The adaptive dynamics of function-valued traits

This study extends the framework of adaptive dynamics to function-valued traits. Such adaptive traits naturally arise in a great variety of settings: variable or heterogeneous environments, age-structured populations, phenotypic plasticity, patterns of growth and form, resource gradients, and in many other areas of evolutionary ecology. Adaptive dynamics theory allows analysing the long-term evolution of such traits under the density-dependent and frequency-dependent selection pressures resulting from feedback between evolving populations and their ecological environment. Starting from individual-based considerations, we derive equations describing the expected dynamics of a function-valued trait in asexually reproducing populations under mutation-limited evolution, thus generalizing the canonical equation of adaptive dynamics to function-valued traits. We explain in detail how to account for various kinds of evolutionary constraints on the adaptive dynamics of function-valued traits. To illustrate the utility of our approach, we present applications to two specific examples that address, respectively, the evolution of metabolic investment strategies along resource gradients, and the evolution of seasonal flowering schedules in temporally varying environments.     

The Price equation framework to study disease within-host evolution

The evolution of infectious diseases is known to affect epidemiological dynamics, but, for some viruses and bacteria, this evolution also takes place inside a host during the course of an infection. I develop an original approach to study intrahost evolutionary dynamics of quantitative disease traits. This approach can be expressed mathematically using the ‘Price equation’ framework recently developed in evolutionary epidemiology. This framework combines population genetics and within-host population dynamics models to identify trade-offs that affect disease intrahost evolution and to predict short-term evolutionary dynamics of life-history traits. I show that this can be applied to study the evolution of viruses competing for host cells or to study the coevolution between parasites and the immune system of the host. This framework can also easily incorporate experimental data. Studying intrahost evolutionary dynamics provides insight at the within-host level, because it allows us to better understand the course of chronic infections, and at the epidemiological level, because it helps to study multi-scale evolutionary processes. This framework can be used to address important biological issues, from immune escape to disease evolutionary response to treatments.     

On the evolutionary dynamics of pathogens with direct and environmental transmission

A number of ecologically and economically important pathogens exhibit a complex transmission dynamics that involves distinct transmission modes. In this paper, we study the evolutionary dynamics of pathogens for which transmission includes direct host-to-host as well as indirect environmental transmission. Different routes of infection spread require specific adaptations of the parasite, which may result in conflicting selection pressures. Using the framework of Adaptive dynamics, we investigate how these conflicting selection pressures are resolved in the course of evolution and determine the conditions for evolutionary diversification of pathogen strains. We show that evolutionary branching and subsequent evolution of specialist strains occurs in wide parameter regions but evolutionary bistability and evolution of generalist pathogens are possible as well. Our analysis reveals that the relative contributions of direct and environmental transmission, as well as the underlying ecological dynamics, play a crucial role in shaping the course of pathogen evolution. Our findings may explain the coexistence of high and low virulence strains observed in several pathogenic organisms using different transmission modes (e.g., influenza viruses) and highlight the importance of considering ecological dynamics in virulence management.     

Neutral Models of Microbiome Evolution

There has been an explosion of research on host-associated microbial communities (i.e.,microbiomes). Much of this research has focused on surveys of microbial diversities across a variety of host species, including humans, with a view to understanding how these microbiomes are distributed across space and time, and how they correlate with host health, disease, phenotype, physiology and ecology. Fewer studies have focused on how these microbiomes may have evolved. In this paper, we develop an agent-based framework to study the dynamics of microbiome evolution. Our framework incorporates neutral models of how hosts acquire their microbiomes, and how the environmental microbial community that is available to the hosts is assembled. Most importantly, our framework also incorporates a Wright-Fisher genealogical model of hosts, so that the dynamics of microbiome evolution is studied on an evolutionary timescale. Our results indicate that the extent of parental contribution to microbial availability from one generation to the next significantly impacts the diversity of microbiomes: the greater the parental contribution, the less diverse the microbiomes. In contrast, even when there is only a very small contribution from a constant environmental pool, microbial communities can remain highly diverse. Finally, we show that our models may be used to construct hypotheses about the types of processes that operate to assemble microbiomes over evolutionary time.     

Evolution in stage-structured populations

For many organisms, stage is a better predictor of demographic rates than age. Yet no general theoretical framework exists for understanding or predicting evolution in stage-structured populations. Here, we provide a general modeling approach that can be used to predict evolution and demography of stage-structured populations. This advances our ability to understand evolution in stage-structured populations to a level previously available only for populations structured by age. We use this framework to provide the first rigorous proof that Lande's theorem, which relates adaptive evolution to population growth, applies to stage-classified populations, assuming only normality and that evolution is slow relative to population dynamics. We extend this theorem to allow for different means or variances among stages. Our next major result is the formulation of Price's theorem, a fundamental law of evolution, for stage-structured populations. In addition, we use data from Trillium grandiflorum to demonstrate how our models can be applied to a real-world population and thereby show their practical potential to generate accurate projections of evolutionary and population dynamics. Finally, we use our framework to compare rates of evolution in age- versus stage-structured populations, which shows how our methods can yield biological insights about evolution in stage-structured populations.     

Symmetric competition as a general model for single-species adaptive dynamics

Adaptive dynamics is a widely used framework for modeling long-term evolution of continuous phenotypes. It is based on invasion fitness functions, which determine selection gradients and the canonical equation of adaptive dynamics. Even though the derivation of the adaptive dynamics from a given invasion fitness function is general and model-independent, the derivation of the invasion fitness function itself requires specification of an underlying ecological model. Therefore, evolutionary insights gained from adaptive dynamics models are generally model-dependent. Logistic models for symmetric, frequency-dependent competition are widely used in this context. Such models have the property that the selection gradients derived from them are gradients of scalar functions, which reflects a certain gradient property of the corresponding invasion fitness function. We show that any adaptive dynamics model that is based on an invasion fitness functions with this gradient property can be transformed into a generalized symmetric competition model. This provides a precise delineation of the generality of results derived from competition models. Roughly speaking, to understand the adaptive dynamics of the class of models satisfying a certain gradient condition, one only needs a complete understanding of the adaptive dynamics of symmetric, frequency-dependent competition. We show how this result can be applied to number of basic issues in evolutionary theory.     

Evolution of dispersal and life history interact to drive accelerating spread of an invasive species

Populations on the edge of an expanding range are subject to unique evolutionary pressures acting on their life‐history and dispersal traits. Empirical evidence and theory suggest that traits there can evolve rapidly enough to interact with ecological dynamics, potentially giving rise to accelerating spread. Nevertheless, which of several evolutionary mechanisms drive this interaction between evolution and spread remains an open question. We propose an integrated theoretical framework for partitioning the contributions of different evolutionary mechanisms to accelerating spread, and we apply this model to invasive cane toads in northern Australia. In doing so, we identify a previously unrecognised evolutionary process that involves an interaction between life‐history and dispersal evolution during range shift. In roughly equal parts, life‐history evolution, dispersal evolution and their interaction led to a doubling of distance spread by cane toads in our model, highlighting the potential importance of multiple evolutionary processes in the dynamics of range expansion.     

A dimensionless number for understanding the evolutionary dynamics of antigenically variable RNA viruses

Antigenically variable RNA viruses are significant contributors to the burden of infectious disease worldwide. One reason for their ubiquity is their ability to escape herd immunity through rapid antigenic evolution and thereby to reinfect previously infected hosts. However, the ways in which these viruses evolve antigenically are highly diverse. Some have only limited diversity in the long-run, with every emergence of a new antigenic variant coupled with a replacement of the older variant. Other viruses rapidly accumulate antigenic diversity over time. Others still exhibit dynamics that can be considered evolutionary intermediates between these two extremes. Here, we present a theoretical framework that aims to understand these differences in evolutionary patterns by considering a virus's epidemiological dynamics in a given host population. Our framework, based on a dimensionless number, probabilistically anticipates patterns of viral antigenic diversification and thereby quantifies a virus's evolutionary potential. It is therefore similar in spirit to the basic reproduction number, the well-known dimensionless number which quantifies a pathogen's reproductive potential. We further outline how our theoretical framework can be applied to empirical viral systems, using influenza A/H3N2 as a case study. We end with predictions of our framework and work that remains to be done to further integrate viral evolutionary dynamics with disease ecology.     

Disease evolution across a range of spatio-temporal scales

Traditional explorations of infectious disease evolution have considered the competition between two cross-reactive strains within the standard framework of disease models. Such techniques predict that diseases should evolve to be highly transmissible, benign to the host and possess a long infectious period: in general, diseases do not conform to this ideal. Here we consider a more holistic approach, suggesting that evolution is a trade-off between adaptive pressures at different scales: within host, between hosts and at the population level. We present a model combining within-host pathogen dynamics and transmission between individuals governed by an explicit contact network, where transmission dynamics between hosts are a function of the interaction between the pathogen and the hosts' immune system, though ultimately constrained by the contacts each infected host possesses. Our results show how each of the scales places constraints on the evolutionary behavior, and that complex dynamics may emerge due to the feedbacks between epidemiological and evolutionary dynamics. In particular, multiple stable states can occur with switching between them stochastically driven.     

The evolution of payoff matrices: providing incentives to cooperate

Most of the work in evolutionary game theory starts with a model of a social situation that gives rise to a particular payoff matrix and analyses how behaviour evolves through natural selection. Here, we invert this approach and ask, given a model of how individuals behave, how the payoff matrix will evolve through natural selection. In particular, we ask whether a prisoner's dilemma game is stable against invasions by mutant genotypes that alter the payoffs. To answer this question, we develop a two-tiered framework with goal-oriented dynamics at the behavioural time scale and a diploid population genetic model at the evolutionary time scale. Our results are two-fold: first, we show that the prisoner's dilemma is subject to invasions by mutants that provide incentives for cooperation to their partners, and that the resulting game is a coordination game similar to the hawk-dove game. Second, we find that for a large class of mutants and symmetric games, a stable genetic polymorphism will exist in the locus determining the payoff matrix, resulting in a complex pattern of behavioural diversity in the population. Our results highlight the importance of considering the evolution of payoff matrices to understand the evolution of animal social systems.     

Individual heterogeneity in life histories and eco‐evolutionary dynamics

Individual heterogeneity in life history shapes eco‐evolutionary processes, and unobserved heterogeneity can affect demographic outputs characterising life history and population dynamical properties. Demographic frameworks like matrix models or integral projection models represent powerful approaches to disentangle mechanisms linking individual life histories and population‐level processes. Recent developments have provided important steps towards their application to study eco‐evolutionary dynamics, but so far individual heterogeneity has largely been ignored. Here, we present a general demographic framework that incorporates individual heterogeneity in a flexible way, by separating static and dynamic traits (discrete or continuous). First, we apply the framework to derive the consequences of ignoring heterogeneity for a range of widely used demographic outputs. A general conclusion is that besides the long‐term growth rate lambda, all parameters can be affected. Second, we discuss how the framework can help advance current demographic models of eco‐evolutionary dynamics, by incorporating individual heterogeneity. For both applications numerical examples are provided, including an empirical example for pike. For instance, we demonstrate that predicted demographic responses to climate warming can be reversed by increased heritability. We discuss how applications of this demographic framework incorporating individual heterogeneity can help answer key biological questions that require a detailed understanding of eco‐evolutionary dynamics.     

Investigating the eco-evolutionary response of microbiomes to environmental change

Microorganisms are the primary engines of biogeochemical processes and foundational to the provisioning of ecosystem services to human society. Free-living microbial communities (microbiomes) and their functioning are now known to be highly sensitive to environmental change. Given microorganisms' capacity for rapid evolution, evolutionary processes could play a role in this response. Currently, however, few models of biogeochemical processes explicitly consider how microbial evolution will affect biogeochemical responses to environmental change. Here, we propose a conceptual framework for explicitly integrating evolution into microbiome–functioning relationships. We consider how microbiomes respond simultaneously to environmental change via four interrelated processes that affect overall microbiome functioning (physiological acclimation, demography, dispersal and evolution). Recent evidence in both the laboratory and the field suggests that ecological and evolutionary dynamics occur simultaneously within microbiomes; however, the implications for biogeochemistry under environmental change will depend on the timescales over which these processes contribute to a microbiome's response. Over the long term, evolution may play an increasingly important role for microbially driven biogeochemical responses to environmental change, particularly to conditions without recent historical precedent.     

How the type of anthropogenic change alters the consequences of ecological traps

Understanding altered ecological and evolutionary dynamics in novel environments is vital for predicting species responses to rapid environmental change. One fundamental concept relevant to such dynamics is the ecological trap, which arises from rapid anthropogenic change and can facilitate extinction. Ecological traps occur when formerly adaptive habitat preferences become maladaptive because the cues individuals preferentially use in selecting habitats lead to lower fitness than other alternatives. While it has been emphasized that traps can arise from different types of anthropogenic change, the resulting consequences of these different types of traps remain unknown. Using a novel model framework that builds upon the Price equation from evolutionary genetics, we provide the first analysis that contrasts the ecological and evolutionary consequences of ecological traps arising from two general types of perturbations known to trigger traps. Our model suggests that traps arising from degradation of existing habitats are more likely to facilitate extinction than those arising from the addition of novel trap habitat. Importantly, our framework reveals the mechanisms of these outcomes and the substantial scope for persistence via rapid evolution that may buffer many populations from extinction, helping to resolve the paradox of continued persistence of many species in dramatically altered landscapes.     

Altruism and the evolution of resource generalism and specialism

The evolution of resource specialism and generalism has attracted widespread interest. Evolutionary drivers affecting niche differentiation and resource specialization have focused on the role of trade-offs. Here, however, we explore how the role of cooperation, mediated through altruistic behaviors, and classic resource-consumer dynamics can influence the evolution of resource utilization. Using an evolutionary invasion approach, we investigate how critical thresholds in levels of altruism are needed for resource specialization to arise and be maintained. Differences between complementary (essential) and substitutable resources affect the evolution of resource generalists. The strength of resource preferences coupled with the levels of altruism are predicted to influence the evolution of generalism. Coupling appropriate evolutionary game and ecological dynamics lead to novel expectations in the feedbacks between social behaviors and population dynamics for understanding classic ecological problems.     

The evolutionary language game.

We explore how evolutionary game dynamics have to be modified to accomodate a mathematical framework for the evolution of language. In particular, we are interested in the evolution of vocabulary, that is associations between signals and objects. We assume that successful communication contributes to biological fitness: individuals who communicate well leave more offspring. Children inherit from their parents a strategy for language learning (a language acquisition device). We consider three mechanisms whereby language is passed from one generation to the next: (i) parental learning: children learn the language of their parents; (ii) role model learning: children learn the language of individuals with a high payoff; and (iii) random learning: children learn the language of randomly chosen individuals. We show that parental and role model learning outperform random learning. Then we introduce mistakes in language learning and study how this process changes language over time. Mistakes increase the overall efficacy of parental and role model learning: in a world with errors evolutionary adaptation is more efficient. Our model also provides a simple explanation why homonomy is common while synonymy is rare.     

Lethal pathogens, non-lethal synergists and the evolutionary ecology of resistance

Mixed pathogenic infections are known to have profound effects on the ecological and evolutionary diversity of both hosts and parasites. Although a variety of mechanisms have been proposed by which hosts can withstand parasitic infections, the role of multiple infections and the trade-off in multiple defence strategies remain relatively unexplored. We develop a stage-structured host-pathogen model to explore the ecological and evolutionary dynamics of host resistance to different modes of infection. In particular, we investigate how the evolution of resistance is influenced through infection by a lethal pathogen and a non-lethal synergist (that only acts to enhance the infectivity of the pathogen). We extend our theoretical framework to explore how trade-offs in the ability to withstand infection by the lethal pathogen and the ability to tolerate the synergist affect the likelihood of coexistence and the evolution of polymorphic host strategies. We show how the underlying structure of the trade-off surface is crucial in the maintenance of resistance polymorphisms. Further, depending on the shape of the trade-off surface, we predict that different levels of host resistance will show individual responses to the presence of non-lethal synergists. Our results are discussed in the wider context of recent developments in understanding the evolution of resistance to pathogen infections and resistance management.     

A general theory for the evolutionary dynamics of virulence

Most theory on the evolution of virulence is based on a game-theoretic approach. One potential shortcoming of this approach is that it does not allow the prediction of the evolutionary dynamics of virulence. Such dynamics are of interest for several reasons: for experimental tests of theory, for the development of useful virulence management protocols, and for understanding virulence evolution in situations where the epidemiological dynamics never reach equilibrium and/or when evolutionary change occurs on a timescale comparable to that of the epidemiological dynamics. Here we present a general theory similar to that of quantitative genetics in evolutionary biology that allows for the easy construction of models that include both within-host mutation as well as superinfection and that is capable of predicting both the short- and long-term evolution of virulence. We illustrate the generality and intuitive appeal of the theory through a series of examples showing how it can lead to transparent interpretations of the selective forces governing virulence evolution. It also leads to novel predictions that are not possible using the game-theoretic approach. The general theory can be used to model the evolution of other pathogen traits as well.