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.
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.
Innate, infection-preventing resistance often varies between host life-stages. Juveniles are more resistant than adults in some species, whereas the converse pattern is true in others. This variation cannot always be explained by prior exposure or physiological constraints and so it has been hypothesised 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.
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 summarising recent developments in the field, specifically the trend towards greater model complexity, and discuss likely future directions for research.