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In this paper we study the a posteriori bounds for a conforming piecewise linear finite element approximation of the Signorini problem. We prove new rigorous a posteriori estimates of residual type in Lp, for p ε (4, ∞) in two spatial dimensions. This new analysis treats the positive and negative parts of the discretization error separately, requiring a novel sign- and bound-preserving interpolant, which is shown to have optimal approximation properties. The estimates rely on the sharp dual stability results on the problem in W2,(4-ε)/3 for any ε 1. We summarize extensive numerical experiments aimed at testing the robustness of the estimator to validate the theory. [ABSTRACT FROM AUTHOR]

Defensive symbionts in the host microbiome can confer protection from infection or reduce the harms of being infected by a parasite. Defensive symbionts are therefore promising agents of biocontrol that could be used to control or ameliorate the impact of infectious diseases. Previous theory has shown how symbionts can evolve along the parasitism–mutualism continuum to confer greater or lesser protection to their hosts and in turn how hosts may coevolve with their symbionts to potentially form a mutualistic relationship. However, the consequences of introducing a defensive symbiont for parasite evolution and how the symbiont may coevolve with the parasite have received relatively little theoretical attention. Here, we investigate the ecological and evolutionary implications of introducing a tolerance-conferring defensive symbiont into an established host–parasite system. We show that while the defensive symbiont may initially have a positive impact on the host population, parasite and symbiont evolution tend to have a net negative effect on the host population in the long term. This is because the introduction of the defensive symbiont always selects for an increase in parasite virulence and may cause diversification into high- and low-virulence strains. Even if the symbiont experiences selection for greater host protection, this simply increases selection for virulence in the parasite, resulting in a net negative effect on the host population. Our results therefore suggest that tolerance-conferring defensive symbionts may be poor biocontrol agents for population-level infectious disease control. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Non-pharmaceutical interventions (NPIs), such as social distancing and contact tracing, are important public health measures that can reduce pathogen transmission. In addition to playing a crucial role in suppressing transmission, NPIs influence pathogen evolution by mediating mutation supply, restricting the availability of susceptible hosts, and altering the strength of selection for novel variants. Yet it is unclear how NPIs might affect the emergence of novel variants that are able to escape pre-existing immunity (partially or fully), are more transmissible or cause greater mortality. We analyse a stochastic two-strain epidemiological model to determine how the strength and timing of NPIs affect the emergence of variants with similar or contrasting life-history characteristics to the wild type. We show that, while stronger and timelier NPIs generally reduce the likelihood of variant emergence, it is possible for more transmissible variants with high cross-immunity to have a greater probability of emerging at intermediate levels of NPIs. This is because intermediate levels of NPIs allow an epidemic of the wild type that is neither too small (facilitating high mutation supply), nor too large (leaving a large pool of susceptible hosts), to prevent a novel variant from becoming established in the host population. However, since one cannot predict the characteristics of a variant, the best strategy to prevent emergence is likely to be an implementation of strong, timely NPIs. [ABSTRACT FROM AUTHOR]

Objectives/aims: Prolonged infections of immunocompromised individuals have been proposed as a crucial source of new variants of SARS-CoV-2 during the COVID-19 pandemic. In principle, sustained within-host antigenic evolution in immunocompromised hosts could allow novel immune escape variants to emerge more rapidly, but little is known about how and when immunocompromised hosts play a critical role in pathogen evolution. Materials and methods: Here, we use a simple mathematical model to understand the effects of immunocompromised hosts on the emergence of immune escape variants in the presence and absence of epistasis. Conclusions: We show that when the pathogen does not have to cross a fitness valley for immune escape to occur (no epistasis), immunocompromised individuals have no qualitative effect on antigenic evolution (although they may accelerate immune escape if within-host evolutionary dynamics are faster in immunocompromised individuals). But if a fitness valley exists between immune escape variants at the between-host level (epistasis), then persistent infections of immunocompromised individuals allow mutations to accumulate, therefore, facilitating rather than simply speeding up antigenic evolution. Our results suggest that better genomic surveillance of infected immunocompromised individuals and better global health equality, including improving access to vaccines and treatments for individuals who are immunocompromised (especially in lower- and middle-income countries), may be crucial to preventing the emergence of future immune escape variants of SARS-CoV-2. [ABSTRACT FROM AUTHOR]

While the negative effects that pathogens have on their hosts are well-documented in humans and agricultural systems, direct evidence of pathogen-driven impacts in wild host populations is scarce and mixed. Here, to determine how the strength of pathogen-imposed selection depends on spatial structure, we analyze growth rates across approximately 4000 host populations of a perennial plant through time coupled with data on pathogen presence-absence. We find that infection decreases growth more in the isolated than well-connected host populations. Our inoculation study reveals isolated populations to be highly susceptible to disease while connected host populations support the highest levels of resistance diversity, regardless of their disease history. A spatial eco-evolutionary model predicts that non-linearity in the costs to resistance may be critical in determining this pattern. Overall, evolutionary feedbacks define the ecological impacts of disease in spatially structured systems with host gene flow being more important than disease history in determining the outcome. The ecological and evolutionary impacts of disease vary in spatially structured populations. Here, the authors study ~4000 populations of Plantago lanceolata and find that resistance evolution depends on both disease history and population structure, with isolated populations more susceptible to fungal disease. [ABSTRACT FROM AUTHOR]

Social contacts can facilitate the spread of both survival‐related information and infectious diseases, but little is known about how these processes combine to shape host and parasite evolution. Here, we use a theoretical model that captures both infection and information transmission processes to investigate how host sociality (contact effort) and parasite virulence (disease‐associated mortality rate) (co)evolve. We show that selection for sociality (and in turn, virulence) depends on both the intrinsic costs and benefits of social information and infection as well as their relative prevalence in the population. Specifically, greater sociality and lower virulence evolve when the risk of infection is either low or high and social information is neither very common nor too rare. Lower sociality and higher virulence evolve when the prevalence patterns are reversed. When infection and social information are both at moderate levels in the population, the direction of selection depends on the relative costs and benefits of being infected or informed. We also show that sociality varies inversely with virulence, and that parasites may be unable to prevent runaway selection for higher contact efforts. Together, these findings provide new insights for our understanding of group living and how apparently opposing ecological processes can influence the evolution of sociality and virulence in a range of ways. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The classical view of sex ratio evolution, popularized by R. A. Fisher, is that the sex ratio at birth should be equal when males and females require the same level of parental investment. Thus, although differences in mortality between the sexes during parental investment will cause deviations from an equal sex ratio at birth, differential mortality after parental investment should have no effect. However, a recent theoretical model appears to contradict this view, suggesting that differential mortality after the period of parental investment does cause deviations from an equal sex ratio at birth. Moreover, the life stage at which mortality differs (juvenile vs. adult) is predicted to cause contrasting effects on sex ratio evolution. These results are in stark contrast with Fisher's hypothesis. Here, we resolve this disparity by analyzing a stage‐ and sex‐ structured model of population dynamics. We find that selection always drives the population to an equal sex ratio at birth regardless of differential mortality effects after parental investment, thus confirming Fisher's hypothesis. The disparity appears to be due to incorrect accounting of mutant‐resident unions, which we avoid by considering separate union classes for different types of mutant‐resident unions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

J. B. S. Haldane is widely quoted to have quipped that the Creator, if one exists, has an inordinate fondness for beetles. Although Coleoptera may not be the most speciose order once Hymenopteran diversity is fully accounted for, as a whole the very clear differences in species diversity among taxa require an explanation. Here we use stochastic simulations to show that dispersal has eco‐evolutionary effects that predict taxa to become particularly species‐rich when dispersal is neither too low nor too high. Our model combines recent advances in understanding coexistence in niche space with previously verbally expressed ideas, where too low dispersal imposes biogeographic constraints that prevent a lineage from finding new areas to colonize (reducing opportunities for speciation), while too high dispersal impedes population divergence, leading to few but widely distributed species. We show that this logic holds for species richness and is robust to a variety of model assumptions, but peak diversification rate is instead predicted to increase with dispersal. Our work unifies findings of increasing and decreasing effects of dispersal rate on speciation, and explains why taxa with moderate dispersal abilities have the best prospects for high global species richness. [ABSTRACT FROM AUTHOR]

Sexually transmitted infections (STIs) are predicted to play an important role in the evolution of host mating strategies, and vice versa, yet our understanding of host‐STI coevolution is limited. Previous theoretical work has shown mate choice can evolve to prevent runaway STI virulence evolution in chronic, sterilizing infections. Here, I generalize this theory to examine how a broader range of life‐history traits influence coevolution; specifically, how host preferences for healthy mates and STI virulence coevolve when infections are acute and can cause mortality or sterility, and hosts do not form long‐term sexual partnerships. I show that mate choice reduces both mortality and sterility virulence, with qualitatively different outcomes depending on the mode of virulence, costs associated with mate choice, recovery rates, and host lifespan. For example, fluctuating selection—a key finding in previous work—is most likely when hosts have moderate lifespans, STIs cause sterility and long infections, and costs of mate choice are low. The results reveal new insights into the coevolution of mate choice and STI virulence as different life‐history traits vary, providing increased support for parasite‐mediated sexual selection as a potential driver of host mate choice, and mate choice as a constraint on the evolution of virulence. [ABSTRACT FROM AUTHOR]

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 lifehistory 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 epidemiologicaldemographic structure of the population can lead to the evolution of elevated juvenile susceptibility. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Understanding how parasites adapt to changes in host resistance is crucial to evolutionary epidemiology. Experimental studies have demonstrated that parasites are more capable of adapting to gradual, rather than sudden changes in host phenotype, as the latter may require multiple mutations that are unlikely to arise simultaneously. A key, but as yet unexplored factor is precisely how interactions between mutations (epistasis) affect parasite evolution. Here, we investigate this phenomenon in the context of infectivity range, where parasites may experience selection to infect broader sets of genotypes. When epistasis is strongly positive, we find that parasites are unlikely to evolve broader infectivity ranges if hosts exhibit sudden, rather than gradual changes in phenotype, in close agreement with empirical observations. This is due to a low probability of fixing multiple mutations that individually confer no immediate advantage. When epistasis is weaker, parasites are more likely to evolve broader infectivity ranges if hosts make sudden changes in phenotype, which can be explained by a balance between mutation supply and selection. Thus, we demonstrate that both the rate of phenotypic change in hosts and the form of epistasis between mutations in parasites are crucial in shaping the evolution of infectivity range. [ABSTRACT FROM AUTHOR]

Antagonistic coevolution between hosts and parasites is thought to drive a range of biological phenomena including the maintenance of sexual reproduction. Of particular interest are conditions that produce persistent fluctuations in the frequencies of genes governing host-parasite specificity (coevolutionary cycling), as sex may be more beneficial than asexual reproduction in a constantly changing environment. Although many studies have shown that coevolutionary cycling can lead to the maintenance of sex, the effects of ecological feedbacks on the persistence of these fluctuations in gene frequencies are not well understood. Here, we use a simple deterministic model that incorporates ecological feedbacks to explore how parasitic reductions in host fecundity affect the maintenance of coevolutionary cycling. We demonstrate that parasitic castration is inherently destabilizing and may be necessary for coevolutionary cycling to persist indefinitely, but also reduces the likelihood that sexually reproducing individuals will find a fertile partner, which may select against sex. These findings suggest that castrators can play an important role in shaping host evolution and are likely to be good targets for observing fluctuations in gene frequencies that govern specificity in host-parasite interactions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Sexually transmitted infections (STIs) are often associated with chronic diseases and can have severe impacts on host reproductive success. For airborne or socially transmitted pathogens, patterns of contact by which the infection spreads tend to be dispersed and each contact may be of very short duration. By contrast, the transmission pathways for STIs are usually characterized by repeated contacts with a small subset of the population. Here we review how heterogeneity in sexual contact patterns can influence epidemiological dynamics, and present a simple model of polygyny/polyandry to illustrate the impact of biased mating systems on disease incidence and pathogen virulence. [ABSTRACT FROM AUTHOR]