Evolutionary dynamics in structured populations

Evolutionary dynamics shape the living world around us. At the centre of every evolutionary process is a population of reproducing individuals. The structure of that population affects evolutionary dynamics. The individuals can be molecules, cells, viruses, multicellular organisms or humans. Whenever the fitness of individuals depends on the relative abundance of phenotypes in the population, we are in the realm of evolutionary game theory. Evolutionary game theory is a general approach that can describe the competition of species in an ecosystem, the interaction between hosts and parasites, between viruses and cells, and also the spread of ideas and behaviours in the human population. In this perspective, we review the recent advances in evolutionary game dynamics with a particular emphasis on stochastic approaches in finite sized and structured populations. We give simple, fundamental laws that determine how natural selection chooses between competing strategies. We study the well-mixed population, evolutionary graph theory, games in phenotype space and evolutionary set theory. We apply these results to the evolution of cooperation. The mechanism that leads to the evolution of cooperation in these settings could be called ‘spatial selection’: cooperators prevail against defectors by clustering in physical or other spaces.     

Eco-evolutionary dynamics

Evolutionary ecologists and population biologists have recently considered that ecological and evolutionary changes are intimately linked and can occur on the same time-scale. Recent theoretical developments have shown how the feedback between ecological and evolutionary dynamics can be linked, and there are now empirical demonstrations showing that ecological change can lead to rapid evolutionary change. We also have evidence that microevolutionary change can leave an ecological signature. We are at a stage where the integration of ecology and evolution is a necessary step towards major advances in our understanding of the processes that shape and maintain biodiversity. This special feature about ‘eco-evolutionary dynamics’ brings together biologists from empirical and theoretical backgrounds to bridge the gap between ecology and evolution and provide a series of contributions aimed at quantifying the interactions between these fundamental processes.     

Stochastic evolutionary dynamics of direct reciprocity

Evolutionary game theory is the study of frequency-dependent selection. The success of an individual depends on the frequencies of strategies that are used in the population. We propose a new model for studying evolutionary dynamics in games with a continuous strategy space. The population size is finite. All members of the population use the same strategy. A mutant strategy is chosen from some distribution over the strategy space. The fixation probability of the mutant strategy in the resident population is calculated. The new mutant takes over the population with this probability. In this case, the mutant becomes the new resident. Otherwise, the existing resident remains. Then, another mutant is generated. These dynamics lead to a stationary distribution over the entire strategy space. Our new approach generalizes classical adaptive dynamics in three ways: (i) the population size is finite; (ii) mutants can be drawn non-locally and (iii) the dynamics are stochastic. We explore reactive strategies in the repeated Prisoner''s Dilemma. We perform ‘knock-out experiments’ to study how various strategies affect the evolution of cooperation. We find that ‘tit-for-tat’ is a weak catalyst for the emergence of cooperation, while ‘always cooperate’ is a strong catalyst for the emergence of defection. Our analysis leads to a new understanding of the optimal level of forgiveness that is needed for the evolution of cooperation under direct reciprocity.     

Whose trait is it anyways? Coevolution of joint phenotypes and genetic architecture in mutualisms

Evolutionary biologists typically envision a trait’s genetic basis and fitness effects occurring within a single species. However, traits can be determined by and have fitness consequences for interacting species, thus evolving in multiple genomes. This is especially likely in mutualisms, where species exchange fitness benefits and can associate over long periods of time. Partners may experience evolutionary conflict over the value of a multi-genomic trait, but such conflicts may be ameliorated by mutualism’s positive fitness feedbacks. Here, we develop a simulation model of a host–microbe mutualism to explore the evolution of a multi-genomic trait. Coevolutionary outcomes depend on whether hosts and microbes have similar or different optimal trait values, strengths of selection and fitness feedbacks. We show that genome-wide association studies can map joint traits to loci in multiple genomes and describe how fitness conflict and fitness feedback generate different multi-genomic architectures with distinct signals around segregating loci. Partner fitnesses can be positively correlated even when partners are in conflict over the value of a multi-genomic trait, and conflict can generate strong mutualistic dependency. While fitness alignment facilitates rapid adaptation to a new optimum, conflict maintains genetic variation and evolvability, with implications for applied microbiome science.     

Footprints in time: comparative quantitative trait loci mapping of the pitcher-plant mosquito,Wyeomyia smithii

Identifying regions of the genome contributing to phenotypic evolution often involves genetic mapping of quantitative traits. The focus then turns to identifying regions of ‘major’ effect, overlooking the observation that traits of ecological or evolutionary relevance usually involve many genes whose individual effects are small but whose cumulative effect is large. Herein, we use the power of fully interfertile natural populations of a single species of mosquito to develop three quantitative trait loci (QTL) maps: one between two post-glacially diverged populations and two between a more ancient and a post-glacial population. All demonstrate that photoperiodic response is genetically a highly complex trait. Furthermore, we show that marker regressions identify apparently ‘non-significant’ regions of the genome not identified by composite interval mapping, that the perception of the genetic basis of adaptive evolution is crucially dependent upon genetic background and that the genetic basis for adaptive evolution of photoperiodic response is highly variable within contemporary populations as well as between anciently diverged populations.     

Pleiotropy of FRIGIDA enhances the potential for multivariate adaptation

An evolutionary response to selection requires genetic variation; however, even if it exists, then the genetic details of the variation can constrain adaptation. In the simplest case, unlinked loci and uncorrelated phenotypes respond directly to multivariate selection and permit unrestricted paths to adaptive peaks. By contrast, ‘antagonistic’ pleiotropic loci may constrain adaptation by affecting variation of many traits and limiting the direction of trait correlations to vectors that are not favoured by selection. However, certain pleiotropic configurations may improve the conditions for adaptive evolution. Here, we present evidence that the Arabidopsis thaliana gene FRI (FRIGIDA) exhibits ‘adaptive’ pleiotropy, producing trait correlations along an axis that results in two adaptive strategies. Derived, low expression FRI alleles confer a ‘drought escape’ strategy owing to fast growth, low water use efficiency and early flowering. By contrast, a dehydration avoidance strategy is conferred by the ancestral phenotype of late flowering, slow growth and efficient water use during photosynthesis. The dehydration avoidant phenotype was recovered when genotypes with null FRI alleles were transformed with functional alleles. Our findings indicate that the well-documented effects of FRI on phenology result from differences in physiology, not only a simple developmental switch.     

Extending eco-evolutionary theory with oligomorphic dynamics

Understanding the interplay between ecological processes and the evolutionary dynamics of quantitative traits in natural systems remains a major challenge. Two main theoretical frameworks are used to address this question, adaptive dynamics and quantitative genetics, both of which have strengths and limitations and are often used by distinct research communities to address different questions. In order to make progress, new theoretical developments are needed that integrate these approaches and strengthen the link to empirical data. Here, we discuss a novel theoretical framework that bridges the gap between quantitative genetics and adaptive dynamics approaches. ‘Oligomorphic dynamics’ can be used to analyse eco-evolutionary dynamics across different time scales and extends quantitative genetics theory to account for multimodal trait distributions, the dynamical nature of genetic variance, the potential for disruptive selection due to ecological feedbacks, and the non-normal or skewed trait distributions encountered in nature. Oligomorphic dynamics explicitly takes into account the effect of environmental feedback, such as frequency- and density-dependent selection, on the dynamics of multi-modal trait distributions and we argue it has the potential to facilitate a much tighter integration between eco-evolutionary theory and empirical data.     

Integrating Evolution into Ecological Modelling: Accommodating Phenotypic Changes in Agent Based Models

Evolutionary change is a characteristic of living organisms and forms one of the ways in which species adapt to changed conditions. However, most ecological models do not incorporate this ubiquitous phenomenon. We have developed a model that takes a ‘phenotypic gambit’ approach and focuses on changes in the frequency of phenotypes (which differ in timing of breeding and fecundity) within a population, using, as an example, seasonal breeding. Fitness per phenotype calculated as the individual’s contribution to population growth on an annual basis coincide with the population dynamics per phenotype. Simplified model variants were explored to examine whether the complexity included in the model is justified. Outputs from the spatially implicit model underestimated the number of individuals across all phenotypes. When no phenotype transitions are included (i.e. offspring always inherit their parent’s phenotype) numbers of all individuals are always underestimated. We conclude that by using a phenotypic gambit approach evolutionary dynamics can be incorporated into individual based models, and that all that is required is an understanding of the probability of offspring inheriting the parental phenotype.     

Gillespie eco‐evolutionary models (GEMs) reveal the role of heritable trait variation in eco‐evolutionary dynamics

Heritable trait variation is a central and necessary ingredient of evolution. Trait variation also directly affects ecological processes, generating a clear link between evolutionary and ecological dynamics. Despite the changes in variation that occur through selection, drift, mutation, and recombination, current eco‐evolutionary models usually fail to track how variation changes through time. Moreover, eco‐evolutionary models assume fitness functions for each trait and each ecological context, which often do not have empirical validation. We introduce a new type of model, Gillespie eco‐evolutionary models (GEMs), that resolves these concerns by tracking distributions of traits through time as eco‐evolutionary dynamics progress. This is done by allowing change to be driven by the direct fitness consequences of model parameters within the context of the underlying ecological model, without having to assume a particular fitness function. GEMs work by adding a trait distribution component to the standard Gillespie algorithm – an approach that models stochastic systems in nature that are typically approximated through ordinary differential equations. We illustrate GEMs with the Rosenzweig–MacArthur consumer–resource model. We show not only how heritable trait variation fuels trait evolution and influences eco‐evolutionary dynamics, but also how the erosion of variation through time may hinder eco‐evolutionary dynamics in the long run. GEMs can be developed for any parameter in any ordinary differential equation model and, furthermore, can enable modeling of multiple interacting traits at the same time. We expect GEMs will open the door to a new direction in eco‐evolutionary and evolutionary modeling by removing long‐standing modeling barriers, simplifying the link between traits, fitness, and dynamics, and expanding eco‐evolutionary treatment of a greater diversity of ecological interactions. These factors make GEMs much more than a modeling advance, but an important conceptual advance that bridges ecology and evolution through the central concept of heritable trait variation.     

Social structure of primate interaction networks facilitates the emergence of cooperation

Animal cooperation has puzzled biologists for a long time as its existence seems to contravene the basic notion of evolutionary biology that natural selection favours ‘selfish’ genes that promote only their own well-being. Evolutionary game theory has shown that cooperators can prosper in populations of selfish individuals if they occur in clusters, interacting more frequently with each other than with the selfish. Here we show that social networks of primates possess the necessary social structure to promote the emergence of cooperation. By simulating evolutionary dynamics of cooperative behaviour on interaction networks of 70 primate groups, we found that for most groups network reciprocity augmented the fixation probability for cooperation. The variation in the strength of this effect can be partly explained by the groups’ community modularity—a network measure for the groups’ heterogeneity. Thus, given selective update and partner choice mechanisms, network reciprocity has the potential to explain socially learned forms of cooperation in primate societies.     

Eco‐evolutionary dynamics in response to selection on life‐history

Understanding the consequences of environmental change on ecological and evolutionary dynamics is inherently problematic because of the complex interplay between them. Using invertebrates in microcosms, we characterise phenotypic, population and evolutionary dynamics before, during and after exposure to a novel environment and harvesting over 20 generations. We demonstrate an evolved change in life‐history traits (the age‐ and size‐at‐maturity, and survival to maturity) in response to selection caused by environmental change (wild to laboratory) and to harvesting (juvenile or adult). Life‐history evolution, which drives changes in population growth rate and thus population dynamics, includes an increase in age‐to‐maturity of 76% (from 12.5 to 22 days) in the unharvested populations as they adapt to the new environment. Evolutionary responses to harvesting are outweighed by the response to environmental change (~ 1.4 vs. 4% change in age‐at‐maturity per generation). The adaptive response to environmental change converts a negative population growth trajectory into a positive one: an example of evolutionary rescue.     

Variant evolutionary trees under phenotypic variance

Evolutionary branching, which is a coevolutionary phenomenon of the development of two or more distinctive traits from a single trait in a population, is the issue of recent studies on adaptive dynamics. In previous studies, it was revealed that trait variance is a minimum requirement for evolutionary branching, and that it does not play an important role in the formation of an evolutionary pattern of branching. Here we demonstrate that the trait evolution exhibits various evolutionary branching paths starting from an identical initial trait to different evolutional terminus traits as determined by only changing the assumption of trait variance. The key feature of this phenomenon is the topological configuration of equilibria and the initial point in the manifold of dimorphism from which dimorphic branches develop. This suggests that the existing monomorphic or polymorphic set in a population is not an unique inevitable consequence of an identical initial phenotype.     

Adaptive dynamics of cooperation may prevent the coexistence of defectors and cooperators and even cause extinction

It has recently been demonstrated that ecological feedback mechanisms can facilitate the emergence and maintenance of cooperation in public goods interactions: the replicator dynamics of defectors and cooperators can result, for example, in the ecological coexistence of cooperators and defectors. Here we show that these results change dramatically if cooperation strategy is not fixed but instead is a continuously varying trait under natural selection. For low values of the factor with which the value of resources is multiplied before they are shared among all participants, evolution will always favour lower cooperation strategies until the population falls below an Allee threshold and goes extinct, thus evolutionary suicide occurs. For higher values of the factor, there exists a unique evolutionarily singular strategy, which is convergence stable. Because the fitness function is linear with respect to the strategy of the mutant, this singular strategy is neutral against mutant invasions. This neutrality disappears if a nonlinear functional response in receiving benefits is assumed. For strictly concave functional responses, singular strategies become uninvadable. Evolutionary branching, which could result in the evolutionary emergence of cooperators and defectors, can occur only with locally convex functional responses, but we illustrate that it can also result in coevolutionary extinction.     

The consequences of polyandry for population viability,extinction risk and conservation

Polyandry, by elevating sexual conflict and selecting for reduced male care relative to monandry, may exacerbate the cost of sex and thereby seriously impact population fitness. On the other hand, polyandry has a number of possible population-level benefits over monandry, such as increased sexual selection leading to faster adaptation and a reduced mutation load. Here, we review existing information on how female fitness evolves under polyandry and how this influences population dynamics. In balance, it is far from clear whether polyandry has a net positive or negative effect on female fitness, but we also stress that its effects on individuals may not have visible demographic consequences. In populations that produce many more offspring than can possibly survive and breed, offspring gained or lost as a result of polyandry may not affect population size. Such ecological ‘masking’ of changes in population fitness could hide a response that only manifests under adverse environmental conditions (e.g. anthropogenic change). Surprisingly few studies have attempted to link mating system variation to population dynamics, and in general we urge researchers to consider the ecological consequences of evolutionary processes.     

What if fertility decline is not permanent? The need for an evolutionarily informed approach to understanding low fertility

‘Demographic transition theory’ assumes that fertility decline is irreversible. This commonly held assumption is based on observations of recent and historical reductions in fertility that accompany modernization and declining mortality. The irreversibility assumption, however, is highly suspect from an evolutionary point of view, because demographic traits are at least partially influenced by genetics and are responsive to social and ecological conditions. Nonetheless, an inevitable shift from high mortality and fertility to low mortality and fertility is used as a guiding framework for projecting human population sizes into the future. This paper reviews some theoretical and empirical evidence suggesting that the assumption of irreversibility is ill-founded, at least without considerable development in theory that incorporates evolutionary and ecological processes. We offer general propositions for how fertility could increase in the future, including natural selection on high fertility variants, the difficulty of maintaining universal norms and preferences in a large, diverse and economically differentiated population, and the escalating resource demands of modernization.     

Eco‐evolutionary feedbacks between private and public goods: evidence from toxic algal blooms

The importance of ‘eco‐evolutionary feedbacks’ in natural systems is currently unclear. Here, we advance a general hypothesis for a particular class of eco‐evolutionary feedbacks with potentially large, long‐lasting impacts in complex ecosystems. These eco‐evolutionary feedbacks involve traits that mediate important interactions with abiotic and biotic features of the environment and a self‐driven reversal of selection as the ecological impact of the trait varies between private (small scale) and public (large scale). Toxic algal blooms may involve such eco‐evolutionary feedbacks due to the emergence of public goods. We review evidence that toxin production by microalgae may yield ‘privatised’ benefits for individual cells or colonies under pre‐ and early‐bloom conditions; however, the large‐scale, ecosystem‐level effects of toxicity associated with bloom states yield benefits that are necessarily ‘public’. Theory predicts that the replacement of private with public goods may reverse selection for toxicity in the absence of higher level selection. Indeed, blooms often harbor significant genetic and functional diversity: bloom populations may undergo genetic differentiation over a scale of days, and even genetically similar lineages may vary widely in toxic potential. Intriguingly, these observations find parallels in terrestrial communities, suggesting that toxic blooms may serve as useful models for eco‐evolutionary dynamics in nature. Eco‐evolutionary feedbacks involving the emergence of a public good may shed new light on the potential for interactions between ecology and evolution to influence the structure and function of entire ecosystems.     

Evolution to alternative levels of stable diversity leaves areas of niche space unexplored

One of the oldest and most persistent questions in ecology and evolution is whether natural communities tend to evolve toward saturation and maximal diversity. Robert MacArthur’s classical theory of niche packing and the theory of adaptive radiations both imply that populations will diversify and fully partition any available niche space. However, the saturation of natural populations is still very much an open area of debate and investigation. Additionally, recent evolutionary theory suggests the existence of alternative evolutionary stable states (ESSs), which implies that some stable communities may not be fully saturated. Using models with classical Lotka-Volterra ecological dynamics and three formulations of evolutionary dynamics (a model using adaptive dynamics, an individual-based model, and a partial differential equation model), we show that following an adaptive radiation, communities can often get stuck in low diversity states when limited by mutations of small phenotypic effect. These low diversity metastable states can also be maintained by limited resources and finite population sizes. When small mutations and finite populations are considered together, it is clear that despite the presence of higher-diversity stable states, natural populations are likely not fully saturating their environment and leaving potential niche space unfilled. Additionally, within-species variation can further reduce community diversity from levels predicted by models that assume species-level homogeneity.     

The Effects of Extra-Somatic Weapons on the Evolution of Human Cooperation towards Non-Kin

Human cooperation and altruism towards non-kin is a major evolutionary puzzle, as is ‘strong reciprocity’ where no present or future rewards accrue to the co-operator/altruist. Here, we test the hypothesis that the development of extra-somatic weapons could have influenced the evolution of human cooperative behaviour, thus providing a new explanation for these two puzzles. Widespread weapons use could have made disputes within hominin groups far more lethal and also equalized power between individuals. In such a cultural niche non-cooperators might well have become involved in such lethal disputes at a higher frequency than cooperators, thereby increasing the relative fitness of genes associated with cooperative behaviour. We employ two versions of the evolutionary Iterated Prisoner''s Dilemma (IPD) model – one where weapons use is simulated and one where it is not. We then measured the performance of 25 IPD strategies to evaluate the effects of weapons use on them. We found that cooperative strategies performed significantly better, and non-cooperative strategies significantly worse, under simulated weapons use. Importantly, the performance of an ‘Always Cooperate’ IPD strategy, equivalent to that of ‘strong reciprocity’, improved significantly more than that of all other cooperative strategies. We conclude that the development of extra-somatic weapons throws new light on the evolution of human altruistic and cooperative behaviour, and particularly ‘strong reciprocity’. The notion that distinctively human altruism and cooperation could have been an adaptive trait in a past environment that is no longer evident in the modern world provides a novel addition to theory that seeks to account for this major evolutionary puzzle.     

Ecological opportunities and specializations shaped genetic divergence in a highly mobile marine top predator

Environmental conditions can shape genetic and morphological divergence. Release of new habitats during historical environmental changes was a major driver of evolutionary diversification. Here, forces shaping population structure and ecotype differentiation (‘pelagic’ and ‘coastal’) of bottlenose dolphins in the North-east Atlantic were investigated using complementary evolutionary and ecological approaches. Inference of population demographic history using approximate Bayesian computation indicated that coastal populations were likely founded by the Atlantic pelagic population after the Last Glacial Maxima probably as a result of newly available coastal ecological niches. Pelagic dolphins from the Atlantic and the Mediterranean Sea likely diverged during a period of high productivity in the Mediterranean Sea. Genetic differentiation between coastal and pelagic ecotypes may be maintained by niche specializations, as indicated by stable isotope and stomach content analyses, and social behaviour. The two ecotypes were only weakly morphologically segregated in contrast to other parts of the World Ocean. This may be linked to weak contrasts between coastal and pelagic habitats and/or a relatively recent divergence. We suggest that ecological opportunity to specialize is a major driver of genetic and morphological divergence. Combining genetic, ecological and morphological approaches is essential to understanding the population structure of mobile and cryptic species.