within the framework of the evolutionary theory. The reasons for this contrast between the saliency of organisms in the biological landscape and their theoretical status are multiple and they are analyzed in the first part of this paper. Starting from this contrast, I argue for a theoretically grounded concept of organism within the framework of evolutionary theory itself. To this effect I argue that the theory of major transitions in evolution (Maynard Smith and Szathmáry 1995; Michod 1999) provides us with the theoretical basis for an understanding of the individuality of organisms and I propose a first characterization of organisms as evolutionary units structured by a division of reproductive labor among their parts. I also discuss one of the most important implications of this definition, namely that some colonial entities are to be counted as superorganisms. Finally, I show that though theoretically satisfying, this definition does not suffice in order fully to individuate the organisms and superorganisms in practice. To this end, physiology is needed, because it offers us some criteria for their individuation in ecological space. These criteria, however, are not immune to errors through misidentification and their shortcomings are discussed in the last section. In conclusion, I emphasize the positive implications of these criteria concerning the ecological significance of organisms.     

Adaptation and habitat selection in the eco-evolutionary process

The struggle for existence occurs through the vital rates of population growth. This basic fact demonstrates the tight connection between ecology and evolution that defines the emerging field of eco-evolutionary dynamics. An effective synthesis of the interdependencies between ecology and evolution is grounded in six principles. The mechanics of evolution specifies the origin and rules governing traits and evolutionary strategies. Traits and evolutionary strategies achieve their selective value through their functional relationships with fitness. Function depends on the underlying structure of variation and the temporal, spatial and organizational scales of evolution. An understanding of how changes in traits and strategies occur requires conjoining ecological and evolutionary dynamics. Adaptation merges these five pillars to achieve a comprehensive understanding of ecological and evolutionary change. I demonstrate the value of this world-view with reference to the theory and practice of habitat selection. The theory allows us to assess evolutionarily stable strategies and states of habitat selection, and to draw the adaptive landscapes for habitat-selecting species. The landscapes can then be used to forecast future evolution under a variety of climate change and other scenarios.     

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.     

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.