Jeremy Van Cleve

Not Just a Theory—The Utility of Mathematical Models in Evolutionary Biology

Models have made numerous contributions to evolutionary biology, but misunderstandings persist regarding their purpose. By formally testing the logic of verbal hypotheses, proof-of-concept models clarify thinking, uncover hidden assumptions, and spur new directions of study. thumbnail image credit: modified from the Biodiversity Heritage Library

Evolution of stochastic switching rates in asymmetric fitness landscapes

Uncertain environments pose a tremendous challenge to populations: The selective pressures imposed by the environment can change so rapidly that adaptation by mutation alone would be too slow. One solution to this problem is given by the phenomenon of stochastic phenotype switching, which causes genetically uniform populations to be phenotypically heterogenous. Stochastic phenotype switching has been observed in numerous microbial species and is generally assumed to be an adaptive bet-hedging strategy to anticipate future environmental change. We use an explicit population genetic model to investigate the evolutionary dynamics of phenotypic switching rates. We find that whether or not stochastic switching is an adaptive strategy is highly contingent upon the fitness landscape given by the changing environment. Unless selection is very strong, asymmetric fitness landscapes—where the cost of being maladapted is not identical in all environments—strongly select against stochastic switching. We further observe a threshold phenomenon that causes switching rates to be either relatively high or completely absent, but rarely intermediate. Our finding that marginal changes in selection pressures can cause fundamentally different evolutionary outcomes is important in a wide range of fields concerned with microbial bet hedging.

PATHWAYS TO SOCIAL EVOLUTION: RECIPROCITY, RELATEDNESS, AND SYNERGY

Many organisms live in populations structured by space and by class, exhibit plastic responses to their social partners, and are subject to nonadditive ecological and fitness effects. Social evolution theory has long recognized that all of these factors can lead to different selection pressures but has only recently attempted to synthesize how these factors interact. Using models for both discrete and continuous phenotypes, we show that analyzing these factors in a consistent framework reveals that they interact with one another in ways previously overlooked. Specifically, behavioral responses (reciprocity), genetic relatedness, and synergy interact in nontrivial ways that cannot be easily captured by simple summary indices of assortment. We demonstrate the importance of these interactions by showing how they have been neglected in previous synthetic models of social behavior both within and between species. These interactions also affect the level of behavioral responses that can evolve in the long run; proximate biological mechanisms are evolutionarily stable when they generate enough responsiveness relative to the level of responsiveness that exactly balances the ecological costs and benefits. Given the richness of social behavior across taxa, these interactions should be a boon for empirical research as they are likely crucial for describing the complex relationship linking ecology, demography, and social behavior.

Demography, kinship, and the evolving theory of genomic imprinting

Genomic imprinting is the differential expression of an allele based on the parent of origin. Recent transcriptome-wide evaluations of the number of imprinted genes reveal complex patterns of imprinted expression among developmental stages and cell types. Such data demand a comprehensive evolutionary framework in which to understand the effect of natural selection on imprinted gene expression. We present such a framework for how asymmetries in demographic parameters and fitness effects can lead to the evolution of genomic imprinting and place recent theoretical advances in this framework. This represents a modern interpretation of the kinship theory, is well suited to studying populations with complex social interactions, and provides predictions which can be tested with forthcoming transcriptomic data. To understand the intricate phenotypic patterns that are emerging from the recent deluge of data, future investigations of genomic imprinting will require integrating evolutionary theory, transcriptomic data, developmental and functional genetics, and natural history.

Behavioral Responses in Structured Populations Pave the Way to Group Optimality

An unresolved controversy regarding social behaviors is exemplified when natural selection might lead to behaviors that maximize fitness at the social-group level but are costly at the individual level. Except for the special case of groups of clones, we do not have a general understanding of how and when group-optimal behaviors evolve, especially when the behaviors in question are flexible. To address this question, we develop a general model that integrates behavioral plasticity in social interactions with the action of natural selection in structured populations. We find that group-optimal behaviors can evolve, even without clonal groups, if individuals exhibit appropriate behavioral responses to each other’s actions. The evolution of such behavioral responses, in turn, is predicated on the nature of the proximate behavioral mechanisms. We model a particular class of proximate mechanisms, prosocial preferences, and find that such preferences evolve to sustain maximum group benefit under certain levels of relatedness and certain ecological conditions. Thus, our model demonstrates the fundamental interplay between behavioral responses and relatedness in determining the course of social evolution. We also highlight the crucial role of proximate mechanisms such as prosocial preferences in the evolution of behavioral responses and in facilitating evolutionary transitions in individuality.

How Demography, Life History, and Kinship Shape the Evolution of Genomic Imprinting

How phenomena like helping, dispersal, or the sex ratio evolve depends critically on demographic and life‐history factors. One phenotype that is of particular interest to biologists is genomic imprinting, which results in parent‐of‐origin‐specific gene expression and thus deviates from the predictions of Mendel’s rules. The most prominent explanation for the evolution of genomic imprinting, the kinship theory, originally specified that multiple paternity can cause the evolution of imprinting when offspring affect maternal resource provisioning. Most models of the kinship theory do not detail how population subdivision, demography, and life history affect the evolution of imprinting. In this work, we embed the classic kinship theory within an island model of population structure and allow for diverse demographic and life‐history features to affect the direction of selection on imprinting. We find that population structure does not change how multiple paternity affects the evolution of imprinting under the classic kinship theory. However, if the degree of multiple paternity is not too large, we find that sex‐specific migration and survival and generation overlap are the primary factors determining which allele is silenced. This indicates that imprinting can evolve purely as a result of sex‐related asymmetries in the demographic structure or life history of a species.

On the evolution of mutation in changing environments: recombination and phenotypic switching.

Phenotypic switching has been observed in laboratory studies of yeast and bacteria, in which the rate of such switching appears to adjust to match the frequency of environmental changes. Among possible mechanisms of switching are epigenetic influences on gene expression and variation in levels of methylation; thus environmental and/or genetic factors may contribute to the rate of switching. Most previous analyses of the evolution of phenotypic switching have compared exponential growth rates of noninteracting populations, and recombination has been ignored. Our genetic model of the evolution of switching rates is framed in terms of a mutation-modifying gene, environments that cause periodic changes in fitness, and recombination between the mutation modifier and the gene under selection. Exact results are obtained for all recombination rates and symmetric fitnesses that strongly generalize earlier results obtained under complete linkage and strong constraints on the relation between fitness and period of switching. Our analytical and numerical results suggest a general principle that recombination reduces the stable rate of switching in symmetric and asymmetric fitness regimes and when the period of switching is random. As the recombination rate increases, it becomes less likely that there is a stable nonzero rate of switching.

Sex-Specific Viability, Sex Linkage and Dominance in Genomic Imprinting

Genomic imprinting is a phenomenon by which the expression of an allele at a locus depends on the parent of origin. Two different two-locus evolutionary models are presented in which a second locus modifies the imprinting status of the primary locus, which is under differential selection in males and females. In the first model, a modifier allele that imprints the primary locus invades the population when the average dominance coefficient among females and males is \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({>}\frac{1}{2}\) \end{document} and selection is weak. The condition for invasion is always heavily contingent upon the extent of dominance. Imprinting is more likely in the sex experiencing weaker selection only under some parameter regimes, whereas imprinting by either sex is equally likely under other regimes. The second model shows that a modifier allele that induces imprinting will increase when imprinting has a direct selective advantage. The results are not qualitatively dependent on whether the modifier locus is autosomal or X linked.

The evolving landscape of imprinted genes in humans and mice: Conflict among alleles, genes, tissues, and kin

Three recent genome-wide studies in mice and humans have produced the most definitive map to date of genomic imprinting (gene expression that depends on parental origin) by incorporating multiple tissue types and developmental stages. Here, we explore the results of these studies in light of the kinship theory of genomic imprinting, which predicts that imprinting evolves due to differential genetic relatedness between maternal and paternal relatives. The studies produce a list of imprinted genes with around 120-180 in mice and ~100 in humans. The studies agree on broad patterns across mice and humans including the complex patterns of imprinted expression at loci like Igf2 and Grb10. We discuss how the kinship theory provides a powerful framework for hypotheses that can explain these patterns. Finally, since imprinting is rare in the genome despite predictions from the kinship theory that it might be common, we discuss evolutionary factors that could favor biallelic expression.

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

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