Spatial evolutionary epidemiology of spreading epidemics

Multiscale selection in spatially structured populations

The spatial structure of populations is key to many (eco-)evolutionary processes. In such cases, the strength and sign of selection on a trait may depend on the spatial scale considered. An example is the evolution of altruism: selection in local environments often favours cheaters over altruists, but this can be outweighed by selection at larger scales, favouring clusters of altruists over clusters of cheaters. For populations subdivided into distinct groups, this effect is described formally by multilevel selection theory. However, many populations do not consist of non-overlapping groups but rather (self-)organize into other ecological patterns. We therefore present a mathematical framework for multiscale selection. This framework decomposes natural selection into two parts: local selection, acting within environments of a certain size, and interlocal selection, acting among them. Varying the size of the local environments subsequently allows one to measure the contribution to selection of each spatial scale. To illustrate the use of this framework, we apply it to models of the evolution of altruism and pathogen transmissibility. The analysis identifies how and to what extent ecological processes at different spatial scales contribute to selection and compete, thus providing a rigorous underpinning to eco-evolutionary intuitions.

Effect of Human Behavior on the Evolution of Viral Strains During an Epidemic

It is well known in the literature that human behavior can change as a reaction to disease observed in others, and that such behavioral changes can be an important factor in the spread of an epidemic. It has been noted that human behavioral traits in disease avoidance are under selection in the presence of infectious diseases. Here, we explore a complementary trend: the pathogen itself might experience a force of selection to become less “visible,” or less “symptomatic,” in the presence of such human behavioral trends. Using a stochastic SIR agent-based model, we investigated the co-evolution of two viral strains with cross-immunity, where the resident strain is symptomatic while the mutant strain is asymptomatic. We assumed that individuals exercised self-regulated social distancing (SD) behavior if one of their neighbors was infected with a symptomatic strain. We observed that the proportion of asymptomatic carriers increased over time with a stronger effect corresponding to higher levels of self-regulated SD. Adding mandated SD made the effect more significant, while the existence of a time-delay between the onset of infection and the change of behavior reduced the advantage of the asymptomatic strain. These results were consistent under random geometric networks, scale-free networks, and a synthetic network that represented the social behavior of the residents of New Orleans.

Ecological and evolutionary dynamics of multi-strain RNA viruses

Potential interactions among co-circulating viral strains in host populations are often overlooked in the study of virus transmission. However, these interactions probably shape transmission dynamics by influencing host immune responses or altering the relative fitness among co-circulating strains. In this Review, we describe multi-strain dynamics from ecological and evolutionary perspectives, outline scales in which multi-strain dynamics occur and summarize important immunological, phylogenetic and mathematical modelling approaches used to quantify interactions among strains. We also discuss how host-pathogen interactions influence the co-circulation of pathogens. Finally, we highlight outstanding questions and knowledge gaps in the current theory and study of ecological and evolutionary dynamics of multi-strain viruses.

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.

Parasite-induced shifts in host movement may explain the transient coexistence of high- and low-pathogenic disease strains

Many parasites induce decreased host movement, known as lethargy, which can impact disease spread and the evolution of virulence. Mathematical models have investigated virulence evolution when parasites cause host death, but disease-induced decreased host movement has received relatively less attention. Here, we consider a model where, due to the within-host parasite replication rate, an infected host can become lethargic and shift from a moving to a resting state, where it can die. We find that when the lethargy and disease-induced mortality costs to the parasites are not high, then evolutionary bistability can arise, and either moderate or high virulence can evolve depending on the initial virulence and the magnitude of mutation. These results suggest, firstly, the coexistence of strains with different virulence, which may explain the transient coexistence of low- and high-pathogenic strains of avian influenza viruses, and secondly, that medical interventions to treat the symptoms of lethargy or prevent disease-induced host deaths can result in a large jump in virulence and the rapid evolution of high virulence. In complement to existing results that show bistability when hosts are heterogeneous at the population level, we show that evolutionary bistability may arise due to transmission heterogeneity at the individual host level.

The three Ts of virulence evolution during zoonotic emergence

There is increasing interest in the role that evolution may play in current and future pandemics, but there is often also considerable confusion about the actual evolutionary predictions. This may be, in part, due to a historical separation of evolutionary and medical fields, but there is a large, somewhat nuanced body of evidence-supported theory on the evolution of infectious disease. In this review, we synthesize this evolutionary theory in order to provide a framework for clearer understanding of the key principles. Specifically, we discuss the selection acting on zoonotic pathogens' transmission rates and virulence at spillover and during emergence. We explain how the direction and strength of selection during epidemics of emerging zoonotic disease can be understood by a three Ts framework: trade-offs, transmission, and time scales. Virulence and transmission rate may trade-off, but transmission rate is likely to be favoured by selection early in emergence, particularly if maladapted zoonotic pathogens have 'no-cost' transmission rate improving mutations available to them. Additionally, the optimal virulence and transmission rates can shift with the time scale of the epidemic. Predicting pathogen evolution, therefore, depends on understanding both the trade-offs of transmission-improving mutations and the time scales of selection.

Evolution of human respiratory virus epidemics

Background: Pathogens are often assumed to evolve towards reduced virulence, but counterexamples abound. Faced with a new pathogen, such as SARS-CoV-2, it is crucial to be able to forecast the case fatality rate (CFR) and the overall disease burden. Considerable effort has been invested towards developing a mathematical framework for predicting virulence evolution. Although many approaches accurately recapitulate complex outcomes, most rely on an assumed trade-off between CFR and infection rate. It is often impractical to empirically validate this constraint for human pathogens. Methods: A compartment model with parameters tuning the degree to which symptomatic individuals are isolated and the duration of immunity is constructed and evaluated at both short timescales and at equilibrium. Results: We reveal kinetic constraints whereby variation of multiple parameters in concert leads to decreased CFR and increased pathogen fitness, whereas independent variation of the parameters decreases pathogen fitness. Smallpox, SARS-CoV-2, and influenza are analyzed as diverse representatives of human respiratory viruses. We show that highly virulent viruses, such as smallpox, are often constrained by the host behavior, whereas moderately virulent viruses, such as SARS-CoV-2, appear to be typically constrained by the relationship between the duration of immunity and CFR. Conclusions: Evolution of human respiratory epidemics appears to be often kinetically constrained and a reduction in CFR should not be assumed. These results agree with previous work demonstrating an increase in virulence for smallpox and further predict that SARS-CoV-2 is likely to continue presenting a substantial disease burden. Herd immunity against SARS-CoV-2 and viruses with similar life history traits might be unachievable without vaccination. However, partial isolation of symptomatic individuals can have a major effect on the epidemic dynamics not only by reducing the number of fatalities in the short term but also by changing the evolutionary trajectory of moderate CFR viruses towards reduced CFR.

Evolution of human respiratory virus epidemics

Background: It is often assumed that pathogens evolve towards reduced virulence, but counterexamples abound. Faced with a new pathogen, such as SARS-CoV-2, it is highly desirable to be able to forecast the case fatality rate (CFR) and overall disease burden into the future. Considerable effort has been invested towards the development of a mathematical framework for predicting virulence evolution. Although many approaches accurately recapitulate complex outcomes, most rely on an assumed trade-off between CFR and infection rate. It is often impractical to empirically validate this constraint for human pathogens. Methods: A compartment model with parameters tuning the degree to which symptomatic individuals are isolated and the duration of immunity is constructed and evaluated at both short timescales and at equilibrium (when it exists). Results: We reveal kinetic constraints where the variation of multiple parameters in concert leads to decreased CFR and increased pathogen fitness, whereas independent variation of the parameters decreases pathogen fitness. Smallpox, SARS-CoV-2, and influenza are analyzed as diverse representatives of human respiratory viruses. We show that highly virulent viruses, such as smallpox, are likely often constrained by host behavior, whereas moderately virulent viruses, such as SARS-CoV-2, appear to be typically constrained by the relationship between the duration of immunity and CFR. Conclusions: Evolution of human respiratory epidemics appears to be often kinetically constrained and a reduction in CFR should not be assumed. Our findings imply that, without continued public health intervention, SARS-CoV-2 is likely to continue presenting a substantial disease burden. The existence of a parameter regime admitting endemic equilibrium suggests that herd immunity is unachievable. However, we demonstrate that even partial isolation of symptomatic individuals can have a major effect not only by reducing the number of fatalities in the short term but also by potentially changing the evolutionary trajectory of the virus towards reduced CFR.

Evolution of Human Respiratory Virus Epidemics

BACKGROUND

While pathogens often evolve towards reduced virulence, many counterexamples are evident. When faced with a new pathogen, such as SARS-CoV-2, it is highly desirable to be able to forecast the case fatality rate (CFR) into the future. Considerable effort has been invested towards the development of a mathematical framework for predicting virulence evolution. Although these approaches accurately recapitulate some complex outcomes, most rely on an assumed trade-off between mortality and infectivity. It is often impractical to empirically validate this constraint for human pathogens.

RESULTS

Using a compartment model with parameters tuning the degree to which symptomatic individuals are isolated and the duration of immunity, we reveal kinetic constraints where the variation of multiple parameters in concert leads to decreased virulence and increased pathogen fitness, whereas independent variation of the parameters decreases pathogen fitness. Smallpox, SARS-CoV-2, and Influenza are analyzed as diverse representatives of human respiratory viruses. We show that highly virulent viruses, such as Smallpox, are likely often constrained by host behavior, whereas moderately virulent viruses, such as SARS-CoV-2, appear to be typically constrained by the relationship between the duration of immunity and CFR.

CONCLUSIONS

The evolution of human respiratory epidemics appears to be often kinetically constrained and a reduction in virulence should not be assumed. Our findings imply that, without continued public health intervention, SARS-CoV-2 is likely to continue presenting a substantial disease burden. The existence of a parameter regime admitting endemic equilibrium suggests that herd immunity is unachievable. However, we demonstrate that even partial isolation of symptomatic individuals can have a major effect not only by reducing the number of fatalities in the short term but also by potentially changing the evolutionary trajectory of the virus towards reduced virulence.

Interplay between competitive and cooperative interactions in a three-player pathogen system

In ecological systems, heterogeneous interactions between pathogens take place simultaneously. This occurs, for instance, when two pathogens cooperate, while at the same time, multiple strains of these pathogens co-circulate and compete. Notable examples include the cooperation of human immunodeficiency virus with antibiotic-resistant and susceptible strains of tuberculosis or some respiratory infections with Streptococcus pneumoniae strains. Models focusing on competition or cooperation separately fail to describe how these concurrent interactions shape the epidemiology of such diseases. We studied this problem considering two cooperating pathogens, where one pathogen is further structured in two strains. The spreading follows a susceptible-infected-susceptible process and the strains differ in transmissibility and extent of cooperation with the other pathogen. We combined a mean-field stability analysis with stochastic simulations on networks considering both well-mixed and structured populations. We observed the emergence of a complex phase diagram, where the conditions for the less transmissible, but more cooperative strain to dominate are non-trivial, e.g. non-monotonic boundaries and bistability. Coupled with community structure, the presence of the cooperative pathogen enables the coexistence between strains by breaking the spatial symmetry and dynamically creating different ecological niches. These results shed light on ecological mechanisms that may impact the epidemiology of diseases of public health concern.

Infection in patchy populations: Contrasting pathogen invasion success and dispersal at varying times since host colonization

Repeated extinction and recolonization events generate a landscape of host populations that vary in their time since colonization. Within this dynamic landscape, pathogens that excel at invading recently colonized host populations are not necessarily those that perform best in host populations at or near their carrying capacity, potentially giving rise to divergent selection for pathogen traits that mediate the invasion process. Rarely, however, has this contention been empirically tested. Using Daphnia magna, we explored how differences in the colonization history of a host population influence the invasion success of different genotypes of the pathogen Pasteuria ramosa. By partitioning the pathogen invasion process into a series of individual steps, we show that each pathogen optimizes invasion differently when encountering host populations that vary in their time since colonization. All pathogen genotypes were more likely to establish successfully in recently colonized host populations, but the production of transmission spores was typically maximized in either the subsequent growth or stationary phase of host colonization. Integrating across the first three pathogen invasion steps (initial establishment, proliferation, and secondary infection) revealed that overall pathogen invasion success (and its variance) was, nonetheless, highest in recently colonized host populations. However, only pathogens that were slow to kill their host were able to maximize host‐facilitated dispersal. This suggests that only a subset of pathogen genotypes—the less virulent and more dispersive—are more likely to encounter newly colonized host populations at the front of a range expansion or in metapopulations with high extinction rates. Our results suggest a fundamental trade‐off for a pathogen between dispersal and virulence, and evidence for higher invasion success in younger host populations, a finding with clear implications for pathogen evolution in spatiotemporally dynamic settings.

Host contact dynamics shapes richness and dominance of pathogen strains

The interaction among multiple microbial strains affects the spread of infectious diseases and the efficacy of interventions. Genomic tools have made it increasingly easy to observe pathogenic strains diversity, but the best interpretation of such diversity has remained difficult because of relationships with host and environmental factors. Here, we focus on host-to-host contact behavior and study how it changes populations of pathogens in a minimal model of multi-strain interaction. We simulated a population of identical strains competing by mutual exclusion and spreading on a dynamical network of hosts according to a stochastic susceptible-infectious-susceptible model. We computed ecological indicators of diversity and dominance in strain populations for a collection of networks illustrating various properties found in real-world examples. Heterogeneities in the number of contacts among hosts were found to reduce diversity and increase dominance by making the repartition of strains among infected hosts more uneven, while strong community structure among hosts increased strain diversity. We found that the introduction of strains associated with hosts entering and leaving the system led to the highest pathogenic richness at intermediate turnover levels. These results were finally illustrated using the spread of Staphylococcus aureus in a long-term health-care facility where close proximity interactions and strain carriage were collected simultaneously. We found that network structural and temporal properties could account for a large part of the variability observed in strain diversity. These results show how stochasticity and network structure affect the population ecology of pathogens and warn against interpreting observations as unambiguous evidence of epidemiological differences between strains.

Causes and Consequences of Spatial Within-Host Viral Spread

The spread of viral pathogens both between and within hosts is inherently a spatial process. While the spatial aspects of viral spread at the epidemiological level have been increasingly well characterized, the spatial aspects of viral spread within infected hosts are still understudied. Here, with a focus on influenza A viruses (IAVs), we first review experimental studies that have shed light on the mechanisms and spatial dynamics of viral spread within hosts. These studies provide strong empirical evidence for highly localized IAV spread within hosts. Since mathematical and computational within-host models have been increasingly used to gain a quantitative understanding of observed viral dynamic patterns, we then review the (relatively few) computational modeling studies that have shed light on possible factors that structure the dynamics of spatial within-host IAV spread. These factors include the dispersal distance of virions, the localization of the immune response, and heterogeneity in host cell phenotypes across the respiratory tract. While informative, we find in these studies a striking absence of theoretical expectations of how spatial dynamics may impact the dynamics of viral populations. To mitigate this, we turn to the extensive ecological and evolutionary literature on range expansions to provide informed theoretical expectations. We find that factors such as the type of density dependence, the frequency of long-distance dispersal, specific life history characteristics, and the extent of spatial heterogeneity are critical factors affecting the speed of population spread and the genetic composition of spatially expanding populations. For each factor that we identified in the theoretical literature, we draw parallels to its analog in viral populations. We end by discussing current knowledge gaps related to the spatial component of within-host IAV spread and the potential for within-host spatial considerations to inform the development of disease control strategies.

Pathogen evolution in finite populations: slow and steady spreads the best

The theory of life-history evolution provides a powerful framework to understand the evolutionary dynamics of pathogens. It assumes, however, that host populations are large and that one can neglect the effects of demographic stochasticity. Here, we expand the theory to account for the effects of finite population size on the evolution of pathogen virulence. We show that demographic stochasticity introduces additional evolutionary forces that can qualitatively affect the dynamics and the evolutionary outcome. We discuss the importance of the shape of the pathogen fitness landscape on the balance between mutation, selection and genetic drift. This analysis reconciles Adaptive Dynamics with population genetics in finite populations and provides a new theoretical toolbox to study life-history evolution in realistic ecological scenarios.

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.

Assessing the durability and efficiency of landscape-based strategies to deploy plant resistance to pathogens

Genetically-controlled plant resistance can reduce the damage caused by pathogens. However, pathogens have the ability to evolve and overcome such resistance. This often occurs quickly after resistance is deployed, resulting in significant crop losses and a continuing need to develop new resistant cultivars. To tackle this issue, several strategies have been proposed to constrain the evolution of pathogen populations and thus increase genetic resistance durability. These strategies mainly rely on varying different combinations of resistance sources across time (crop rotations) and space. The spatial scale of deployment can vary from multiple resistance sources occurring in a single cultivar (pyramiding), in different cultivars within the same field (cultivar mixtures) or in different fields (mosaics). However, experimental comparison of the efficiency (i.e. ability to reduce disease impact) and durability (i.e. ability to limit pathogen evolution and delay resistance breakdown) of landscape-scale deployment strategies presents major logistical challenges. Therefore, we developed a spatially explicit stochastic model able to assess the epidemiological and evolutionary outcomes of the four major deployment options described above, including both qualitative resistance (i.e. major genes) and quantitative resistance traits against several components of pathogen aggressiveness: infection rate, latent period duration, propagule production rate, and infectious period duration. This model, implemented in the R package landsepi, provides a new and useful tool to assess the performance of a wide range of deployment options, and helps investigate the effect of landscape, epidemiological and evolutionary parameters. This article describes the model and its parameterisation for rust diseases of cereal crops, caused by fungi of the genus Puccinia. To illustrate the model, we use it to assess the epidemiological and evolutionary potential of the combination of a major gene and different traits of quantitative resistance. The comparison of the four major deployment strategies described above will be the objective of future studies.

There are many recent examples which demonstrate the evolutionary potential of plant pathogens to overcome the resistances deployed in agricultural landscapes to protect our crops. Increasingly, it is recognised that how resistance is deployed spatially and temporally can impact on rates of pathogen evolution and resistance breakdown. Such deployment strategies are mainly based on the combination of several sources of resistance at different spatiotemporal scales. However, comparison of these strategies in a predictive sense is not an easy task, owing to the logistical difficulties associated with experiments involving the spread of a pathogen at large spatio-temporal scales. Moreover, both the durability of a strategy and the epidemiological protection it provides to crops must be assessed since these evaluation criteria are not necessarily correlated. Surprisingly, no current simulation model allows a thorough comparison of the different options. Here we describe a spatio-temporal model able to simulate a wide range of deployment strategies and resistance sources. This model, implemented in the R package landsepi, facilitates assessment of both epidemiological and evolutionary outcomes across simulated scenarios. In this work, the model is used to investigate the combination of different sources of resistance against fungal diseases such as rusts of cereal crops.

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.

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.