Effect of unequal vaccination coverage and migration on long-term pathogen evolution in a metapopulation.

Worldwide inequalities in vaccine availability are expected to affect the spread and spatial distribution of infectious diseases. It is unclear, however, how spatial variation in vaccination coverage can affect the long-term evolution of pathogens. Here we use an analytical model and numerical simulations to analyse the influence of different imperfect vaccines on the potential evolution of pathogen virulence in a two-population model where vaccination coverage varies between populations. We focus on four vaccines, with different modes of action on the life cycle of a pathogen infecting two host populations coupled by migration. We show that, for vaccines that reduce infection risk or transmissibility, spatial heterogeneity has little effect on pathogen prevalence and host mortality, and no effect on the evolution of pathogen virulence. In contrast, vaccines that reduce pathogen virulence can select for more virulent pathogens and may lead to the coexistence of different pathogen strains, depending on the degree of spatial heterogeneity in the metapopulation. This heterogeneity is driven by two parameters: pathogen migration and the difference in the vaccination rate between the two populations. We show that vaccines that only reduce pathogen virulence select mainly for a single pathogen strategy in the long term, while vaccines that reduce both transmission and virulence can favor the coexistence of two pathogen genotypes. We discuss the implications and potential extensions of our analysis.

Phenotypic evolution of SARS-CoV-2: a statistical inference approach.

Since its emergence in late 2019, the SARS-CoV-2 virus has spread globally, causing the ongoing COVID-19 pandemic. In the fall of 2020, the Alpha variant (lineage B.1.1.7) was detected in England and spread rapidly, outcompeting the previous lineage. Yet, very little is known about the underlying modifications of the infection process that can explain this selective advantage. Here, we try to quantify how the Alpha variant differed from its predecessor on two phenotypic traits: The transmission rate and the duration of infectiousness. To this end, we analyzed the joint epidemiological and evolutionary dynamics as a function of the Stringency Index, a measure of the amount of Non-Pharmaceutical Interventions. Assuming that these control measures reduce contact rates and transmission, we developed a two-step approach based on ${{SEIR}}$ models and the analysis of a combination of epidemiological and evolutionary information. First, we quantify the link between the Stringency Index and the reduction in viral transmission. Second, based on a novel theoretical derivation of the selection gradient in an ${{SEIR}}$ model, we infer the phenotype of the Alpha variant from its frequency changes. We show that its selective advantage is more likely to result from a higher transmission than from a longer infectious period. Our work illustrates how the analysis of the joint epidemiological and evolutionary dynamics of infectious diseases can help understand the phenotypic evolution driving pathogen adaptation.

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.

Multimorph Eco-Evolutionary Dynamics in Structured Populations.

AbstractOur understanding of the evolution of quantitative traits in nature is still limited by the challenge of including realistic trait distributions in the context of frequency-dependent selection and ecological feedbacks. We extend to class-structured populations a recently introduced "oligomorphic approximation," which bridges the gap between adaptive dynamics and quantitative genetics approaches and allows for the joint description of the dynamics of ecological variables and of the moments of multimodal trait distributions. Our theoretical framework allows us to analyze the dynamics of populations composed of several morphs and structured into distinct classes (e.g., age, size, habitats, infection status, and species). We also introduce a new approximation to simplify the eco-evolutionary dynamics using reproductive values. We illustrate the effectiveness of this approach by applying it to the important conceptual case of two-habitat migration-selection models. In particular, we show that our approach allows us to predict both the long-term evolutionary end points and the short-term transient dynamics of the eco-evolutionary process, including fast evolution regimes. We discuss the theoretical and practical implications of our results and sketch perspectives for future work.

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.

An epi-evolutionary model for predicting the adaptation of spore-producing pathogens to quantitative resistance in heterogeneous environments.

We have modeled the evolutionary epidemiology of spore-producing plant pathogens in heterogeneous environments sown with several cultivars carrying quantitative resistances. The model explicitly tracks the infection-age structure and genetic composition of the pathogen population. Each strain is characterized by pathogenicity traits determining its infection efficiency and a time-varying sporulation curve taking into account lesion aging. We first derived a general expression of the basic reproduction number R 0 for fungal pathogens in heterogeneous environments. We show that the evolutionary attractors of the model coincide with local maxima of R 0 only if the infection efficiency is the same on all host types. We then studied the contribution of three basic resistance characteristics (the pathogenicity trait targeted, resistance effectiveness, and adaptation cost), in interaction with the deployment strategy (proportion of fields sown with a resistant cultivar), to (i) pathogen diversification at equilibrium and (ii) the shaping of transient dynamics from evolutionary and epidemiological perspectives. We show that quantitative resistance affecting only the sporulation curve will always lead to a monomorphic population, whereas dimorphism (i.e., pathogen diversification) can occur if resistance alters infection efficiency, notably with high adaptation costs and proportions of the resistant cultivar. Accordingly, the choice of the quantitative resistance genes operated by plant breeders is a driver of pathogen diversification. From an evolutionary perspective, the time to emergence of the evolutionary attractor best adapted to the resistant cultivar tends to be shorter when resistance affects infection efficiency than when it affects sporulation. Conversely, from an epidemiological perspective, epidemiological control is always greater when the resistance affects infection efficiency. This highlights the difficulty of defining deployment strategies for quantitative resistance simultaneously maximizing epidemiological and evolutionary outcomes.

Targeted vaccination and the speed of SARS-CoV-2 adaptation.

The limited supply of vaccines against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) raises the question of targeted vaccination. Many countries have opted to vaccinate older and more sensitive hosts first to minimize the disease burden. However, what are the evolutionary consequences of targeted vaccination? We clarify the consequences of different vaccination strategies through the analysis of the speed of viral adaptation measured as the rate of change of the frequency of a vaccine-adapted variant. We show that such a variant is expected to spread faster if vaccination targets individuals who are likely to be involved in a higher number of contacts. We also discuss the pros and cons of dose-sparing strategies. Because delaying the second dose increases the proportion of the population vaccinated with a single dose, this strategy can both speed up the spread of the vaccine-adapted variant and reduce the cumulative number of deaths. Hence, strategies that are most effective at slowing viral adaptation may not always be epidemiologically optimal. A careful assessment of both the epidemiological and evolutionary consequences of alternative vaccination strategies is required to determine which individuals should be vaccinated first.

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.

Regulation of prophage induction and lysogenization by phage communication systems.

Many viruses cause both lytic infections, where they release viral particles, and dormant infections, where they await future opportunities to reactivate.1 The benefits of each transmission mode depend on the density of susceptible hosts in the environment.2-4 Some viruses infecting bacteria use molecular signaling to respond plastically to changes in host availability.5 These viruses produce a signal during lytic infection and regulate, based on the signal concentration in the environment, the probability with which they switch to causing dormant infections.5,6 We present an analytical framework to examine the adaptive significance of plasticity in viral life-history traits in fluctuating environments. Our model generalizes and extends previous theory7 and predicts that host density fluctuations should select for plasticity in entering lysogeny as well as virus reactivation once signal concentrations decline. Using Bacillus subtilis and its phage phi3T, we experimentally confirm the prediction that phages use signal to make informed decisions over prophage induction. We also demonstrate that lysogens produce signaling molecules and that signal is degraded by hosts in a density-dependent manner. Declining signal concentrations therefore potentially indicate the presence of uninfected hosts and trigger prophage induction. Finally, we find that conflict over the responses of lysogenization and reactivation to signal is resolved through the evolution of different response thresholds for each trait. Collectively, these findings deepen our understanding of the ways viruses use molecular communication to regulate their infection strategies, which can be leveraged to manipulate host and phage population dynamics in natural environments.

Epidemiological and evolutionary consequences of periodicity in treatment coverage.

Host heterogeneity is a key driver of host-pathogen dynamics. In particular, the use of treatments against infectious diseases creates variation in quality among hosts, which can have both epidemiological and evolutionary consequences. We present a general theoretical model to highlight the consequences of different imperfect treatments on pathogen prevalence and evolution. These treatments differ in their action on host and pathogen traits. In contrast with previous studies, we assume that treatment coverage can vary in time, as in seasonal or pulsed treatment strategies. We show that periodic treatment strategies can limit both disease spread and virulence evolution, depending on the type of treatment. We also introduce a new method to analytically calculate the selection gradient in periodic environments, which allows our predictions to be interpreted using the concept of reproductive value, and can be applied more generally to analyse eco-evolutionary dynamics in class-structured populations and fluctuating environments.

On the evolutionary epidemiology of SARS-CoV-2.

There is no doubt that the novel coronavirus SARS-CoV-2 that causes COVID-19 is mutating and thus has the potential to adapt during the current pandemic. Whether this evolution will lead to changes in the transmission, the duration, or the severity of the disease is not clear. This has led to considerable scientific and media debate, from raising alarms about evolutionary change to dismissing it. Here we review what little is currently known about the evolution of SARS-CoV-2 and extend existing evolutionary theory to consider how selection might be acting upon the virus during the COVID-19 pandemic. Although there is currently no definitive evidence that SARS-CoV-2 is undergoing further adaptation, continued evidence-based analysis of evolutionary change is important so that public health measures can be adjusted in response to substantive changes in the infectivity or severity of COVID-19.

Variability in the durability of CRISPR-Cas immunity.

The durability of host resistance is challenged by the ability of pathogens to escape the defence of their hosts. Understanding the variability in the durability of host resistance is of paramount importance for designing more effective control strategies against infectious diseases. Here, we study the durability of various clustered regularly interspaced short palindromic repeats-Cas (CRISPR-Cas) alleles of the bacteria Streptococcus thermophilus against lytic phages. We found substantial variability in durability among different resistant bacteria. Since the escape of the phage is driven by a mutation in the phage sequence targeted by CRISPR-Cas, we explored the fitness costs associated with these escape mutations. We found that, on average, escape mutations decrease the fitness of the phage. Yet, the magnitude of this fitness cost does not predict the durability of CRISPR-Cas immunity. We contend that this variability in the durability of resistance may be because of variations in phage mutation rate or in the proportion of lethal mutations across the phage genome. These results have important implications on the coevolutionary dynamics between bacteria and phages and for the optimal deployment of resistance strategies against pathogens and pests. Understanding the durability of CRISPR-Cas immunity may also help develop more effective gene-drive strategies based on CRISPR-Cas9 technology. This article is part of a discussion meeting issue 'The ecology and evolution of prokaryotic CRISPR-Cas adaptive immune systems'.

Evolutionary emergence of infectious diseases in heterogeneous host populations.

The emergence and re-emergence of pathogens remains a major public health concern. Unfortunately, when and where pathogens will (re-)emerge is notoriously difficult to predict, as the erratic nature of those events is reinforced by the stochastic nature of pathogen evolution during the early phase of an epidemic. For instance, mutations allowing pathogens to escape host resistance may boost pathogen spread and promote emergence. Yet, the ecological factors that govern such evolutionary emergence remain elusive because of the lack of ecological realism of current theoretical frameworks and the difficulty of experimentally testing their predictions. Here, we develop a theoretical model to explore the effects of the heterogeneity of the host population on the probability of pathogen emergence, with or without pathogen evolution. We show that evolutionary emergence and the spread of escape mutations in the pathogen population is more likely to occur when the host population contains an intermediate proportion of resistant hosts. We also show that the probability of pathogen emergence rapidly declines with the diversity of resistance in the host population. Experimental tests using lytic bacteriophages infecting their bacterial hosts containing Clustered Regularly Interspaced Short Palindromic Repeat and CRISPR-associated (CRISPR-Cas) immune defenses confirm these theoretical predictions. These results suggest effective strategies for cross-species spillover and for the management of emerging infectious diseases.

Class Structure, Demography, and Selection: Reproductive-Value Weighting in Nonequilibrium, Polymorphic Populations.

In natural populations, individuals of a given genotype may belong to different classes. Such classes can represent different age groups, developmental stages, or habitats. Class structure has important evolutionary consequences because the fitness of individuals with the same genetic background may vary depending on their class. As a result, demographic transitions between classes can cause fluctuations in the trait mean that need to be removed when estimating selection on a trait. Intrinsic differences between classes are classically taken into account by weighting individuals by class-specific reproductive values, defined as the relative contribution of individuals in a given class to the future of the population. These reproductive values are generally constant weights calculated from a constant projection matrix. Here, I show for large populations and clonal reproduction that reproductive values can be defined as time-dependent weights satisfying dynamical demographic equations that depend only on the average between-class transition rates over all genotypes. Using these time-dependent demographic reproductive values yields a simple Price equation where the nonselective effects of between-class transitions are removed from the dynamics of the trait. This generalizes previous theory to a large class of ecological scenarios, taking into account density dependence, ecological feedbacks, arbitrary strength of selection, and arbitrary trait distributions. I discuss the role of reproductive values for prospective and retrospective analyses of the dynamics of phenotypic traits.

Beyond R0 Maximisation: On Pathogen Evolution and Environmental Dimensions.

A widespread tenet is that evolution of pathogens maximises their basic reproduction ratio, R0. The breakdown of this principle is typically discussed as exception. Here, we argue that a radically different stance is needed, based on evolutionarily stable strategy (ESS) arguments that take account of the 'dimension of the environmental feedback loop'. The R0 maximisation paradigm requires this feedback loop to be one-dimensional, which notably excludes pathogen diversification. By contrast, almost all realistic ecological ingredients of host-pathogen interactions (density-dependent mortality, multiple infections, limited cross-immunity, multiple transmission routes, host heterogeneity, and spatial structure) will lead to multidimensional feedbacks.

From the Price equation to the selection gradient in class-structured populations: a quasi-equilibrium route.

Recent studies in theoretical evolutionary ecology have emphasised two approaches to modelling evolution. On the one hand, models based on a separation of time scales rely on the concept of invasion fitness. On the other hand, models based on the Price equation track the dynamics of a trait average, coupled with a description of ecological dynamics. The aim of this article is to show that, in class-structured populations, both approaches yield the same expression for the selection gradient under weak selection. Although the result is not new, I propose an alternative route to its derivation using the dynamics of scaled measures of between-class phenotypic differentiation. Under weak selection, these measures of phenotypic differentiation can be treated as fast variables compared to the trait mean, which allows for a quasi-equilibrium approximation. This suggests a different approach to calculating weak selection approximations of evolutionary dynamics, and clarifies the links between short- and long-term perspectives on evolution in structured populations.

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.

Moment equations in spatial evolutionary ecology.

How should we model evolution in spatially structured populations? Here, I review an evolutionary ecology approach based on the technique of spatial moment equations. I first provide a mathematical underpinning to the derivation of equations for the densities of various spatial configurations in network-based models. I then show how this spatial ecological framework can be coupled with an adaptive dynamics approach to compute the invasion fitness of a rare mutant in a resident population at equilibrium. Under the additional assumption that mutations have small phenotypic effects, I show that the selection gradient can be expressed as a function of neutral measures of genetic and demographic structure. I discuss the connections between this approach and inclusive fitness theory, as well as the applicability and limits of this technique. My main message is that spatial moment equations can be used as a means to obtain compact qualitative arguments about the evolution of life-history traits for a variety of life cycles.

Beyond Mortality: Sterility As a Neglected Component of Parasite Virulence.

Virulence is generally defined as the reduction in host fitness following infection by a parasite (see Box 1 for glossary) [1]. In general, parasite exploitation of host resources may reduce host survival (mortality virulence), decrease host fecundity (sterility virulence), or even have sub-lethal effects that disturb the way individuals interact within a community (morbidity) [2,3]. In fact, the virulence of many parasites involves a combination of these various effects (Box 2). In practice, however, virulence is most often defined as disease-induced mortality [1, 4-6]. This is especially true in the theoretical literature, where the evolution of sterility virulence, morbidity, and mixed strategies of host exploitation have received relatively little attention. While the focus on mortality effects has allowed for easy comparison between models and, thus, rapid advancement of the field, we ask whether these theoretical simplifications have led us to inadvertently minimize the evolutionary importance of host sterilization and secondary virulence effects. As explicit theoretical work on morbidity is currently lacking (but see [7]), our aim in this Opinion piece is to discuss what is understood about sterility virulence evolution, its adaptive potential, and the implications for parasites that utilize a combination of host survival and reproductive resources.

Spatial structure, host heterogeneity and parasite virulence: implications for vaccine-driven evolution.

Natural host-parasite interactions exhibit considerable variation in host quality, with profound consequences for disease ecology and evolution. For instance, treatments (such as vaccination) may select for more transmissible or virulent strains. Previous theory has addressed the ecological and evolutionary impact of host heterogeneity under the assumption that hosts and parasites disperse globally. Here, we investigate the joint effects of host heterogeneity and local dispersal on the evolution of parasite life-history traits. We first formalise a general theoretical framework combining variation in host quality and spatial structure. We then apply this model to the specific problem of parasite evolution following vaccination. We show that, depending on the type of vaccine, spatial structure may select for higher or lower virulence compared to the predictions of non-spatial theory. We discuss the implications of our results for disease management, and their broader fundamental relevance for other causes of host heterogeneity in nature.