Evolutionary branching of virulence in a single-infection model

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.

Coevolutionary dynamics of host-pathogen interaction with density-dependent mortality

This study explores the coevolutionary dynamics of host-pathogen interaction based on a susceptible-infected population model with density-dependent mortality. We assume that both the host’s resistance and the pathogen’s virulence will adaptively evolve, but there are inevitable costs in terms of host birth rate and disease-related mortality rate. Particularly, it is assumed that both the host resistance and pathogen virulence can affect the transmission rate. By using the approach of adaptive dynamics and numerical simulation, we find that the finally coevolutionary outcome depends on the strength of host-pathogen asymmetric interaction, the curvature of trade-off functions, and the intensity of density-dependent natural mortality. To be specific, firstly, we find that if the strengths of host-pathogen asymmetric interaction and disease-related mortality are relatively weak, or the density-dependent natural mortality is relatively strong, then the host resistance and pathogen virulence will evolve to a continuously stable strategy. However, if the strength of host-pathogen asymmetric interaction and disease-related mortality becomes stronger, then the host resistance and pathogen virulence will evolve periodically. Secondly, we find that if the intensities of both the birth rate trade-off function and the density-dependent natural mortality are relatively weak, but the strength of host-pathogen asymmetric interaction becomes relatively strong, then the evolution of host resistance will have a relatively strongly accelerating benefit, the evolutionary branching of host resistance will first arise. However, if the strength of host-pathogen asymmetric interaction is relatively weak, but the intensity of the trade-off function of disease-related mortality becomes relatively strong, then the evolution of pathogen virulence will have a relatively strongly decelerating cost, and the evolutionary branching of pathogen virulence will first arise. Thirdly, after the evolutionary branching of host resistance and pathogen virulence, we further study the coevolutionary dynamics of two-hosts-one-pathogen interaction and one-host-two-pathogens interaction. We find that if the evolutionary branching of host resistance arises firstly, then the finally evolutionary outcome contains a dimorphic host and a monomorphic pathogen population. If the evolutionary branching of pathogen virulence arises firstly, then the finally evolutionary outcome may contain a monomorphic host and a dimorphic pathogen population.

Treating symptomatic infections and the co-evolution of virulence and drug resistance

Antimicrobial therapeutic treatments are by definition applied after the onset of symptoms, which tend to correlate with infection severity. Using mathematical epidemiology models, I explore how this link affects the coevolutionary dynamics between the virulence of an infection, measured via host mortality rate, and its susceptibility to chemotherapy. I show that unless resistance pre-exists in the population, drug-resistant infections are initially more virulent than drug-sensitive ones. As the epidemic unfolds, virulence is more counter-selected in drug-sensitive than in drug-resistant infections. This difference decreases over time and, eventually, the exact shape of genetic trade-offs govern long-term evolutionary dynamics. Using adaptive dynamics, I show that two types of evolutionary stable strategies (ESS) may be reached in the context of this simple model and that, depending on the parameter values, an ESS may only be locally stable. In general, the more the treatment rate increases with virulence, the lower the ESS value. Overall, both on the short-term and long-term, having treatment rate depend on infection virulence tend to favour less virulent strains in drug-sensitive infections. These results highlight the importance of the feedbacks between epidemiology, public health policies and parasite evolution, and have implications for the monitoring of virulence evolution.

Revisiting the Role of Hyperparasitism in the Evolution of Virulence

AbstractHyperparasitism denotes the natural phenomenon where a parasite infecting a host is in turn infected by its own parasite. Hyperparasites can shape the dynamics of host-parasite interactions and often have a deleterious impact on pathogens, an important class of parasites, causing a reduction in their virulence and transmission rate. Hyperparasitism thus could be an important tool of biological control. However, host-parasite-hyperparasite systems have so far been outside the mainstream of modeling studies, especially those dealing with eco-evolutionary aspects of species interactions. Here, we theoretically explore the evolution of life-history traits in a generic host-parasite-hyperparasite system, focusing on parasite virulence and the positive impact that hyperparasitism has on the host population. We also explore the coevolution of life-history traits of the parasite and hyperparasite, using adaptive dynamics and quantitative genetics frameworks to identify evolutionarily singular strategies. We find that in the presence of hyperparasites, the evolutionarily optimal pathogen virulence generally shifts toward more virulent strains. However, even in this case the use of hyperparasites in biocontrol could be justified, since overall host mortality decreases. An intriguing possible outcome of the evolution of the hyperparasite can be its evolutionary suicide.

Effects of pollution on individual size of a single species

In this paper, we develop a single species evolutionary model with a continuous phenotypic trait in a pulsed pollution discharge environment and discuss the effects of pollution on the individual size of the species. The invasion fitness function of a monomorphic species is given, which involves the long-term average exponential growth rate of the species. Then the critical function analysis method is used to obtain the evolutionary dynamics of the system, which is related to interspecific competition intensity between mutant species and resident species and the curvature of the trade-off between individual size and the intrinsic growth rate. We conclude that the pollution affects the evolutionary traits and evolutionary dynamics. The worsening of the pollution can lead to rapid stable evolution toward a smaller individual size, while the opposite is more likely to generate evolutionary branching and promote species diversity. The adaptive dynamics of coevolution of dimorphic species is further analyzed when evolutionary branching occurs.

Fecundity-Longevity Trade-Off, Vertical Transmission, and Evolution of Virulence in Sterilizing Pathogens

Sterilizing pathogens are common, yet studies focused on how such pathogens respond adaptively to fecundity reductions caused in their hosts are rare. Here we assume that the infected hosts, as a result of redistributing energy resources saved by reduced fecundity, have increased longevity and focus on exploring the consequences of such a fecundity-longevity trade-off on sterility virulence evolution in the pathogens. We find that the trade-off itself cannot prevent the evolution of full sterilization. Therefore, we allow for vertical transmission and reveal that the fecundity-longevity trade-off strongly determines the threshold efficiency of vertical transmission above which partial host sterilization evolves. Partial sterilization may appear as an intermediate level of sterility virulence or as a stable dimorphism at which avirulent and highly virulent strains coexist. The fecundity-longevity trade-off significantly contributes to determining the actual outcome, in many cases countering predictions made in the absence of this trade-off. It is known that in well-mixed populations, partial sterilization may evolve in pathogens under a combination of horizontal and vertical transmission. Our study highlights that this is independent of the form of horizontal transmission and the type of density dependence in host demography and that the fecundity-longevity trade-off is an important player in sterility virulence evolution.

Can Ebola virus evolve to be less virulent in humans?

Understanding Ebola virus (EBOV) virulence evolution not only is timely but also raises specific questions because it causes one of the most virulent human infections and it is capable of transmission after the death of its host. Using a compartmental epidemiological model that captures three transmission routes (by regular contact, via dead bodies and by sexual contact), we infer the evolutionary dynamics of case fatality ratio on the scale of an outbreak and in the long term. Our major finding is that the virus's specific life cycle imposes selection for high levels of virulence and that this pattern is robust to parameter variations in biological ranges. In addition to shedding a new light on the ultimate causes of EBOV's high virulence, these results generate testable predictions and contribute to informing public health policies. In particular, burial management stands out as the most appropriate intervention since it decreases the R0 of the epidemics, while imposing selection for less virulent strains.

Adaptive dynamics of saturated polymorphisms

We study the joint adaptive dynamics of n scalar-valued strategies in ecosystems where n is the maximum number of coexisting strategies permitted by the (generalized) competitive exclusion principle. The adaptive dynamics of such saturated systems exhibits special characteristics, which we first demonstrate in a simple example of a host-pathogen-predator model. The main part of the paper characterizes the adaptive dynamics of saturated polymorphisms in general. In order to investigate convergence stability, we give a new sufficient condition for absolute stability of an arbitrary (not necessarily saturated) polymorphic singularity and show that saturated evolutionarily stable polymorphisms satisfy it. For the case [Formula: see text], we also introduce a method to construct different pairwise invasibility plots of the monomorphic population without changing the selection gradients of the saturated dimorphism.

Evolution of acuteness in pathogen metapopulations: conflicts between "classical" and invasion-persistence trade-offs

Classical life-history theory predicts that acute, immunizing pathogens should maximize between-host transmission. When such pathogens induce violent epidemic outbreaks, however, a pathogen's short-term advantage at invasion may come at the expense of its ability to persist in the population over the long term. Here, we seek to understand how the classical and invasion-persistence trade-offs interact to shape pathogen life-history evolution as a function of the size and structure of the host population. We develop an individual-based infection model at three distinct levels of organization: within an individual host, among hosts within a local population, and among local populations within a metapopulation. We find a continuum of evolutionarily stable pathogen strategies. At one end of the spectrum-in large well-mixed populations-pathogens evolve to greater acuteness to maximize between-host transmission: the classical trade-off theory applies in this regime. At the other end of the spectrum-when the host population is broken into many small patches-selection favors less acute pathogens, which persist longer within a patch and thereby achieve enhanced between-patch transmission: the invasion-persistence tradeoff dominates in this regime. Between these extremes, we explore the effects of the size and structure of the host population in determining pathogen strategy. In general, pathogen strategies respond to evolutionary pressures arising at both scales.

A limited host immune range facilitates the creation and maintenance of diversity in parasite virulence

A vast theoretical literature has explored the evolutionary dynamics of parasite virulence. The classic result from this modelling work is that, assuming a saturating transmission-virulence trade-off, there is a single evolutionary optimum where the parasite optimizes the epidemiological R 0. However, there are an increasing number of models that have shown how ecological and epidemiological feedbacks to evolution can instead result in the creation and maintenance of multiple parasite strains. Here, we fully explore one such example, where recovered hosts have a limited 'immune range' resulting in partial cross-immunity to parasite strains that they have not previously encountered. Taking an adaptive dynamics approach, we show that, provided this immune range is not too wide, high levels of diversity can evolve and be maintained through multiple branching events. We argue that our model provides a more realistic picture of disease dynamics in vertebrate host populations and may be a key explanatory factor in the high levels of parasite diversity seen in natural systems.

Adaptive evolution of attack ability promotes the evolutionary branching of predator species

In this paper, with the methods of adaptive dynamics and critical function analysis, we investigate the evolutionary branching phenomenon of predator species. We assume that both the prey and predators are density-dependent and the predator's attack ability can adaptively evolve, but this has a cost in terms of its death rate. First, we identify the general properties of trade-off relationships that allow for a continuously stable strategy and evolutionary branching in the predator strategy. It is found that if the trade-off curve is weakly concave near the singular strategy, then the singular strategy may be an evolutionary branching point. Second, we find that after the branching has occurred in the predator strategy, if the trade-off curve is convex-concave-convex, the predator species will eventually evolve into two different types, which can stably coexist on the much longer evolutionary timescale and no further branching is possible.

Evolution of pathogen virulence under selective predation: a construction method to find eco-evolutionary cycles

We investigate eco-evolutionary cycles in the joint dynamics of pathogen virulence and predator population density when hosts carrying virulent infections are exposed to increased risk of predation. We introduce a new technique to find trade-off functions under which the model exhibits limit cycles; this technique provides a constructive proof that the system is able to generate limit cycles, and can be applied to other eco-evolutionary models as well. We also study a concrete example to confirm that eco-evolutionary cycles occur in a significant part of the parameter space and to briefly explore other evolutionary outcomes in the same model.

Seasonality selects for more acutely virulent parasites when virulence is density dependent

Host condition is often likely to influence parasite virulence. Furthermore, condition may often be correlated with host density, and therefore, it is important to understand the role of density-dependent virulence (DDV). We examine the consequences of DDV to the evolution of parasites in both seasonal and non-seasonal environments. In particular, we consider seasonality in host birth rate that results in a fluctuating host density and therefore a variable virulence. We show that parasites are selected for lower exploitation, and therefore lower transmission and virulence as the strength of DDV increases without seasonality. This is an important insight from our models; DDV has the opposite effect on the evolution of parasites to that of higher baseline mortality. Our key result is that although seasonality does not affect the evolution of virulence in classical models, with DDV parasites in seasonal environments are predicted to evolve to be more acute. This suggests that in more seasonal environments wildlife disease is likely to be more rather than less virulent if DDV is widespread.

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

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

Interactions among virulence, coinfection and drug resistance in a complex life-cycle parasite

Motivated by relatively recent empirical studies on Schistosoma mansoni, we use a mathematical model to investigate the impacts of drug treatment of the definitive human host and coinfection of the intermediate snail host by multiple parasite strains on the evolution of parasites' drug resistance. Through the examination of evolutionarily stable strategies (ESS) of parasites, our study suggests that higher levels of drug treatment rates (which usually tend to promote monomorphism as the evolutionary equilibrium) favor parasite strains that have a higher level of drug resistance. Our study also shows that whether coinfection of intermediate hosts affects the levels of drug resistance at ESS points and their stability depends on the assumptions on the cost of parasites paid for drug resistance, coinfection functions and parasites' reproduction within coinfected hosts. This calls for more empirical studies on the parasite.

A unified model for the coevolution of resistance, tolerance, and virulence

We present a general host-parasite model that unifies previous theory by investigating the coevolution of virulence, resistance, and tolerance, with respect to multiple physiological, epidemiological, and environmental parameters. Four sets of new predictions emerge. First, compared to virulence coevolving with resistance or tolerance, three-trait coevolution promotes more virulence and less tolerance, and broadens conditions under which pure defenses evolve. Second, the cost and efficiency of virulence and the epidemiological rates are the key factors of virulence coevolving with resistance and tolerance. Maximum virulence evolves for intermediate infection rate, at which coevolved levels of resistance and tolerance are both high. The influence of host and parasite background mortalities is strong on the evolution of defenses and weak on the coevolution of virulence. Third, evolutionary correlations between defenses can switch sign along single-parameter gradients. The evolutionary trade-off between resistance and tolerance may coevolve with virulence that either increases or decreases monotonically, depending on the underlying parameter gradient. Fourth, despite global attractiveness and stability of coevolutionary equilibria, not-so-rare and not-so-small mutations can beget large variation in virulence and defenses around equilibrium, in the form of transient "evolutionary spikes." Implications for evolutionary management of infections are discussed and directions for future research are outlined.

Resistance is futile but tolerance can explain why parasites do not always castrate their hosts

The disease caused by parasites and pathogens often causes sublethal effects that reduce host fecundity. Theory suggests that if parasites can "target" the detrimental effects of their growth on either host mortality or fecundity, they should always fully sterilize. This is because a reduction in host fecundity does not reduce the infectious period and is therefore neutral to a horizontally transmitted infectious organism. However, in nature fully castrating parasites are relatively rare, no doubt in part because of defense mechanisms in the host. Here, we examine in detail the evolution of host defense to the sterilizing effects of parasites and show that intermediate levels of sterility tolerance are found to evolve for a wide range of cost structures. Our key result arises when the host and parasite coevolve. Investment in tolerance by the host may prevent castration, but if host defense is through resistance (by controlling the parasite's growth rate) coevolution by the parasite results in the complete loss of infected host fecundity. Resistance is therefore a waste of resources, but tolerance can explain why parasites do not castrate their hosts. Our results further emphasize the importance of tolerance as opposed to resistance to parasites.

The implications of coevolutionary dynamics to host-parasite interactions

Due to the importance of infectious disease, there is a large body of theory on the evolution of either hosts or, more commonly, parasites. Here we present a fully coevolutionary model of a host-parasite system that includes ecological dynamics that feed back into the coevolutionary outcome, and we show that highly virulent parasites may evolve due to the coevolutionary process. Parasite evolution is very sensitive to evolution in the host, and virulence fluctuates substantially when mutation rates vary between host and parasite. Evolutionary branching in the host leads to parasites increasing their virulence, and small changes in host resistance drive large changes in parasite virulence. Evolutionary branching in one species does not cause branching in the other. Our work emphasizes the importance of considering coevolutionary dynamics and shows that certain highly virulent parasites may result from responses to host evolution.

Virulence evolution and the trade-off hypothesis: history, current state of affairs and the future

It has been more than two decades since the formulation of the so-called 'trade-off' hypothesis as an alternative to the then commonly accepted idea that parasites should always evolve towards avirulence (the 'avirulence hypothesis'). The trade-off hypothesis states that virulence is an unavoidable consequence of parasite transmission; however, since the 1990s, this hypothesis has been increasingly challenged. We discuss the history of the study of virulence evolution and the development of theories towards the trade-off hypothesis in order to illustrate the context of the debate. We investigate the arguments raised against the trade-off hypothesis and argue that trade-offs exist, but may not be of the simple form that is usually assumed, involving other mechanisms (and life-history traits) than those originally considered. Many processes such as pathogen adaptation to within-host competition, interactions with the immune system and shifting transmission routes, will all be interrelated making sweeping evolutionary predictions harder to obtain. We argue that this is the heart of the current debate in the field and while species-specific models may be better predictive tools, the trade-off hypothesis and its basic extensions are necessary to assess the qualitative impacts of virulence management strategies.