Abstract:Theoretical models of the evolution of parasites and their hosts have shaped our understanding of infectious disease dynamics for over 40 years. Many theoretical models assume that the underlying ecological dynamics are at equilibrium or constant, yet we know that in a great many systems there are fluctuations in the ecological dynamics owing to a variety of intrinsic or extrinsic factors. Here, we discuss the challenges presented when modelling evolution in systems with fluctuating ecological dynamics and sum… Show more
“…By examining our model system consisting of two hosts and two parasites (system 3.1 for m = 2), we were able to identify limit cycles in the population dynamics (as shown in figure 3 e ). This fluctuating behaviour in our ecological model can cause shifts in the evolutionary outcomes, affecting the coexistence of such dimorphic strains (see Best & Ashby [ 57 ] for more details). Figure 3 ( a , b ) Simulations showing branching in the parasite occurs after the host branches when ϕ h = ϕ p .…”
Section: Resultsmentioning
confidence: 99%
“…Theoretical models have examined the impact of fluctuating ecological dynamics on parasite and host evolution [63,[67][68][69][70], but only one study investigated this for a host-parasite coevolutionary model [31]. A recent study serves relevant insights in this context, showing how the presence of population cycles can alter selection and how evolution can shift the population dynamics between cycles and ecological equilibria [57]. In our two host-two parasite population dynamics system, increasing differences between trait values in each species resulted in limit cycles, causing quantitative changes in coevolutionary outcomes.…”
Section: Discussionmentioning
confidence: 99%
“…A possible explanation could be due to the impact of fluctuating ecological dynamics over coevolution. It is understood that population dynamics play a considerable role in the host-parasite evolution and feedbacks caused by the ecological and evolutionary interactions can lead to qualitative shifts in the evolutionary outcomes [5,[56][57][58]. By examining our model system consisting of two hosts and two parasites (system 3.1 for m = 2), we were able to identify limit cycles in the population dynamics (as shown in figure 3e).…”
Understanding the coevolutionary dynamics of hosts and their parasites remains a major focus of much theoretical literature. Despite empirical evidence supporting the presence of sterility-mortality tolerance trade-offs in hosts and recovery-transmission trade-offs in parasites, none of the current models have explored the potential outcomes when both trade-offs are considered within a coevolutionary framework. In this study, we consider a model where the host evolves sterility tolerance at the cost of increased mortality and the parasite evolves higher transmission rate at the cost of increased recovery rate (reduced infection duration), and use adaptive dynamics to predict the coevolutionary outcomes under such trade-off assumptions. We particularly aim to understand how our coevolutionary dynamics compare with single species evolutionary models. We find that evolutionary branching in the host can drive the parasite population to branch, but that cycles in the population dynamics can prevent the coexisting strains from reaching their extremes. We also find that varying crowding does not impact the recovery rate when only the parasite evolves, yet coevolution reduces recovery as crowding intensifies. We conclude by discussing how different host and parasite trade-offs shape coevolutionary outcomes, underscoring the pivotal role of trade-offs in coevolution.
“…By examining our model system consisting of two hosts and two parasites (system 3.1 for m = 2), we were able to identify limit cycles in the population dynamics (as shown in figure 3 e ). This fluctuating behaviour in our ecological model can cause shifts in the evolutionary outcomes, affecting the coexistence of such dimorphic strains (see Best & Ashby [ 57 ] for more details). Figure 3 ( a , b ) Simulations showing branching in the parasite occurs after the host branches when ϕ h = ϕ p .…”
Section: Resultsmentioning
confidence: 99%
“…Theoretical models have examined the impact of fluctuating ecological dynamics on parasite and host evolution [63,[67][68][69][70], but only one study investigated this for a host-parasite coevolutionary model [31]. A recent study serves relevant insights in this context, showing how the presence of population cycles can alter selection and how evolution can shift the population dynamics between cycles and ecological equilibria [57]. In our two host-two parasite population dynamics system, increasing differences between trait values in each species resulted in limit cycles, causing quantitative changes in coevolutionary outcomes.…”
Section: Discussionmentioning
confidence: 99%
“…A possible explanation could be due to the impact of fluctuating ecological dynamics over coevolution. It is understood that population dynamics play a considerable role in the host-parasite evolution and feedbacks caused by the ecological and evolutionary interactions can lead to qualitative shifts in the evolutionary outcomes [5,[56][57][58]. By examining our model system consisting of two hosts and two parasites (system 3.1 for m = 2), we were able to identify limit cycles in the population dynamics (as shown in figure 3e).…”
Understanding the coevolutionary dynamics of hosts and their parasites remains a major focus of much theoretical literature. Despite empirical evidence supporting the presence of sterility-mortality tolerance trade-offs in hosts and recovery-transmission trade-offs in parasites, none of the current models have explored the potential outcomes when both trade-offs are considered within a coevolutionary framework. In this study, we consider a model where the host evolves sterility tolerance at the cost of increased mortality and the parasite evolves higher transmission rate at the cost of increased recovery rate (reduced infection duration), and use adaptive dynamics to predict the coevolutionary outcomes under such trade-off assumptions. We particularly aim to understand how our coevolutionary dynamics compare with single species evolutionary models. We find that evolutionary branching in the host can drive the parasite population to branch, but that cycles in the population dynamics can prevent the coexisting strains from reaching their extremes. We also find that varying crowding does not impact the recovery rate when only the parasite evolves, yet coevolution reduces recovery as crowding intensifies. We conclude by discussing how different host and parasite trade-offs shape coevolutionary outcomes, underscoring the pivotal role of trade-offs in coevolution.
“…The first two papers in this theme evaluate how well current modelling approaches perform in capturing the rapidly changing environments that host and pathogens face. Best & Ashby [ 31 ] review the main approaches used to model host–pathogen evolution when ecological dynamics fluctuate owing to either extrinsic (seasonality, food availability) or intrinsic (time lags) factors. They then provide an in-depth guide on how to implement one main method and apply this approach to fluctuations arising from seasonally varying resources, among others.…”
Section: Theme 2: Understanding Host–pathogen Interactions In Dynamic...mentioning
“…Adaptive dynamics (also known as evolutionary invasion analysis) is especially useful for modelling the long-term evolutionary dynamics of quantitative traits, as it naturally incorporates population (ecological) dynamics and is relatively straightforward to implement. A key assumption of this method is a separation of ecological and evolutionary timescales, so that the system reaches its ecological attractor (usually a stable equilibrium or limit cycle (Best and Ashby, 2023)) before a new mutation arises. This greatly simplifies the analysis because ecological dynamics (for instance, changes in population density) can be considered separately to evolutionary (trait) dynamics.…”
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.
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