The curse of the Pharaoh revisited: evolutionary bi-stability in environmentally transmitted pathogens

It is increasingly evident that for a number of high-profile pathogens, transmission involves both direct and environmental pathways. Much of the distinguished evolutionary theory has, however, focused on each of transmission component separately. Herein, we use the framework of adaptive dynamics to study the evolutionary consequences of mixed transmission. We find that environmental transmission can select for increased virulence when direct transmission is low. Increasing the efficiency of direct transmission gives rise to an evolutionary bi-stability, with coexistence of different levels of virulence. We conclude that the overlooked contribution of environmental transmission may explain the curious appearance of high virulence in pathogens that are typically only moderately pathogenic, as observed for avian influenza viruses and cholera.     

Ecological bistability and evolutionary reversals under asymmetrical competition

Abstract How does the process of life‐history evolution interplay with population dynamics? Almost all models that have addressed this question assume that any combination of phenotypic traits uniquely determine the ecological population state. Here we show that if multiple ecological equilibria can exist, the evolution of a trait that relates to competitive performance can undergo adaptive reversals that drive cyclic alternation between population equilibria. The occurrence of evolutionary reversals requires neither environmentally driven changes in selective forces nor the coevolution of interactions with other species. The mechanism inducing evolutionary reversals is twofold. First, there exist phenotypes near which mutants can invade and yet fail to become fixed; although these mutants are eventually eliminated, their transitory growth causes the resident population to switch to an alternative ecological equilibrium. Second, asymmetrical competition causes the direction of selection to revert between high and low density. When ecological conditions for evolutionary reversals are not satisfied, the population evolves toward a steady state of either low or high abundance, depending on the degree of competitive asymmetry and environmental parameters. A sharp evolutionary transition between evolutionary stasis and evolutionary reversals and cycling can occur in response to a smooth change in ecological parameters, and this may have implications for our understanding of size‐abundance patterns.     

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.     

The evolution of environmental and genetic sex determination in fluctuating environments

Twenty years ago, Bulmer and Bull suggested that disruptive selection, produced by environmental fluctuations, can result in an evolutionary transition from environmental sex determination (ESD) to genetic sex determination (GSD). We investigated the feasibility of such a process, using mutation-limited adaptive dynamics and individual-based computer simulations. Our model describes the evolution of a reaction norm for sex determination in a metapopulation setting with partial migration and variation in an environmental variable both within and between local patches. The reaction norm represents the probability of becoming a female as a function of environmental state and was modeled as a sigmoid function with two parameters, one giving the location (i.e., the value of the environmental variable for which an individual has equal chance of becoming either sex) and the other giving the slope of the reaction norm for that environment. The slope can be interpreted as being set by the level of developmental noise in morph determination, with less noise giving a steeper slope and a more switchlike reaction norm. We found convergence stable reaction norms with intermediate to large amounts of developmental noise for conditions characterized by low migration rates, small differential competitive advantages between the sexes over environments, and little variation between individual environments within patches compared to variation between patches. We also considered reaction norms with the slope parameter constrained to a high value, corresponding to little developmental noise. For these we found evolutionary branching in the location parameter and a transition from ESD toward GSD, analogous to the original analysis by Bulmer and Bull. Further evolutionary change, including dominance evolution, produced a polymorphism acting as a GSD system with heterogamety. Our results point to the role of developmental noise in the evolution of sex determination.     

Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree

We present a general framework for modelling adaptive trait dynamics in which we integrate various concepts and techniques from modern ESS-theory. The concept of evolutionarily singular strategies is introduced as a generalization of the ESS-concept. We give a full classification of the singular strategies in terms of ESS-stability, convergence stability, the ability of the singular strategy to invade other populations if initially rare itself, and the possibility of protected dimorphisms occurring within the singular strategy's neighbourhood. Of particular interest is a type of singular strategy that is an evolutionary attractor from a great distance, but once in its neighbourhood a population becomes dimorphic and undergoes disruptive selection leading to evolutionary branching. Modelling the adaptive growth and branching of the evolutionary tree can thus be considered as a major application of the framework. A haploid version of Levene's soft selection model is developed as a specific example to demonstrate evolutionary dynamics and branching in monomorphic and polymorphic populations.     

On the evolutionary interplay between dispersal and local adaptation in heterogeneous environments

Dispersal, whether in the form of a dandelion seed drifting on the breeze, or a salmon migrating upstream to breed in a nonnatal stream, transports genes between locations. At these locations, local adaptation modifies the gene frequencies so their carriers are better suited to particular conditions, be those of newly disturbed soil or a quiet river pool. Both dispersal and local adaptation are major drivers of population structure; however, in general, their respective roles are not independent and the two may often be at odds with one another evolutionarily, each one exhibiting negative feedback on the evolution of the other. Here, we investigate their joint evolution within a simple, discrete‐time, metapopulation model. Depending on environmental conditions, their evolutionary interplay leads to either a monomorphic population of highly dispersing generalists or a collection of rarely dispersing, locally adapted, polymorphic sub‐populations, each adapted to a particular habitat type. A critical value of environmental heterogeneity divides these two selection regimes and the nature of the transition between them is determined by the level of kin competition. When kin competition is low, at the transition we observe discontinuities, bistability, and hysteresis in the evolved strategies; however, when high, kin competition moderates the evolutionary feedback and the transition is smooth.     

A model for the evolutionary dynamics of cross-feeding polymorphisms in microorganisms

 Understanding mechanisms of evolutionary diversification is central to evolutionary biology. Microbes constitute promising model systems for observing processes of diversification directly in the laboratory. One of the main existing paradigms for microbial diversification is the evolution of cross-feeding polymorphisms, in which a strain specializing on a primary resource coexists with a cross-feeding strain that specializes on a waste product resulting from consumption of the primary resource. Here I propose a theoretical model for the evolutionary dynamics through which cross-feeding polymorphisms can gradually emerge from a single ancestral strain. The model is based on the framework of adaptive dynamics, which has proved to be very useful for studying adaptive processes of divergence under sympatric conditions. In particular, the phenomenon of evolutionary branching serves as a general paradigm for diversification. I show that evolutionary branching naturally occurs in evolutionary models of cross-feeding if (1) there is a trade-off between uptake efficiencies on the primary and secondary resources, and (2) this trade-off has positive curvature. The model also suggests that the evolution of cross-feeding should be more likely in chemostat cultures than in serial batch cultures, which conforms with empirical observations. Overall, the model provides a theoretical metaphor for the evolution of cross-feeding polymorphisms. Received: February 19, 2002 / Accepted: May 8, 2002     

Adaptive dynamics of Lotka-Volterra systems with trade-offs: the role of interspecific parameter dependence in branching

We determine the adaptive dynamics of a general Lotka-Volterra system containing an intraspecific parameter dependency--in the form of an explicit functional trade-off between evolving parameters--and interspecific parameter dependencies--arising from modelling species interactions. We develop expressions for the fitness of a mutant strategy in a multi-species resident environment, the position of the singular strategy in such systems and the non-mixed second-order partial derivatives of the mutant fitness. These expressions can be used to determine the evolutionary behaviour of the system. The type of behaviour expected depends on the curvature of the trade-off function and can be interpreted in a biologically intuitive manner using the rate of acceleration/deceleration of the costs implicit in the trade-off function. We show that for evolutionary branching to occur we require that one (or both) of the traded-off parameters includes an interspecific parameter dependency and that the trade-off function has weakly accelerating costs. This could have important implications for understanding the type of mechanisms that cause speciation. The general theory is motivated by using adaptive dynamics to examine evolution in a predator-prey system. The applicability of the general theory as a tool for examining specific systems is highlighted by calculating the evolutionary behaviour in a three species (prey-predator-predator) system.     

Eco-evolutionary feedbacks,adaptive dynamics and evolutionary rescue theory

Adaptive dynamics theory has been devised to account for feedbacks between ecological and evolutionary processes. Doing so opens new dimensions to and raises new challenges about evolutionary rescue. Adaptive dynamics theory predicts that successive trait substitutions driven by eco-evolutionary feedbacks can gradually erode population size or growth rate, thus potentially raising the extinction risk. Even a single trait substitution can suffice to degrade population viability drastically at once and cause ‘evolutionary suicide’. In a changing environment, a population may track a viable evolutionary attractor that leads to evolutionary suicide, a phenomenon called ‘evolutionary trapping’. Evolutionary trapping and suicide are commonly observed in adaptive dynamics models in which the smooth variation of traits causes catastrophic changes in ecological state. In the face of trapping and suicide, evolutionary rescue requires that the population overcome evolutionary threats generated by the adaptive process itself. Evolutionary repellors play an important role in determining how variation in environmental conditions correlates with the occurrence of evolutionary trapping and suicide, and what evolutionary pathways rescue may follow. In contrast with standard predictions of evolutionary rescue theory, low genetic variation may attenuate the threat of evolutionary suicide and small population sizes may facilitate escape from evolutionary traps.     

Protected polymorphism and evolutionary stability in pleiotropic models with trait-specific dominance

When alleles have pleiotropic effects on a number of quantitative traits, the degree of dominance between a pair of alleles can be different for each trait. Such trait-specific dominance has been studied previously in models for the maintenance of genetic variation by antagonistic effects of an allele on two fitness components. By generalizing these models to an arbitrary number of fitness components or other phenotypic traits with different degrees of dominance, I show that genetic polymorphism is generally impossible without antagonistic fitness effects of different traits and without trait-specific dominance. I also investigate dominance and pleiotropy from a more long-term evolutionary perspective, allowing for the study of general ecological scenarios, and I discuss the effects of trait-specific dominance on evolutionary stability criteria. When selection is mainly directional and only trait-specific dominance and antagonism cause the emergence of polymorphism, then these polymorphisms can be overtaken by single mutants again, such that they are probably short-lived on an evolutionary time scale. Near evolutionarily singular points where directional selection is absent, trait-specific dominance and overdominance facilitate the emergence of polymorphism and cause evolutionary divergence in some cases. An important outcome of these models is that trait-specific dominance allows for the emergence of genetic polymorphisms without a selective disadvantage for heterozygotes. This removes the scope for the evolution of assortative mate choice and affects dominance modification. Sympatric speciation by disruptive ecological selection requires this heterozygote disadvantage in order to evolve, and therefore it becomes less plausible if the emergence of genetic polymorphism usually occurs via trait-specific dominance and antagonistic effects.     

A construction method to study the role of incidence in the adaptive dynamics of pathogens with direct and environmental transmission

We study the adaptive dynamics of virulence of a pathogen transmitted both via direct contacts between hosts and via free pathogens that survive in the environment. The model is very flexible with a number of trade-off functions linking virulence to other pathogen-related parameters and with two incidence functions that describe the contact rates between hosts and between a host and free pathogens. Instead of making a priori particular assumptions about the shapes of these functions, we introduce a construction method to create specific pairs of incidence functions such that the model becomes an optimization model. Unfolding the optimization model leads to coexistence of pathogen strains and evolutionary branching of virulence. The construction method is applicable to a wide range of eco-evolutionary models.     

The adaptive dynamics of the evolution of host resistance to indirectly transmitted microparasites

We use adaptive dynamics and pairwise invadability plots to examine the evolutionary dynamics of host resistance to microparasitic infection transmitted indirectly via free stages. We investigate trade-offs between pathogen transmission rate and intrinsic growth rate. Adaptive dynamics distinguishes various evolutionary outcomes associated with repellors, attractors or branching points. We find criteria corresponding to these and demonstrate that a major factor deciding the evolutionary outcome is whether trade-offs are acceleratingly or deceleratingly costly. We compare and contrast two models and show how the differences between them lead to different evolutionary outcomes.     

Joint evolution of dispersal and connectivity

Functional connectivity, the realized flow of individuals between the suitable sites of a heterogeneous landscape, is a prime determinant of the maintenance and evolution of populations in fragmented habitats. While a large body of literature examines the evolution of dispersal propensity, it is less known how evolution shapes functional connectivity via traits that influence the distribution of the dispersers. Here, we use a simple model to demonstrate that, in a heterogeneous environment with clustered and solitary sites (i.e., with variable structural connectivity), the evolutionarily stable population contains strains that are strongly differentiated in their pattern of connectivity (local vs. global dispersal), but not necessarily in the fraction of dispersed individuals. Also during evolutionary branching, selection is disruptive predominantly on the pattern of connectivity rather than on dispersal propensity itself. Our model predicts diversification along a hitherto neglected axis of dispersal strategies and highlights the role of the solitary sites—the more isolated and therefore seemingly less important patches of habitat—in maintaining global dispersal that keeps all sites connected.     

Metaphysiological and evolutionary dynamics of populations exploiting constant and interactive resources:R—K selection revisited

Summary I begin by reviewing the derivation of continuous logistic growth and dynamic consumer—resource interaction equations in terms of specific resource extraction and biomass conversion functions that are considered to hold at a population level. Evolutionary stable strategy (ESS) methods are discussed for analysing populations modelled by these equations. The question of selection trade-offs is then considered, particularly in the context of populations being efficient at extracting resources versus converting resources to their own biomass. Questions relating to single populations with high versus low conversion rates and interacting populations with high versus low self-interference rates are also considered. The models discussed here demonstrate conclusively that self-interference is an essential part of any consumption process: without it population growth and interaction processes do not make any sense. The analysis clarifies concepts relating to the somewhat discredited notion ofr—K selection.     

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.     

Beyond simple adaptation: Incorporating other evolutionary processes and concepts into eco-evolutionary dynamics

Studies of eco-evolutionary dynamics have integrated evolution with ecological processes at multiple scales (populations, communities and ecosystems) and with multiple interspecific interactions (antagonistic, mutualistic and competitive). However, evolution has often been conceptualised as a simple process: short-term directional adaptation that increases population growth. Here we argue that diverse other evolutionary processes, well studied in population genetics and evolutionary ecology, should also be considered to explore the full spectrum of feedback between ecological and evolutionary processes. Relevant but underappreciated processes include (1) drift and mutation, (2) disruptive selection causing lineage diversification or speciation reversal and (3) evolution driven by relative fitness differences that may decrease population growth. Because eco-evolutionary dynamics have often been studied by population and community ecologists, it will be important to incorporate a variety of concepts in population genetics and evolutionary ecology to better understand and predict eco-evolutionary dynamics in nature.     

Population dynamics and evolutionary processes: the manifold roles of habitat selection

Summary Any character that has a substantial effect on a species' distribution and abundance can exert a variety of indirect effects on evolutionary processes. It is suggested that an organism's capacity for habitat selection is just such a character. Habitat selection can constrain the selective environment experienced by a population. Habitat selection can also indirectly influence the relative importance of natural selection, drift, and gene flow, through its effect on population size and growth rate. In many circumstances (but not all), habitat selection increases population size and growth rate, and thereby makes selection in a local environment more effective than drift and gene flow.     

Multiple scales of selection influence the evolutionary emergence of novel pathogens

When pathogens encounter a novel environment, such as a new host species or treatment with an antimicrobial drug, their fitness may be reduced so that adaptation is necessary to avoid extinction. Evolutionary emergence is the process by which new pathogen strains arise in response to such selective pressures. Theoretical studies over the last decade have clarified some determinants of emergence risk, but have neglected the influence of fitness on evolutionary rates and have not accounted for the multiple scales at which pathogens must compete successfully. We present a cross-scale theory for evolutionary emergence, which embeds a mechanistic model of within-host selection into a stochastic model for emergence at the population scale. We explore how fitness landscapes at within-host and between-host scales can interact to influence the probability that a pathogen lineage will emerge successfully. Results show that positive correlations between fitnesses across scales can greatly facilitate emergence, while cross-scale conflicts in selection can lead to evolutionary dead ends. The local genotype space of the initial strain of a pathogen can have disproportionate influence on emergence probability. Our cross-scale model represents a step towards integrating laboratory experiments with field surveillance data to create a rational framework to assess emergence risk.     

A stochastic model of evolutionary dynamics with deterministic large-population asymptotics

An evolutionary birth-death process is proposed as a model of evolutionary dynamics. Agents residing in a continuous spatial environment X, play a game G, with a continuous strategy set S, against other agents in the environment. The agents’ positions and strategies continuously change in response to other agents and to random effects. Agents spawn asexually at rates that depend on their current fitness, and agents die at rates that depend on their local population density. Agents’ individual evolutionary trajectories in X and S are governed by a system of stochastic ODEs. When the number of agents is large and distributed in a smooth density on (X,S), the collective dynamics of the entire population is governed by a certain (deterministic) PDE, which we call a fitness-diffusion equation.