Applying population-genetic models in theoretical evolutionary epidemiology

Rapid Evolution of Resistance and Tolerance Leads to Variable Host Recoveries following Disease-Induced Declines

AbstractRecoveries of populations that have suffered severe disease-induced declines are being observed across disparate taxa. Yet we lack theoretical understanding of the drivers and dynamics of recovery in host populations and communities impacted by infectious disease. Motivated by disease-induced declines and nascent recoveries in amphibians, we developed a model to ask the following question: How does the rapid evolution of different host defense strategies affect the transient recovery trajectories of hosts following pathogen invasion and disease-induced declines? We found that while host life history is predictably a major driver of variability in population recovery trajectories (including declines and recoveries), populations that use different host defense strategies (i.e., tolerance, avoidance resistance, and intensity-reduction resistance) experience notably different recoveries. In single-species host populations, populations evolving tolerance recovered on average four times slower than populations evolving resistance. Moreover, while populations using avoidance resistance strategies had the fastest potential recovery rates, these populations could get trapped in long transient states at low abundance prior to recovery. In contrast, the recovery of populations evolving intensity-reduction resistance strategies were more consistent across ecological contexts. Overall, host defense strategies strongly affect the transient dynamics of population recovery and may affect the ultimate fate of real populations recovering from disease-induced declines.

Approximate Bayesian Computation applied to time series of population genetic data disentangles rapid genetic changes and demographic variations in a pathogen population

Adaptation can occur at remarkably short timescales in natural populations, leading to drastic changes in phenotypes and genotype frequencies over a few generations only. The inference of demographic parameters can allow understanding how evolutionary forces interact and shape the genetic trajectories of populations during rapid adaptation. Here we propose a new Approximate Bayesian Computation (ABC) framework that couples a forward and individual-based model with temporal genetic data to disentangle genetic changes and demographic variations in a case of rapid adaptation. We test the accuracy of our inferential framework and evaluate the benefit of considering a dense versus sparse sampling. Theoretical investigations demonstrate high accuracy in both model and parameter estimations, even if a strong thinning is applied to time series data. Then, we apply our ABC inferential framework to empirical data describing the population genetic changes of the poplar rust pathogen following a major event of resistance overcoming. We successfully estimate key demographic and genetic parameters, including the proportion of resistant hosts deployed in the landscape and the level of standing genetic variation from which selection occurred. Inferred values are in accordance with our empirical knowledge of this biological system. This new inferential framework, which contrasts with coalescent-based ABC analyses, is promising for a better understanding of evolutionary trajectories of populations subjected to rapid adaptation.

Separation of evolutionary timescales in coevolving species

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

Resource asynchrony and landscape homogenization as drivers of virulence evolution: The case of a directly transmitted disease in a social host

Throughout the last decades, the emergence of zoonotic diseases and the frequency of disease outbreaks have increased substantially, fuelled by habitat encroachment and vectors overlapping with more hosts due to global change. The virulence of pathogens is one key trait for successful invasion. In order to understand how global change drivers such as habitat homogenization and climate change drive pathogen virulence evolution, we adapted an established individual-based model of host-pathogen dynamics. Our model simulates a population of social hosts affected by a directly transmitted evolving pathogen in a dynamic landscape. Pathogen virulence evolution results in multiple strains in the model that differ in their transmission capability and lethality. We represent the effects of global change by simulating environmental changes both in time (resource asynchrony) and space (homogenization). We found an increase in pathogenic virulence and a shift in strain dominance with increasing landscape homogenization. Our model further indicated that lower virulence is dominant in fragmented landscapes, although pulses of highly virulent strains emerged under resource asynchrony. While all landscape scenarios favoured co-occurrence of low- and high-virulent strains, the high-virulence strains capitalized on the possibility for transmission when host density increased and were likely to become dominant. With asynchrony likely to occur more often due to global change, our model showed that a subsequent evolution towards lower virulence could lead to some diseases becoming endemic in their host populations.

Evolutionary stability of antigenically escaping viruses

Antigenic variation is the main immune escape mechanism for RNA viruses like influenza or SARS-CoV-2. While high mutation rates promote antigenic escape, they also induce large mutational loads and reduced fitness. It remains unclear how this cost-benefit trade-off selects the mutation rate of viruses. Using a traveling wave model for the coevolution of viruses and host immune systems in a finite population, we investigate how immunity affects the evolution of the mutation rate and other nonantigenic traits, such as virulence. We first show that the nature of the wave depends on how cross-reactive immune systems are, reconciling previous approaches. The immune-virus system behaves like a Fisher wave at low cross-reactivities, and like a fitness wave at high cross-reactivities. These regimes predict different outcomes for the evolution of nonantigenic traits. At low cross-reactivities, the evolutionarily stable strategy is to maximize the speed of the wave, implying a higher mutation rate and increased virulence. At large cross-reactivities, where our estimates place H3N2 influenza, the stable strategy is to increase the basic reproductive number, keeping the mutation rate to a minimum and virulence low.

Asymptotic behavior of an epidemic model with infinitely many variants

We investigate the long-time dynamics of a SIR epidemic model with infinitely many pathogen variants infecting a homogeneous host population. We show that the basic reproduction number [Formula: see text] of the pathogen can be defined in that case and corresponds to a threshold between the persistence ([Formula: see text]) and the extinction ([Formula: see text]) of the pathogen population. When [Formula: see text] and the maximal fitness is attained by at least one variant, we show that the systems reaches an endemic equilibrium state that can be explicitly determined from the initial data. When [Formula: see text] but none of the variants attain the maximal fitness, the situation is more intricate. We show that, in general, the pathogen is uniformly persistent and any family of variants that have a fitness which is uniformly lower than the optimal fitness, eventually gets extinct. We derive a condition under which the total pathogen population converges to a limit which can be computed explicitly. We also find counterexamples that show that, when our condition is not met, the total pathogen population may converge to an unexpected value, or the system can even reach an eternally transient behavior where the total pathogen population between several values. We illustrate our results with numerical simulations that emphasize the wide variety of possible dynamics.

Geographic migration and vaccine-induced fitness changes of Streptococcus pneumoniae

Streptococcus pneumoniae is a leading cause of pneumonia and meningitis worldwide. Many different serotypes co-circulate endemically in any one location. The extent and mechanisms of spread, and vaccine-driven changes in fitness and antimicrobial resistance (AMR), remain largely unquantified. Using geolocated genome sequences from South Africa (N=6910, 2000-2014) we developed models to reconstruct spread, pairing detailed human mobility data and genomic data. Separately we estimated the population level changes in fitness of strains that are (vaccine type, VT) and are not (non-vaccine type, NVT) included in the vaccine, first implemented in 2009, as well as differences in strain fitness between those that are and are not resistant to penicillin. We estimated that pneumococci only become homogenously mixed across South Africa after about 50 years of transmission, with the slow spread driven by the focal nature of human mobility. Further, in the years following vaccine implementation the relative fitness of NVT compared to VT strains increased (RR: 1.29 [95% CI 1.20-1.37]) - with an increasing proportion of these NVT strains becoming penicillin resistant. Our findings point to highly entrenched, slow transmission and indicate that initial vaccine-linked decreases in AMR may be transient.

Dietary restriction and ageing: Recent evolutionary perspectives

Dietary restriction (DR) represents one of the most robust interventions for extending lifespan. It is not known how DR increases lifespan. The prevailing evolutionary hypothesis suggests the DR response redirects metabolic resources towards somatic maintenance at the expense of investment in reproduction. Consequently, DR acts as a proximate mechanism which promotes a pro-longevity phenotype. This idea is known as resource reallocation. However, growing findings suggest this paradigm could be incomplete. It has been argued that during DR it is not always possible to identify a trade-off between reproduction and lifespan. It is also suggested the relationship between reproduction and somatic maintenance can be uncoupled by the removal or inclusion of specific nutrients. These findings have created an imperative to re-explore the nexus between DR and evolutionary theory. In this review I will address this evolutionary conundrum. My overarching objectives are fourfold: (1) to outline some of the evidence for and against resource reallocation; (2) to examine recent findings which have necessitated a theoretical re-evaluation of the link between life history theory and DR; (3) to present alternatives to the resource reallocation model; (4) to present emerging variables which potentially influence how DR effects evolutionary trade-offs.

Reservoir population ecology, viral evolution and the risk of emerging infectious disease

The ecology and life history of wild animals influences their potential to harbour infectious disease. This observation has motivated studies identifying empirical relationships between traits of wild animals and historical patterns of spillover and emergence into humans. Although these studies have identified compelling broad-scale patterns, they are generally agnostic with respect to underlying mechanisms. Here, we develop mathematical models that couple reservoir population ecology with viral epidemiology and evolution to clarify existing verbal arguments and pinpoint the conditions that favour spillover and emergence. Our results support the idea that average lifespan influences the likelihood of an animal serving as a reservoir for human infectious disease. At the same time, however, our results show that the magnitude of this effect is sensitive to the rate of viral mutation. Our results also demonstrate that viral pathogens causing persistent infections or a transient immune response within the reservoir are more likely to fuel emergence. Genetically explicit stochastic simulations enrich these mathematical results by identifying relationships between the genetic basis of transmission and the risk of spillover and emergence. Together, our results clarify the scope of applicability for existing hypotheses and refine our understanding of emergence risk.

Improving sustainable crop protection using population genetics concepts

Growing genetically resistant plants allows pathogen populations to be controlled and reduces the use of pesticides. However, pathogens can quickly overcome such resistance. In this context, how can we achieve sustainable crop protection? This crucial question has remained largely unanswered despite decades of intense debate and research effort. In this study, we used a bibliographic analysis to show that the research field of resistance durability has evolved into three subfields: (i) 'plant breeding' (generating new genetic material), (ii) 'molecular interactions' (exploring the molecular dialogue governing plant-pathogen interactions) and (iii) 'epidemiology and evolution' (explaining and forecasting of pathogen population dynamics resulting from selection pressure(s) exerted by resistant plants). We argue that this triple split of the field impedes integrated research progress and ultimately compromises the sustainable management of genetic resistance. After identifying a gap among the three subfields, we argue that the theoretical framework of population genetics could bridge this gap. Indeed, population genetics formally explains the evolution of all heritable traits, and allows genetic changes to be tracked along with variation in population dynamics. This provides an integrated view of pathogen adaptation, in particular via evolutionary-epidemiological feedbacks. In this Opinion Note, we detail examples illustrating how such a framework can better inform best practices for developing and managing genetically resistant cultivars.

Mutation induced infection waves in diseases like COVID-19

After more than 6 million deaths worldwide, the ongoing vaccination to conquer the COVID-19 disease is now competing with the emergence of increasingly contagious mutations, repeatedly supplanting earlier strains. Following the near-absence of historical examples of the long-time evolution of infectious diseases under similar circumstances, models are crucial to exemplify possible scenarios. Accordingly, in the present work we systematically generalize the popular susceptible-infected-recovered model to account for mutations leading to repeatedly occurring new strains, which we coarse grain based on tools from statistical mechanics to derive a model predicting the most likely outcomes. The model predicts that mutations can induce a super-exponential growth of infection numbers at early times, which self-amplify to giant infection waves which are caused by a positive feedback loop between infection numbers and mutations and lead to a simultaneous infection of the majority of the population. At later stages-if vaccination progresses too slowly-mutations can interrupt an ongoing decrease of infection numbers and can cause infection revivals which occur as single waves or even as whole wave trains featuring alternative periods of decreasing and increasing infection numbers. This panorama of possible mutation-induced scenarios should be tested in more detailed models to explore their concrete significance for specific infectious diseases. Further, our results might be useful for discussions regarding the importance of a release of vaccine-patents to reduce the risk of mutation-induced infection revivals but also to coordinate the release of measures following a downwards trend of infection numbers.

Modelling: Understanding pandemics and how to control them

New disease challenges, societal demands and better or novel types of data, drive innovations in the structure, formulation and analysis of epidemic models. Innovations in modelling can lead to new insights into epidemic processes and better use of available data, yielding improved disease control and stimulating collection of better data and new data types. Here we identify key challenges for the structure, formulation, analysis and use of mathematical models of pathogen transmission relevant to current and future pandemics.

Selection for infectivity profiles in slow and fast epidemics, and the rise of SARS-CoV-2 variants

Evaluating the characteristics of emerging SARS-CoV-2 variants of concern is essential to inform pandemic risk assessment. A variant may grow faster if it produces a larger number of secondary infections (“R advantage”) or if the timing of secondary infections (generation time) is better. So far, assessments have largely focused on deriving the R advantage assuming the generation time was unchanged. Yet, knowledge of both is needed to anticipate the impact. Here, we develop an analytical framework to investigate the contribution of both the R advantage and generation time to the growth advantage of a variant. It is known that selection on a variant with larger R increases with levels of transmission in the community. We additionally show that variants conferring earlier transmission are more strongly favored when the historical strains have fast epidemic growth, while variants conferring later transmission are more strongly favored when historical strains have slow or negative growth. We develop these conceptual insights into a new statistical framework to infer both the R advantage and generation time of a variant. On simulated data, our framework correctly estimates both parameters when it covers time periods characterized by different epidemiological contexts. Applied to data for the Alpha and Delta variants in England and in Europe, we find that Alpha confers a+54% [95% CI, 45–63%] R advantage compared to previous strains, and Delta +140% [98–182%] compared to Alpha, and mean generation times are similar to historical strains for both variants. This work helps interpret variant frequency dynamics and will strengthen risk assessment for future variants of concern.

Mutations in genes of the SARS-CoV-2 virus have generated new variants of concern, like Alpha, Delta, and more recently Omicron. These strains contain genetic modifications that help the virus spread more easily as well as altering the severity of the illness it causes. This has led to rising numbers of infections, known as epidemic waves, in many parts of the world.

Tracking new variants of concern is crucial to protecting the public. To do this, scientists monitor how many people one person with the virus can infect, also known as the number of secondary infections. They may also measure when in the course of the illness an individual may pass along the virus to others. Together, these metrics help determine how fast and large an outbreak caused by a new variant will grow. The more people the new variant infects and the quicker it spreads, the more likely it is to replace existing strains of the virus.

So far, most studies have assumed that the growth rate of a new variant solely depends on the number of secondary infections, and the timing of secondary infections is often not considered. To address this, Blanquart et al. built a mathematical model that combines both these parameters to determine the growth rate of new viral strains.

The model showed that variants which rapidly cause secondary infections have a larger growth advantage over existing strains when the virus is more easily transmitted between individuals and the epidemic spreads rapidly. But when there is less transmission and the epidemic is declining, variants that generate secondary infections after a longer time have an advantage. For example, when control measures like mask wearing or social distancing are in place, delayed secondary infections may be more advantageous.

Blanquart et al. then applied their model to data from the Alpha and Delta variant outbreaks in the United Kingdom. They found that Alpha and Delta did not change the timing of secondary infections compared to previously circulating strains. But the Alpha variant had a 54% transmission advantage over previous strains and the Delta variant had a 140% transmission advantage over Alpha.

Taken together, these findings suggest that the timing of secondary infections and transmission rates both play an important role in how quickly a virus spreads. The new mathematical model created by Blanquart et al. may help epidemiologists better predict the trajectory of new SARS-CoV-2 variants and determine how to best control their spread.

Global spatial dynamics and vaccine-induced fitness changes of Bordetella pertussis

As with other pathogens, competitive interactions between Bordetella pertussis strains drive infection risk. Vaccines are thought to perturb strain diversity through shifts in immune pressures; however, this has rarely been measured because of inadequate data and analytical tools. We used 3344 sequences from 23 countries to show that, on average, there are 28.1 transmission chains circulating within a subnational region, with the number of chains strongly associated with host population size. It took 5 to 10 years for B. pertussis to be homogeneously distributed throughout Europe, with the same time frame required for the United States. Increased fitness of pertactin-deficient strains after implementation of acellular vaccines, but reduced fitness otherwise, can explain long-term genotype dynamics. These findings highlight the role of vaccine policy in shifting local diversity of a pathogen that is responsible for 160,000 deaths annually.

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.

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.

Redundancy-selection trade-off in phenotype-structured populations

Realistic fitness landscapes generally display a redundancy-fitness trade-off: highly fit trait configurations are inevitably rare, while less fit trait configurations are expected to be more redundant. The resulting sub-optimal patterns in the fitness distribution are typically described by means of effective formulations, where redundancy provided by the presence of neutral contributions is modelled implicitly, e.g. with a bias of the mutation process. However, the extent to which effective formulations are compatible with explicitly redundant landscapes is yet to be understood, as well as the consequences of a potential miss-match. Here we investigate the effects of such trade-off on the evolution of phenotype-structured populations, characterised by continuous quantitative traits. We consider a typical replication-mutation dynamics, and we model redundancy by means of two dimensional landscapes displaying both selective and neutral traits. We show that asymmetries of the landscapes will generate neutral contributions to the marginalised fitness-level description, that cannot be described by effective formulations, nor disentangled by the full trait distribution. Rather, they appear as effective sources, whose magnitude depends on the geometry of the landscape. Our results highlight new important aspects on the nature of sub-optimality. We discuss practical implications for rapidly mutant populations such as pathogens and cancer cells, where the qualitative knowledge of their trait and fitness distributions can drive disease management and intervention policies.

Integrating Infection Intensity into Within- and Between-Host Pathogen Dynamics: Implications for Invasion and Virulence Evolution

AbstractInfection intensity can dictate disease outcomes but is typically ignored when modeling infection dynamics of microparasites (e.g., bacteria, virus, and fungi). However, for a number of pathogens of wildlife typically categorized as microparasites, accounting for infection intensity and within-host infection processes is critical for predicting population-level responses to pathogen invasion. Here, we develop a modeling framework we refer to as reduced-dimension host-parasite integral projection models (reduced IPMs) that we use to explore how within-host infection processes affect the dynamics of pathogen invasion and virulence evolution. We find that individual-level heterogeneity in pathogen load-a nearly ubiquitous characteristic of host-parasite interactions that is rarely considered in models of microparasites-generally reduces pathogen invasion probability and dampens virulence-transmission trade-offs in host-parasite systems. The latter effect likely contributes to widely predicted virulence-transmission trade-offs being difficult to observe empirically. Moreover, our analyses show that intensity-dependent host mortality does not always induce a virulence-transmission trade-off, and systems with steeper than linear relationships between pathogen intensity and host mortality rate are significantly more likely to exhibit these trade-offs. Overall, reduced IPMs provide a useful framework to expand our theoretical and data-driven understanding of how within-host processes affect population-level disease dynamics.

Models of Plant Resistance Deployment

Owing to their evolutionary potential, plant pathogens are able to rapidly adapt to genetically controlled plant resistance, often resulting in resistance breakdown and major epidemics in agricultural crops. Various deployment strategies have been proposed to improve resistance management. Globally, these rely on careful selection of resistance sources and their combination at various spatiotemporal scales (e.g., via gene pyramiding, crop rotations and mixtures, landscape mosaics). However, testing and optimizing these strategies using controlled experiments at large spatiotemporal scales are logistically challenging. Mathematical models provide an alternative investigative tool, and many have been developed to explore resistance deployment strategies under various contexts. This review analyzes 69 modeling studies in light of specific model structures (e.g., demographic or demogenetic, spatial or not), underlying assumptions (e.g., whether preadapted pathogens are present before resistance deployment), and evaluation criteria (e.g., resistance durability, disease control, cost-effectiveness). It highlights major research findings and discusses challenges for future modeling efforts.

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.

The origins and potential future of SARS-CoV-2 variants of concern in the evolving COVID-19 pandemic

One year into the global COVID-19 pandemic, the focus of attention has shifted to the emergence and spread of SARS-CoV-2 variants of concern (VOCs). After nearly a year of the pandemic with little evolutionary change affecting human health, several variants have now been shown to have substantial detrimental effects on transmission and severity of the virus. Public health officials, medical practitioners, scientists, and the broader community have since been scrambling to understand what these variants mean for diagnosis, treatment, and the control of the pandemic through nonpharmaceutical interventions and vaccines. Here we explore the evolutionary processes that are involved in the emergence of new variants, what we can expect in terms of the future emergence of VOCs, and what we can do to minimise their impact.

Estimated transmissibility and impact of SARS-CoV-2 lineage B.1.1.7 in England

A severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variant, VOC 202012/01 (lineage B.1.1.7), emerged in southeast England in September 2020 and is rapidly spreading toward fixation. Using a variety of statistical and dynamic modeling approaches, we estimate that this variant has a 43 to 90% (range of 95% credible intervals, 38 to 130%) higher reproduction number than preexisting variants. A fitted two-strain dynamic transmission model shows that VOC 202012/01 will lead to large resurgences of COVID-19 cases. Without stringent control measures, including limited closure of educational institutions and a greatly accelerated vaccine rollout, COVID-19 hospitalizations and deaths across England in the first 6 months of 2021 were projected to exceed those in 2020. VOC 202012/01 has spread globally and exhibits a similar transmission increase (59 to 74%) in Denmark, Switzerland, and the United States.

Estimated transmissibility and impact of SARS-CoV-2 lineage B.1.1.7 in England

A severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variant, VOC 202012/01 (lineage B.1.1.7), emerged in southeast England in September 2020 and is rapidly spreading toward fixation. Using a variety of statistical and dynamic modeling approaches, we estimate that this variant has a 43 to 90% (range of 95% credible intervals, 38 to 130%) higher reproduction number than preexisting variants. A fitted two-strain dynamic transmission model shows that VOC 202012/01 will lead to large resurgences of COVID-19 cases. Without stringent control measures, including limited closure of educational institutions and a greatly accelerated vaccine rollout, COVID-19 hospitalizations and deaths across England in the first 6 months of 2021 were projected to exceed those in 2020. VOC 202012/01 has spread globally and exhibits a similar transmission increase (59 to 74%) in Denmark, Switzerland, and the United States.

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.

The problem of mediocre generalists: population genetics and eco-evolutionary perspectives on host breadth evolution in pathogens

Many of our theories for the generation and maintenance of diversity in nature depend on the existence of specialist biotic interactions which, in host-pathogen systems, also shape cross-species disease emergence. As such, niche breadth evolution, especially in host-parasite systems, remains a central focus in ecology and evolution. The predominant explanation for the existence of specialization in the literature is that niche breadth is constrained by trade-offs, such that a generalist is less fit on any particular environment than a given specialist. This trade-off theory has been used to predict niche breadth (co)evolution in both population genetics and eco-evolutionary models, with the different modelling methods providing separate, complementary insights. However, trade-offs may be far from universal, so population genetics theory has also proposed alternate mechanisms for costly generalism, including mutation accumulation. However, these mechanisms have yet to be integrated into eco-evolutionary models in order to understand how the mechanism of costly generalism alters the biological and ecological circumstances predicted to maintain specialism. In this review, we outline how population genetics and eco-evolutionary models based on trade-offs have provided insights for parasite niche breadth evolution and argue that the population genetics-derived mutation accumulation theory needs to be better integrated into eco-evolutionary theory.

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.

The Price equation and evolutionary epidemiology

The Price equation has found widespread application in many areas of evolutionary biology, including the evolutionary epidemiology of infectious diseases. In this paper, we illustrate the utility of this approach to modelling disease evolution by first deriving a version of Price's equation that can be applied in continuous time and to populations with overlapping generations. We then show how this version of Price's equation provides an alternative perspective on pathogen evolution by considering the epidemiological meaning of each of its terms. Finally, we extend these results to the case where population size is small and generates demographic stochasticity. We show that the particular partitioning of evolutionary change given by Price's equation is also a natural way to partition the evolutionary consequences of demographic stochasticity, and demonstrate how such stochasticity tends to weaken selection on birth rate (e.g. the transmission rate of an infectious disease) and enhance selection on mortality rate (e.g. factors, like virulence, that cause the end of an infection). In the long term, if there is a trade-off between virulence and transmission across parasite strains, the weaker selection on transmission and stronger selection on virulence that arises from demographic stochasticity will tend to drive the evolution of lower levels of virulence. This article is part of the theme issue 'Fifty years of the Price equation'.

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.

Viral invasion fitness across a continuum from lysis to latency

The prevailing paradigm in ecological studies of viruses and their microbial hosts is that the reproductive success of viruses depends on the proliferation of the 'predator', that is, the virus particle. Yet, viruses are obligate intracellular parasites, and the virus genome-the actual unit of selection-can persist and proliferate from one cell generation to the next without lysis or the production of new virus particles. Here, we propose a theoretical framework to quantify the invasion fitness of viruses using an epidemiological cell-centric metric that focuses on the proliferation of viral genomes inside cells instead of virus particles outside cells. This cell-centric metric enables direct comparison of viral strategies characterized by obligate killing of hosts (e.g. via lysis), persistence of viral genomes inside hosts (e.g. via lysogeny), and strategies along a continuum between these extremes (e.g. via chronic infections). As a result, we can identify environmental drivers, life history traits, and key feedbacks that govern variation in viral propagation in nonlinear population models. For example, we identify threshold conditions given relatively low densities of susceptible cells and relatively high growth rates of infected cells in which lysogenic and other chronic strategies have higher potential viral reproduction than lytic strategies. Altogether, the theoretical framework helps unify the ongoing study of eco-evolutionary drivers of viral strategies in natural environments.

To block or not to block: The adaptive manipulation of plague transmission

The ability of the agent of plague, Yersinia pestis, to form a biofilm blocking the gut of the flea has been considered to be a key evolutionary step in maintaining flea‐borne transmission. However, blockage decreases dramatically the life expectancy of fleas, challenging the adaptive nature of blockage. Here, we develop an epidemiological model of plague that accounts for its different transmission routes, as well as the within‐host competition taking place between bacteria within the flea vector. We use this theoretical framework to identify the environmental conditions promoting the evolution of blockage. We also show that blockage is favored at the onset of an epidemic, and that the frequencies of bacterial strains exhibiting different strategies of blockage can fluctuate in seasonal environments. This analysis quantifies the contribution of different transmission routes in plague and makes testable predictions on the adaptive nature of blockage.

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.

Rapid evolution rescues hosts from competition and disease but-despite a dilution effect-increases the density of infected hosts

Virulent parasites can depress the densities of their hosts. Taxa that reduce disease via dilution effects might alleviate this burden. However, 'diluter' taxa can also depress host densities through competition for shared resources. The combination of disease and interspecific competition could even drive hosts extinct. Then again, genetically variable host populations can evolve in response to both competitors and parasites. Can rapid evolution rescue host density from the harm caused by these ecological enemies? How might such evolution influence dilution effects or the size of epidemics? In a mesocosm experiment with planktonic hosts, we illustrate the joint harm of competition and disease: hosts with constrained evolutionary ability (limited phenotypic variation) suffered greatly from both. However, populations starting with broader phenotypic variation evolved stronger competitive ability during epidemics. In turn, enhanced competitive ability-driven especially by parasites-rescued host densities from the negative impacts of competition, disease, and especially their combination. Interspecific competitors reduced disease (supporting dilution effects) even when hosts rapidly evolved. However, this evolutionary response also elicited a potential problem. Populations that evolved enhanced competitive ability and maintained robust total densities also supported higher densities of infections. Thus, rapid evolution rescued host densities but also unleashed larger epidemics.

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.

Spatial evolutionary epidemiology of spreading epidemics

Most spatial models of host-parasite interactions either neglect the possibility of pathogen evolution or consider that this process is slow enough for epidemiological dynamics to reach an equilibrium on a fast timescale. Here, we propose a novel approach to jointly model the epidemiological and evolutionary dynamics of spatially structured host and pathogen populations. Starting from a multi-strain epidemiological model, we use a combination of spatial moment equations and quantitative genetics to analyse the dynamics of mean transmission and virulence in the population. A key insight of our approach is that, even in the absence of long-term evolutionary consequences, spatial structure can affect the short-term evolution of pathogens because of the build-up of spatial differentiation in mean virulence. We show that spatial differentiation is driven by a balance between epidemiological and genetic effects, and this quantity is related to the effect of kin competition discussed in previous studies of parasite evolution in spatially structured host populations. Our analysis can be used to understand and predict the transient evolutionary dynamics of pathogens and the emergence of spatial patterns of phenotypic variation.

Variability in fitness effects can preclude selection of the fittest

Evolutionary biologists often predict the outcome of natural selection on an allele by measuring its effects on lifetime survival and reproduction of individual carriers. However, alleles affecting traits like sex, evolvability, and cooperation can cause fitness effects that depend heavily on differences in the environmental, social, and genetic context of individuals carrying the allele. This variability makes it difficult to summarize the evolutionary fate of an allele based solely on its effects on any one individual. Attempts to average over this variability can sometimes salvage the concept of fitness. In other cases evolutionary outcomes can only be predicted by considering the entire genealogy of an allele, thus limiting the utility of individual fitness altogether. We describe a number of intriguing new evolutionary phenomena that have emerged in studies that explicitly model long-term lineage dynamics and discuss implications for the evolution of infectious diseases.

A transmission-virulence evolutionary trade-off explains attenuation of HIV-1 in Uganda

Evolutionary theory hypothesizes that intermediate virulence maximizes pathogen fitness as a result of a trade-off between virulence and transmission, but empirical evidence remains scarce. We bridge this gap using data from a large and long-standing HIV-1 prospective cohort, in Uganda. We use an epidemiological-evolutionary model parameterised with this data to derive evolutionary predictions based on analysis and detailed individual-based simulations. We robustly predict stabilising selection towards a low level of virulence, and rapid attenuation of the virus. Accordingly, set-point viral load, the most common measure of virulence, has declined in the last 20 years. Our model also predicts that subtype A is slowly outcompeting subtype D, with both subtypes becoming less virulent, as observed in the data. Reduction of set-point viral loads should have resulted in a 20% reduction in incidence, and a three years extension of untreated asymptomatic infection, increasing opportunities for timely treatment of infected individuals.

Forecasting Epidemiological and Evolutionary Dynamics of Infectious Diseases

Mathematical models have been powerful tools in developing mechanistic understanding of infectious diseases. Furthermore, they have allowed detailed forecasting of epidemiological phenomena such as outbreak size, which is of considerable public-health relevance. The short generation time of pathogens and the strong selection they are subjected to (by host immunity, vaccines, chemotherapy, etc.) mean that evolution is also a key driver of infectious disease dynamics. Accurate forecasting of pathogen dynamics therefore calls for the integration of epidemiological and evolutionary processes, yet this integration remains relatively rare. We review previous attempts to model and predict infectious disease dynamics with or without evolution and discuss major challenges facing the development of the emerging science of epidemic forecasting.

Eco-evolutionary dynamics of social dilemmas

Social dilemmas are an integral part of social interactions. Cooperative actions, ranging from secreting extra-cellular products in microbial populations to donating blood in humans, are costly to the actor and hence create an incentive to shirk and avoid the costs. Nevertheless, cooperation is ubiquitous in nature. Both costs and benefits often depend non-linearly on the number and types of individuals involved-as captured by idioms such as 'too many cooks spoil the broth' where additional contributions are discounted, or 'two heads are better than one' where cooperators synergistically enhance the group benefit. Interaction group sizes may depend on the size of the population and hence on ecological processes. This results in feedback mechanisms between ecological and evolutionary processes, which jointly affect and determine the evolutionary trajectory. Only recently combined eco-evolutionary processes became experimentally tractable in microbial social dilemmas. Here we analyse the evolutionary dynamics of non-linear social dilemmas in settings where the population fluctuates in size and the environment changes over time. In particular, cooperation is often supported and maintained at high densities through ecological fluctuations. Moreover, we find that the combination of the two processes routinely reveals highly complex dynamics, which suggests common occurrence in nature.

Why Be Temperate: Lessons from Bacteriophage λ

Many pathogens have evolved the ability to induce latent infections of their hosts. The bacteriophage λ is a classical model for exploring the regulation and the evolution of latency. Here, I review recent experimental studies on phage λ that identify specific conditions promoting the evolution of lysogenic life cycles. In addition, I present specific adaptations of phage λ that allow this virus to react plastically to variations in the environment and to reactivate its lytic life cycle. All of these different examples are discussed in the light of evolutionary epidemiology theory to disentangle the different evolutionary forces acting on temperate phages. Understanding phage λ adaptations yield important insights into the evolution of latency in other microbes, including several life-threatening human pathogens.

Host-parasite coevolution: why changing population size matters

Host-parasite coevolution is widely assumed to have a major influence on biological evolution, especially as these interactions impose high selective pressure on the reciprocally interacting antagonists. The exact nature of the underlying dynamics is yet under debate and may be determined by recurrent selective sweeps (i.e., arms race dynamics), negative frequency-dependent selection (i.e., Red Queen dynamics), or a combination thereof. These interactions are often associated with reciprocally induced changes in population size, which, in turn, should have a strong impact on co-adaptation processes, yet are neglected in most current work on the topic. Here, we discuss potential consequences of temporal variations in population size on host-parasite coevolution. The limited empirical data available and the current theoretical literature in this field highlight that the consideration of such interaction-dependent population size changes is likely key for the full understanding of the coevolutionary dynamics, and, thus, a more realistic view on the complex nature of species interactions.

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.

Evolutionary Stability of Minimal Mutation Rates in an Evo-epidemiological Model

We consider the evolution of mutation rate in a seasonally forced, deterministic, compartmental epidemiological model with a transmission-virulence trade-off. We model virulence as a quantitative genetic trait in a haploid population and mutation as continuous diffusion in the trait space. There is a mutation rate threshold above which the pathogen cannot invade a wholly susceptible population. The evolutionarily stable (ESS) mutation rate is the one which drives the lowest average density, over the course of one forcing period, of susceptible individuals at steady state. In contrast with earlier eco-evolutionary models in which higher mutation rates allow for better evolutionary tracking of a dynamic environment, numerical calculations suggest that in our model the minimum average susceptible population, and hence the ESS, is achieved by a pathogen strain with zero mutation. We discuss how this result arises within our model and how the model might be modified to obtain a nonzero optimum.

Virulence evolution at the front line of spreading epidemics

Understanding and predicting the spatial spread of emerging pathogens is a major challenge for the public health management of infectious diseases. Theoretical epidemiology shows that the speed of an epidemic is governed by the life-history characteristics of the pathogen and its ability to disperse. Rapid evolution of these traits during the invasion may thus affect the speed of epidemics. Here we study the influence of virulence evolution on the spatial spread of an epidemic. At the edge of the invasion front, we show that more virulent and transmissible genotypes are expected to win the competition with other pathogens. Behind the front line, however, more prudent exploitation strategies outcompete virulent pathogens. Crucially, even when the presence of the virulent mutant is limited to the edge of the front, the invasion speed can be dramatically altered by pathogen evolution. We support our analysis with individual-based simulations and we discuss the additional effects of demographic stochasticity taking place at the front line on virulence evolution. We confirm that an increase of virulence can occur at the front, but only if the carrying capacity of the invading pathogen is large enough. These results are discussed in the light of recent empirical studies examining virulence evolution at the edge of spreading epidemics.

The adaptive evolution of virulence: a review of theoretical predictions and empirical tests

Why is it that some parasites cause high levels of host damage (i.e. virulence) whereas others are relatively benign? There are now numerous reviews of virulence evolution in the literature but it is nevertheless still difficult to find a comprehensive treatment of the theory and data on the subject that is easily accessible to non-specialists. Here we attempt to do so by distilling the vast theoretical literature on the topic into a set of relatively few robust predictions. We then provide a comprehensive assessment of the available empirical literature that tests these predictions. Our results show that there have been some notable successes in integrating theory and data but also that theory and empiricism in this field do not ‘speak’ to each other very well. We offer a few suggestions for how the connection between the two might be improved.