Oligomorphic dynamics for analyzing the quantitative genetics of adaptive speciation

Dispersal evolution and eco-evolutionary dynamics in antagonistic species interactions

Dispersal evolution modifies diverse spatial processes, such as range expansions or biological invasions of single species, but we are currently lacking a realistic vision for metacommunities. Focusing on antagonistic species interactions, we review existing theory of dispersal evolution between natural enemies, and explain how this might be relevant for classic themes in host-parasite evolutionary ecology, namely virulence evolution or local adaptation. Specifically, we highlight the importance of considering the simultaneous (co)evolution of dispersal and interaction traits. Linking such multi-trait evolution with reciprocal demographic and epidemiological feedbacks might change basic predictions about coevolutionary processes and spatial dynamics of interacting species. Future challenges concern the integration of system-specific disease ecology or spatial modifiers, such as spatial network structure or environmental heterogeneity.

Separation of evolutionary timescales in coevolving species

Many coevolutionary processes, including host-parasite and host-symbiont interactions, involve one species or trait which evolves much faster than the other. Whether or not a coevolutionary trajectory converges depends on the relative rates of evolutionary change in the two species, and so current adaptive dynamics approaches generally either determine convergence stability by considering arbitrary (often comparable) rates of evolutionary change or else rely on necessary or sufficient conditions for convergence stability. We propose a method for determining convergence stability in the case where one species is expected to evolve much faster than the other. This requires a second separation of timescales, which assumes that the faster evolving species will reach its evolutionary equilibrium (if one exists) before a new mutation arises in the more slowly evolving species. This method, which is likely to be a reasonable approximation for many coevolving species, both provides straightforward conditions for convergence stability and is less computationally expensive than traditional analysis of coevolution models, as it reduces the trait space from a two-dimensional plane to a one-dimensional manifold. In this paper, we present the theory underlying this new separation of timescales and provide examples of how it could be used to determine coevolutionary outcomes from models.

Ecological determinants of Cope's rule and its inverse

Cope's rule posits that evolution gradually increases the body size in lineages. Over the last decades, two schools of thought have fueled a debate on the applicability of Cope's rule by reporting empirical evidence, respectively, for and against Cope's rule. The apparent contradictions thus documented highlight the need for a comprehensive process-based synthesis through which both positions of this debate can be understood and reconciled. Here, we use a process-based community-evolution model to investigate the eco-evolutionary emergence of Cope's rule. We report three characteristic macroevolutionary patterns, of which only two are consistent with Cope's rule. First, we find that Cope's rule applies when species interactions solely depend on relative differences in body size and the risk of lineage extinction is low. Second, in environments with higher risk of lineage extinction, the recurrent evolutionary elimination of top predators induces cyclic evolution toward larger body sizes, according to a macroevolutionary pattern we call the recurrent Cope's rule. Third, when interactions between species are determined not only by their body sizes but also by their ecological niches, the recurrent Cope's rule may get inverted, leading to cyclic evolution toward smaller body sizes. This recurrent inverse Cope's rule is characterized by highly dynamic community evolution, involving the diversification of species with large body sizes and the extinction of species with small body sizes. To our knowledge, these results provide the first theoretical foundation for reconciling the contrasting empirical evidence reported on body-size evolution.

A Theoretical Framework for Trait-Based Eco-Evolutionary Dynamics: Population Structure, Intraspecific Variation, and Community Assembly

AbstractHow is trait diversity in a community apportioned between and within coevolving species? Disruptive selection may result in either a few species with large intraspecific trait variation (ITV) or many species with different mean traits but little ITV. Similar questions arise in spatially structured communities: heterogeneous environments could result in either a few species that exhibit local adaptation or many species with different mean traits but little local adaptation. To date, theory has been well-equipped to either include ITV or to dynamically determine the number of coexisting species, but not both. Here, we devise a theoretical framework that combines these facets and apply it to the above questions of how trait variation is apportioned within and between species in unstructured and structured populations, using two simple models of Lotka-Volterra competition. For unstructured communities, we find that as the breadth of the resource spectrum increases, ITV goes from being unimportant to crucial for characterizing the community. For spatially structured communities on two patches, we find no local adaptation, symmetric local adaptation, or asymmetric local adaptation, depending on how much the patches differ. Our framework provides a general approach to incorporate ITV in models of eco-evolutionary community assembly.

Evolution of class-structured populations in periodic environments

What is the influence of periodic environmental fluctuations on life-history evolution? We present a general theoretical framework to understand and predict the long-term evolution of life-history traits under a broad range of ecological scenarios. Specifically, we investigate how periodic fluctuations affect selection when the population is also structured in distinct classes. This analysis yields time-varying selection gradients that clarify the influence of the fluctuations of the environment on the competitive ability of a specific life-history mutation. We use this framework to analyse the evolution of key life-history traits of pathogens. We examine three different epidemiological scenarios and we show how periodic fluctuations of the environment can affect the evolution of virulence and transmission as well as the preference for different hosts. These examples yield new and testable predictions on pathogen evolution, and illustrate how our approach can provide a better understanding of the evolutionary consequences of time-varying environmental fluctuations in a broad range of scenarios.

How does genetic architecture affect eco-evolutionary dynamics? A theoretical perspective

Recent studies have revealed the importance of feedbacks between contemporary rapid evolution (i.e. evolution that occurs through changes in allele frequencies) and ecological dynamics. Despite its inherent interdisciplinary nature, however, studies on eco-evolutionary feedbacks have been mostly ecological and tended to focus on adaptation at the phenotypic level without considering the genetic architecture of evolutionary processes. In empirical studies, researchers have often compared ecological dynamics when the focal species under selection has a single genotype with dynamics when it has multiple genotypes. In theoretical studies, common approaches are models of quantitative traits where mean trait values change adaptively along the fitness gradient and Mendelian traits with two alleles at a single locus. On the other hand, it is well known that genetic architecture can affect short-term evolutionary dynamics in population genetics. Indeed, recent theoretical studies have demonstrated that genetic architecture (e.g. the number of loci, linkage disequilibrium and ploidy) matters in eco-evolutionary dynamics (e.g. evolutionary rescue where rapid evolution prevents extinction and population cycles driven by (co)evolution). I propose that theoretical approaches will promote the synthesis of functional genomics and eco-evolutionary dynamics through models that combine population genetics and ecology as well as nonlinear time-series analyses using emerging big data.

This article is part of the theme issue ‘Genetic basis of adaptation and speciation: from loci to causative mutations’.

Coevolutionary theory of hosts and parasites

Host and parasite evolution are closely intertwined, with selection for adaptations and counter‐adaptations forming a coevolutionary feedback loop. Coevolutionary dynamics are often difficult to intuit due to these feedbacks and are hard to demonstrate empirically in most systems. Theoretical models have therefore played a crucial role in shaping our understanding of host–parasite coevolution. Theoretical models vary widely in their assumptions, approaches and aims, and such variety makes it difficult, especially for non‐theoreticians and those new to the field, to: (1) understand how model approaches relate to one another; (2) identify key modelling assumptions; (3) determine how model assumptions relate to biological systems; and (4) reconcile the results of different models with contrasting assumptions. In this review, we identify important model features, highlight key results and predictions and describe how these pertain to model assumptions. We carry out a literature survey of theoretical studies published since the 1950s (n = 219 papers) to support our analysis. We identify two particularly important features of models that tend to have a significant qualitative impact on the outcome of host–parasite coevolution: population dynamics and the genetic basis of infection. We also highlight the importance of other modelling features, such as stochasticity and whether time proceeds continuously or in discrete steps, that have received less attention but can drastically alter coevolutionary dynamics. We finish by summarizing recent developments in the field, specifically the trend towards greater model complexity, and discuss likely future directions for research.

Antigenic escape selects for the evolution of higher pathogen transmission and virulence

Despite the propensity for complex and non-equilibrium dynamics in nature, eco-evolutionary analytical theory typically assumes that populations are at equilibria. In particular, pathogens often show antigenic escape from host immune defences, leading to repeated epidemics, fluctuating selection and diversification, but we do not understand how this impacts the evolution of virulence. We model the impact of antigenic drift and escape on the evolution of virulence in a generalized pathogen and apply a recently introduced oligomorphic methodology that captures the dynamics of the mean and variance of traits, to show analytically that these non-equilibrium dynamics select for the long-term persistence of more acute pathogens with higher virulence. Our analysis predicts both the timings and outcomes of antigenic shifts leading to repeated epidemics and predicts the increase in variation in both antigenicity and virulence before antigenic escape. There is considerable variation in the degree of antigenic escape that occurs across pathogens and our results may help to explain the difference in virulence between related pathogens including, potentially, human influenzas. Furthermore, it follows that these pathogens will have a lower R₀, with clear implications for epidemic behaviour, endemic behaviour and control. More generally, our results show the importance of examining the evolutionary consequences of non-equilibrium dynamics.

The dynamics of trait variance in multi-species communities

In this paper, we establish the explicit connection between deterministic trait-based population-level models (in the form of partial differential equations) and species-level models (in the form of ordinary differential equations), in the context of eco-evolutionary systems. In particular, by starting from a population-level model of density distributions in trait space, we derive what amounts to an extension of the typical models at the species level known from adaptive dynamics literature, to account not only for abundance and mean trait values, but also explicitly for trait variances. Thus, we arrive at an explicitly polymorphic model at the species level. The derivations make precise the relationship between the parameters in the two classes of models and allow us to distinguish between notions of fitness on the population and species levels. Through a formal stability analysis, we see that exponential growth of an eigenvalue in the trait covariance matrix corresponds to a breakdown of the underlying assumptions of the species-level model. In biological terms, this may be interpreted as a speciation event: that is, we obtain an explicit notion of the blow-up of the variance of (possibly a linear combination of) traits as a precursor to speciation. Moreover, since evolutionary volatility of the mean trait value is proportional to trait variance, this provides a notion that species at the cusp of speciation are also the most adaptive. We illustrate these concepts and considerations using a numerical simulation.

An evolutionary quantitative genetics model for phenotypic (co)variances under limited dispersal, with an application to socially synergistic traits

Darwinian evolution consists of the gradual transformation of heritable traits due to natural selection and the input of random variation by mutation. Here, we use a quantitative genetics approach to investigate the coevolution of multiple quantitative traits under selection, mutation, and limited dispersal. We track the dynamics of trait means and of variance-covariances between traits that experience frequency-dependent selection. Assuming a multivariate-normal trait distribution, we recover classical dynamics of quantitative genetics, as well as stability and evolutionary branching conditions of invasion analyses, except that due to limited dispersal, selection depends on indirect fitness effects and relatedness. In particular, correlational selection that associates different traits within-individuals depends on the fitness effects of such associations between-individuals. We find that these kin selection effects can be as relevant as pleiotropy for the evolution of correlation between traits. We illustrate this with an example of the coevolution of two social traits whose association within-individuals is costly but synergistically beneficial between-individuals. As dispersal becomes limited and relatedness increases, associations between-traits between-individuals become increasingly targeted by correlational selection. Consequently, the trait distribution goes from being bimodal with a negative correlation under panmixia to unimodal with a positive correlation under limited dispersal.

Evolutionarily stable communities: a framework for understanding the role of trait evolution in the maintenance of diversity

Biological diversity depends on the interplay between evolutionary diversification and ecological mechanisms allowing species to coexist. Current research increasingly integrates ecology and evolution over a range of timescales, but our common conceptual framework for understanding species coexistence requires better incorporation of evolutionary processes. Here, we focus on the idea of evolutionarily stable communities (ESCs), which are theoretical endpoints of evolution in a community context. We use ESCs as a unifying framework to highlight some important but under-appreciated theoretical results, and we review empirical research relevant to these theoretical predictions. We explain how, in addition to generating diversity, evolution can also limit diversity by reducing the effectiveness of coexistence mechanisms. The coevolving traits of competing species may either diverge or converge, depending on whether the number of species in the community is low (undersaturated) or high (oversaturated) relative to the ESC. Competition in oversaturated communities can lead to extinction or neutrally coexisting, ecologically equivalent species. It is critical to consider trait evolution when investigating fundamental ecological questions like the strength of different coexistence mechanisms, the feasibility of ecologically equivalent species, and the interpretation of different patterns of trait dispersion.

Theoretical Approaches in Evolutionary Ecology: Environmental Feedback as a Unifying Perspective

Evolutionary biology and ecology have a strong theoretical underpinning, and this has fostered a variety of modeling approaches. A major challenge of this theoretical work has been to unravel the tangled feedback loop between ecology and evolution. This has prompted the development of two main classes of models. While quantitative genetics models jointly consider the ecological and evolutionary dynamics of a focal population, a separation of timescales between ecology and evolution is assumed by evolutionary game theory, adaptive dynamics, and inclusive fitness theory. As a result, theoretical evolutionary ecology tends to be divided among different schools of thought, with different toolboxes and motivations. My aim in this synthesis is to highlight the connections between these different approaches and clarify the current state of theory in evolutionary ecology. Central to this approach is to make explicit the dependence on environmental dynamics of the population and evolutionary dynamics, thereby materializing the eco-evolutionary feedback loop. This perspective sheds light on the interplay between environmental feedback and the timescales of ecological and evolutionary processes. I conclude by discussing some potential extensions and challenges to our current theoretical understanding of eco-evolutionary dynamics.

Evolutionary Stability of Jointly Evolving Traits in Subdivided Populations

The evolutionary stability of quantitative traits depends on whether a population can resist invasion by any mutant. While uninvadability is well understood in well-mixed populations, it is much less so in subdivided populations when multiple traits evolve jointly. Here, we investigate whether a spatially subdivided population at a monomorphic equilibrium for multiple traits can withstand invasion by any mutant or is subject to diversifying selection. Our model also explores the correlations among traits arising from diversifying selection and how they depend on relatedness due to limited dispersal. We find that selection tends to favor a positive (negative) correlation between two traits when the selective effects of one trait on relatedness is positively (negatively) correlated to the indirect fitness effects of the other trait. We study the evolution of traits for which this matters: dispersal that decreases relatedness and helping that has positive indirect fitness effects. We find that when dispersal cost is low and the benefits of helping accelerate faster than its costs, selection leads to the coexistence of mobile defectors and sessile helpers. Otherwise, the population evolves to a monomorphic state with intermediate helping and dispersal. Overall, our results highlight the effects of population subdivision for evolutionary stability and correlations among traits.

Sympatric speciation in structureless environments

BACKGROUND

Darwin and the architects of the Modern Synthesis found sympatric speciation difficult to explain and suggested it is unlikely to occur. Increasingly, evidence over the past few decades suggest that sympatric speciation can occur under ecological conditions that require at most intraspecific competition for a structured resource. Here we used an individual-based population model with variable foraging strategies to study the evolution of mating behavior among foraging strategy types. Initially, individuals were placed at random on a structureless resource landscape, with subsequent spatial variation induced through foraging activity itself. The fitness of individuals was determined by their biomass at the end of each generational cycle. The model incorporates three diallelic, codominant foraging strategy genes, and one mate-choice or m-trait (i.e. incipient magic trait) gene, where the latter is inactive when random mating is assumed.

RESULTS

Under non-random mating, the m-trait gene promotes increasing levels of either disassortative or assortative mating when the frequency of m respectively increases or decreases from 0.5. Our evolutionary simulations demonstrate that, under initial random mating conditions, an activated m-trait gene evolves to promote assortative mating because the system, in trying to fit a multipeak adaptive landscape, causes heterozygous individuals to be less fit than homozygous individuals.

CONCLUSION

Our results extend our theoretical understanding that sympatric speciation can evolve under nicheless or gradientless resource conditions: i.e. the underlying resource is monomorphic and initially spatially homogeneous. Further the simplicity and generality of our model suggests that sympatric speciation may be more likely than previously thought to occur in mobile, sexually-reproducing organisms.

Evolutionary dynamics of a quantitative trait in a finite asexual population

In finite populations, mutation limitation and genetic drift can hinder evolutionary diversification. We consider the evolution of a quantitative trait in an asexual population whose size can vary and depends explicitly on the trait. Previous work showed that evolutionary branching is certain ("deterministic branching") above a threshold population size, but uncertain ("stochastic branching") below it. Using the stationary distribution of the population's trait variance, we identify three qualitatively different sub-domains of "stochastic branching" and illustrate our results using a model of social evolution. We find that in very small populations, branching will almost never be observed; in intermediate populations, branching is intermittent, arising and disappearing over time; in larger populations, finally, branching is expected to occur and persist for substantial periods of time. Our study provides a clearer picture of the ecological conditions that facilitate the appearance and persistence of novel evolutionary lineages in the face of genetic drift.

Modes of competition and the fitness of evolved populations

Competition between individuals drives the evolution of whole species. Although the fittest individuals survive the longest and produce the most offspring, in some circumstances the resulting species may not be optimally fit. Here, using theoretical analysis and stochastic simulations of a simple model ecology, we show how the mode of competition can profoundly affect the fitness of evolved species. When individuals compete directly with one another, the adaptive dynamics framework provides accurate predictions for the number and distribution of species, which occupy positions of maximal fitness. By contrast, if competition is mediated by the consumption of a common resource, then demographic noise leads to the stabilization of species with near minimal fitness.

Multidimensional (co)evolutionary stability

The complexity of biotic and abiotic environmental conditions is such that the fitness of individuals is likely to depend on multiple traits. Using a synthetic framework of phenotypic evolution that draws from adaptive dynamics and quantitative genetics approaches, we explore how the number of traits under selection influences convergence stability and evolutionary stability in models for coevolution in multidimensional phenotype spaces. Our results allow us to identify three different effects of trait dimensionality on stability. First are (i) a "combinatorial effect": without epistasis and genetic correlations, a higher number of trait dimensions offers more opportunities for equilibria to be unstable; and (ii) epistatic interactions, that is, fitness interactions between traits, which tend to destabilize evolutionary equilibria; this effect increases with the dimension of phenotype space. These first two effects influence both convergence stability and evolutionary stability, while (iii) genetic correlations (due, e.g., to pleiotropy or linkage disequilibrium) can affect only convergence stability. We illustrate the general prediction that increased dimensionality destabilizes evolutionary equilibria using examples drawn from well-studied classical models of frequency-dependent competition for resources, adaptation to a spatially heterogeneous environment, and antagonistic coevolution. In addition, our analyses show that increased dimensionality can favor diversification, for example, in the form of local adaptation, as well as evolutionary escape.

How specificity and epidemiology drive the coevolution of static trait diversity in hosts and parasites

There is typically considerable variation in the level of infectivity of parasites and the degree of resistance of hosts within populations. This trait variation is critical not only to the evolutionary dynamics but also to the epidemiology, and potentially the control of infectious disease. However, we lack an understanding of the processes that generate and maintain this trait diversity. We examine theoretically how epidemiological feedbacks and the characteristics of the interaction between host types and parasites strains determine the coevolution of host-parasite diversity. The interactions include continuous characterizations of the key phenotypic features of classic gene-for-gene and matching allele models. We show that when there are costs to resistance in the hosts and infectivity in the parasite, epidemiological feedbacks may generate diversity but this is limited to dimorphism, often of extreme types, in a broad range of realistic infection scenarios. For trait polymorphism, there needs to be both specificity of infection between host types and parasite strains as well as incompatibility between particular strains and types. We emphasize that although the high specificity is well known to promote temporal "Red Queen" diversity, it is costs and combinations of hosts and parasites that cannot infect that will promote static trait diversity.

Evolutionary branching in deme-structured populations

Adaptive dynamics shows that a continuous trait under frequency dependent selection may first converge to a singular point followed by spontaneous transition from a unimodal trait distribution into a bimodal one, which is called "evolutionary branching". Here, we study evolutionary branching in a deme-structured population by constructing a quantitative genetic model for the trait variance dynamics, which allows us to obtain an analytic condition for evolutionary branching. This is first shown to agree with previous conditions for branching expressed in terms of relatedness between interacting individuals within demes and obtained from mutant-resident systems. We then show this branching condition can be markedly simplified when the evolving trait affect fecundity and/or survival, as opposed to affecting population structure, which would occur in the case of the evolution of dispersal. As an application of our model, we evaluate the threshold migration rate below which evolutionary branching cannot occur in a pairwise interaction game. This agrees very well with the individual-based simulation results.

Limiting similarity, species packing, and the shape of competition kernels

A traditional question in community ecology is whether species' traits are distributed as more-or-less regularly spaced clusters. Interspecific competition has been suggested to play a role in such structuring of communities. The seminal theoretical work on limiting similarity and species packing, presented four decades ago by Robert MacArthur, Richard Levins and Robert May, has recently been extended. There is now a deeper understanding of how competitive interactions influence community structure, for instance, how the shape of competition kernels can determine the clustering of species' traits. Competition is typically weaker for greater phenotypic difference, and the shape of the dependence defines a competition kernel. The clustering tendencies of kernels interact with other effects, such as variation in resource availability along a niche axis, but the kernel shape can have a decisive influence on community structure. Here we review and further extend the recent developments and evaluate their importance.

Evolutionary branching in a finite population: deterministic branching vs. stochastic branching

Adaptive dynamics formalism demonstrates that, in a constant environment, a continuous trait may first converge to a singular point followed by spontaneous transition from a unimodal trait distribution into a bimodal one, which is called “evolutionary branching.” Most previous analyses of evolutionary branching have been conducted in an infinitely large population. Here, we study the effect of stochasticity caused by the finiteness of the population size on evolutionary branching. By analyzing the dynamics of trait variance, we obtain the condition for evolutionary branching as the one under which trait variance explodes. Genetic drift reduces the trait variance and causes stochastic fluctuation. In a very small population, evolutionary branching does not occur. In larger populations, evolutionary branching may occur, but it occurs in two different manners: in deterministic branching, branching occurs quickly when the population reaches the singular point, while in stochastic branching, the population stays at singularity for a period before branching out. The conditions for these cases and the mean branching-out times are calculated in terms of population size, mutational effects, and selection intensity and are confirmed by direct computer simulations of the individual-based model.