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.

Coevolution of Age-Structured Tolerance and Virulence.

Hosts can evolve a variety of defences against parasitism, including resistance (which prevents or reduces the spread of infection) and tolerance (which protects against virulence). Some organisms have evolved different levels of tolerance at different life-stages, which is likely to be the result of coevolution with pathogens, and yet it is currently unclear how coevolution drives patterns of age-specific tolerance. Here, we use a model of tolerance-virulence coevolution to investigate how age structure influences coevolutionary dynamics. Specifically, we explore how coevolution unfolds when tolerance and virulence (disease-induced mortality) are age-specific compared to when these traits are uniform across the host lifespan. We find that coevolutionary cycling is relatively common when host tolerance is age-specific, but cycling does not occur when tolerance is the same across all ages. We also find that age-structured tolerance can lead to selection for higher virulence in shorter-lived than in longer-lived hosts, whereas non-age-structured tolerance always leads virulence to increase with host lifespan. Our findings therefore suggest that age structure can have substantial qualitative impacts on host-pathogen coevolution.

The evolution of age-specific resistance to infectious disease.

Innate, infection-preventing resistance often varies between host life stages. Juveniles are more resistant than adults in some species, whereas the opposite pattern is true in others. This variation cannot always be explained by prior exposure or physiological constraints and so it has been hypothesized that trade-offs with other life-history traits may be involved. However, little is known about how trade-offs between various life-history traits and resistance at different life stages affect the evolution of age-specific resistance. Here, we use a mathematical model to explore how trade-offs with natural mortality, reproduction and maturation combine to affect the evolution of resistance at different life stages. Our results show that certain combinations of trade-offs have substantial effects on whether adults or juveniles are more resistant, with trade-offs between juvenile resistance and adult reproduction inherently more costly than trade-offs involving maturation or mortality (all else being equal), resulting in consistent evolution of lower resistance at the juvenile stage even when infection causes a lifelong fecundity reduction. Our model demonstrates how the differences between patterns of age-structured resistance seen in nature may be explained by variation in the trade-offs involved and our results suggest conditions under which trade-offs tend to select for lower resistance in juveniles than adults.

The Evolution of the Age of Onset of Resistance to Infectious Disease.

Many organisms experience an increase in disease resistance as they age, but the time of life at which this change occurs varies. Increases in resistance are partially due to prior exposure and physiological constraints, but these cannot fully explain the observed patterns of age-related resistance. An alternative explanation is that developing resistance at an earlier age incurs costs to other life-history traits. Here, we explore how trade-offs with host reproduction or mortality affect the evolution of the onset of resistance, depending on when during the host's life cycle the costs are paid (only when resistance is developing, only when resistant or throughout the lifetime). We find that the timing of the costs is crucial to determining evolutionary outcomes, often making the difference between resistance developing at an early or late age. Accurate modelling of biological systems therefore relies on knowing not only the shape of trade-offs but also when they take effect. We also find that the evolution of the rate of onset of resistance can result in evolutionary branching. This provides an alternative, possible evolutionary history of populations which are dimorphic in disease resistance, where the rate of onset of resistance has diversified rather than the level of resistance.

Coevolutionary theory of hosts and parasites.

Host and parasite evolution are closely intertwined, with selection for adaptations and counter-adaptations forming a coevolutionary feedback loop. Coevolutionary dynamics are often difficult to intuit due to these feedbacks and are hard to demonstrate empirically in most systems. Theoretical models have therefore played a crucial role in shaping our understanding of host-parasite coevolution. Theoretical models vary widely in their assumptions, approaches and aims, and such variety makes it difficult, especially for non-theoreticians and those new to the field, to: (1) understand how model approaches relate to one another; (2) identify key modelling assumptions; (3) determine how model assumptions relate to biological systems; and (4) reconcile the results of different models with contrasting assumptions. In this review, we identify important model features, highlight key results and predictions and describe how these pertain to model assumptions. We carry out a literature survey of theoretical studies published since the 1950s (n = 219 papers) to support our analysis. We identify two particularly important features of models that tend to have a significant qualitative impact on the outcome of host-parasite coevolution: population dynamics and the genetic basis of infection. We also highlight the importance of other modelling features, such as stochasticity and whether time proceeds continuously or in discrete steps, that have received less attention but can drastically alter coevolutionary dynamics. We finish by summarizing recent developments in the field, specifically the trend towards greater model complexity, and discuss likely future directions for research.

The diversity-generating benefits of a prokaryotic adaptive immune system.

Prokaryotic CRISPR-Cas adaptive immune systems insert spacers derived from viruses and other parasitic DNA elements into CRISPR loci to provide sequence-specific immunity. This frequently results in high within-population spacer diversity, but it is unclear if and why this is important. Here we show that, as a result of this spacer diversity, viruses can no longer evolve to overcome CRISPR-Cas by point mutation, which results in rapid virus extinction. This effect arises from synergy between spacer diversity and the high specificity of infection, which greatly increases overall population resistance. We propose that the resulting short-lived nature of CRISPR-dependent bacteria-virus coevolution has provided strong selection for the evolution of sophisticated virus-encoded anti-CRISPR mechanisms.

How do biases in sex ratio and disease characteristics affect the spread of sexually transmitted infections?

The epidemiology of sexually transmitted infections (STIs) is inherently linked to host mating dynamics. Studies across many taxa show that adult sex ratio, a major determinant of host mating dynamics, is often skewed - sometimes strongly - toward males or females. However, few predictions exist for the effects of skewed sex ratio on STI epidemiology, and none when coupled with sex biased disease characteristics. Here we use mathematical modelling to examine how interactions between sex ratio and disease characteristics affect STI prevalence in males and females. Notably, we find that while overall disease prevalence peaks at equal sex ratios, prevalence per sex peaks at skewed sex ratios. Furthermore, disease characteristics, sex-biased or not, drive predictable differences in male and female STI prevalence as sex ratio varies, with higher transmission and lower virulence generally increasing differences between the sexes for a given sex ratio. Our work reveals new insights into how STI prevalence in males and females depends on a complex interaction between host population sex ratio and disease characteristics.

Key questions for modelling COVID-19 exit strategies.

Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute 'Models for an exit strategy' workshop (11-15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.

When does parasitism maintain sex in the absence of Red Queen Dynamics?

Parasites can select for sexual reproduction in host populations, preventing replacement by faster-growing asexual genotypes. This is usually attributed to so-called 'Red Queen dynamics' (RQD), where antagonistic coevolution causes fluctuating selection in allele frequencies, which provides sex with an advantage over asex. However, parasitism may also maintain sex in the absence of RQD when sexual populations are more genetically diverse-and hence more resistant, on average-than clonal populations, allowing sex and asex to coexist at a stable equilibrium. Although the maintenance of sex due to RQD has been studied extensively, the conditions that allow sex and asex to stably coexist have yet to be explored in detail. In particular, we lack an understanding of how host demography and parasite epidemiology affect the maintenance of sex in the absence of RQD. Here, I use an eco-evolutionary model to show that both population density and the type and strength of virulence are important for maintaining sex, which can be understood in terms of their effects on disease prevalence and severity. In addition, I show that even in the absence of heterozygote advantage, asexual heterozygosity affects coexistence with sex due to variation in niche overlap. These results reveal which host and parasite characteristics are most important for the maintenance of sex in the absence of RQD, and provide empirically testable predictions for how demography and epidemiology mediate competition between sex and asex.

Understanding the role of eco-evolutionary feedbacks in host-parasite coevolution.

It is widely recognised that eco-evolutionary feedbacks can have important implications for evolution. However, many models of host-parasite coevolution omit eco-evolutionary feedbacks for the sake of simplicity, typically by assuming the population sizes of both species are constant. It is often difficult to determine whether the results of these models are qualitatively robust if eco-evolutionary feedbacks are included. Here, by allowing interspecific encounter probabilities to depend on population densities without otherwise varying the structure of the models, we provide a simple method that can test whether eco-evolutionary feedbacks per se affect evolutionary outcomes. Applying this approach to explicit genetic and quantitative trait models from the literature, our framework shows that qualitative changes to the outcome can be directly attributable to eco-evolutionary feedbacks. For example, shifting the dynamics between stable monomorphism or polymorphism and cycling, as well as changing the nature of the cycles. Our approach, which can be readily applied to many different models of host-parasite coevolution, offers a straightforward method for testing whether eco-evolutionary feedbacks qualitatively change coevolutionary outcomes.

The evolution of juvenile susceptibility to infectious disease.

Infection prior to reproduction usually carries greater fitness costs for hosts than infection later in life, suggesting selection should tend to favour juvenile resistance. Yet, juveniles are generally more susceptible than adults across a wide spectrum of host taxa. While physiological constraints and a lack of prior exposure can explain some of this pattern, studies in plants and insects suggest that hosts may trade off juvenile susceptibility against other life-history traits. However, it is unclear precisely how trade-offs shape the evolution of juvenile susceptibility. Here, we theoretically explore the evolution of juvenile susceptibility subject to trade-offs with maturation or reproduction, which could realistically occur due to resource allocation during development (e.g. prioritizing growth over immune defence). We show how host lifespan, the probability of maturation (i.e. of reaching the adult stage) and transmission mode affect the results. Our key finding is that elevated juvenile susceptibility is expected to evolve over a wide range of conditions, but should be lowest when hosts have moderate lifespans and an intermediate probability of reaching the adult stage. Our results elucidate how interactions between trade-offs and the epidemiological-demographic structure of the population can lead to the evolution of elevated juvenile susceptibility.

Coevolution of parasite virulence and host mating strategies.

Parasites are thought to play an important role in sexual selection and the evolution of mating strategies, which in turn are likely to be critical to the transmission and therefore the evolution of parasites. Despite this clear interdependence we have little understanding of parasite-mediated sexual selection in the context of reciprocal parasite evolution. Here we develop a general coevolutionary model between host mate preference and the virulence of a sexually transmitted parasite. We show when the characteristics of both the host and parasite lead to coevolutionarily stable strategies or runaway selection, and when coevolutionary cycling between high and low levels of host mate choosiness and virulence is possible. A prominent argument against parasites being involved in sexual selection is that they should evolve to become less virulent when transmission depends on host mating success. The present study, however, demonstrates that coevolution can maintain stable host mate choosiness and parasite virulence or indeed coevolutionary cycling of both traits. We predict that choosiness should vary inversely with parasite virulence and that both relatively long and short life spans select against choosy behavior in the host. The model also reveals that hosts can evolve different behavioral responses from the same initial conditions, which highlights difficulties in using comparative analysis to detect parasite-mediated sexual selection. Taken as a whole, our results emphasize the importance of viewing parasite-mediated sexual selection in the context of coevolution.

Multi-mode fluctuating selection in host-parasite coevolution.

Understanding fluctuating selection is important for our understanding of patterns of spatial and temporal diversity in nature. Host-parasite theory has classically assumed fluctuations either occur between highly specific genotypes (matching allele: MA) or from specialism to generalism (gene-for-gene: GFG). However, while MA can only generate one mode of fluctuating selection, we show that GFG can in fact produce both rapid 'within-range' fluctuations (among genotypes with identical levels of investment but which specialise on different subsets of the population) and slower cycling 'between ranges' (different levels of investment), emphasising that MA is a subset of GFG. Our findings closely match empirical observations, although sampling rates need to be high to detect these novel dynamics empirically. Within-range cycling is an overlooked process by which fluctuating selection can occur in nature, suggesting that fluctuating selection may be a more common and important process than previously thought in generating and maintaining diversity.

Host-parasite fluctuating selection in the absence of specificity.

Fluctuating selection driven by coevolution between hosts and parasites is important for the generation of host and parasite diversity across space and time. Theory has focused primarily on infection genetics, with highly specific 'matching-allele' frameworks more likely to generate fluctuating selection dynamics (FSD) than 'gene-for-gene' (generalist-specialist) frameworks. However, the environment, ecological feedbacks and life-history characteristics may all play a role in determining when FSD occurs. Here, we develop eco-evolutionary models with explicit ecological dynamics to explore the ecological, epidemiological and host life-history drivers of FSD. Our key result is to demonstrate for the first time, to our knowledge, that specificity between hosts and parasites is not required to generate FSD. Furthermore, highly specific host-parasite interactions produce unstable, less robust stochastic fluctuations in contrast to interactions that lack specificity altogether or those that vary from generalist to specialist, which produce predictable limit cycles. Given the ubiquity of ecological feedbacks and the variation in the nature of specificity in host-parasite interactions, our work emphasizes the underestimated potential for host-parasite coevolution to generate fluctuating selection.

Pathogen selection drives nonoverlapping associations between HLA loci.

Pathogen-mediated selection is commonly invoked as an explanation for the exceptional polymorphism of the HLA gene cluster, but its role in generating and maintaining linkage disequilibrium between HLA loci is unclear. Here we show that pathogen-mediated selection can promote nonrandom associations between HLA loci. These associations may be distinguished from linkage disequilibrium generated by other population genetic processes by virtue of being nonoverlapping as well as nonrandom. Within our framework, immune selection forces the pathogen population to exist as a set of antigenically discrete strains; this then drives nonoverlapping associations between the HLA loci through which recognition of these antigens is mediated. We demonstrate that this signature of pathogen-driven selection can be observed in existing data, and propose that analyses of HLA population structure can be combined with laboratory studies to help us uncover the functional relationships between HLA alleles. In a wider coevolutionary context, our framework also shows that the inclusion of memory immunity can lead to robust cyclical dynamics across a range of host-pathogen systems.

Population mixing promotes arms race host-parasite coevolution.

The consequences of host-parasite coevolution are highly contingent on the qualitative coevolutionary dynamics: whether selection fluctuates (fluctuating selection dynamic; FSD), or is directional towards increasing infectivity/resistance (arms race dynamic; ARD). Both genetics and ecology can play an important role in determining whether coevolution follows FSD or ARD, but the ecological conditions under which FSD shifts to ARD, and vice versa, are not well understood. The degree of population mixing is thought to increase host exposure to parasites, hence selecting for greater resistance and infectivity ranges, and we hypothesize this promotes ARD. We tested this by coevolving bacteria and viruses in soil microcosms and found that population mixing shifted bacteria-virus coevolution from FSD to ARD. A simple theoretical model produced qualitatively similar results, showing that mechanisms that increase host exposure to parasites tend to push dynamics towards ARD. The shift from FSD to ARD with increased population mixing may help to explain variation in coevolutionary dynamics between different host-parasite systems, and more specifically the observed discrepancies between laboratory and field bacteria-virus coevolutionary studies.

Spatial structure mitigates fitness costs in host-parasite coevolution.

The extent of population mixing is known to influence the coevolutionary outcomes of many host and parasite traits, including the evolution of generalism (the ability to resist or infect a broad range of genotypes). While the segregation of populations into interconnected demes has been shown to influence the evolution of generalism, the role of local interactions between individuals is unclear. Here, we combine an individual-based model of microbial communities with a well-established framework of genetic specificity that matches empirical observations of bacterium-phage interactions. We find the evolution of generalism in well-mixed populations to be highly sensitive to the severity of associated fitness costs, but the constraining effect of costs on the evolution of generalism is lessened in spatially structured populations. The contrasting outcomes between the two environments can be explained by different scales of competition (i.e., global vs. local). These findings suggest that local interactions may have important effects on the evolution of generalism in host-parasite interactions, particularly in the presence of high fitness costs.

Hyperparasitism and the evolution of parasite virulence.

Hyperparasites (species which parasitize other parasites) are common in natural populations, affecting many parasitic taxa, including: eukaryotic parasites; bacterial and fungal pathogens. Hyperparasitism is therefore likely to shape the ecology and evolution of many host-parasite systems, representing a promising method for biocontrol (e.g., treating antimicrobial resistant infections). However, the eco-evolutionary consequences of hyperparasitism have received little attention. We use a host-parasite-hyperparasite model to explore how introducing a hyperparasite drives the evolution of parasite virulence, and what impact this has on the host population. We show when the introduction of a hyperparasite selects for higher or lower parasite virulence, and the changes in virulence experienced by the host population. Crucially, we show that variation in the direct effects of hyperparasites on virulence and transmission, and the probability of cotransmission, can lead to a previously unseen hysteresis effect, whereby small shifts in hyperparasite characteristics can lead to sudden shifts in parasite virulence. We also show that hyperparasites can induce diversification in parasite virulence, leading to the coexistence of high and low virulence strains. Our results show hyperparasites can have dramatic effects on the evolution of parasite virulence, and that the use of hyperparasites in biocontrol should be approached with caution.