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En raison de la pandemie de la maladie a coronavirus 2019 (COVID-19), les gouvernements partout au monde ont du adopter de strictes mesures d'eloignement physique pour reduire la propagation du [...]

The coronavirus disease 2019 (COVID-19) pandemic has required governments around the world to institute severe physical-distancing measures to reduce the spread of the virus in order to protect public health [...]

Why is it that some parasites cause high levels of host damage (i.e. virulence) whereas others are relatively benign? There are now numerous reviews of virulence evolution in the literature but it is nevertheless still difficult to find a comprehensive treatment of the theory and data on the subject that is easily accessible to non-specialists. Here we attempt to do so by distilling the vast theoretical literature on the topic into a set of relatively few robust predictions. We then provide a comprehensive assessment of the available empirical literature that tests these predictions. Our results show that there have been some notable successes in integrating theory and data but also that theory and empiricism in this field do not ‘speak’ to each other very well. We offer a few suggestions for how the connection between the two might be improved. [ABSTRACT FROM AUTHOR]

The process of evolutionary diversification unfolds in a vast genotypic space of potential outcomes. During the past century, there have been remarkable advances in the development of theory for this diversification, and the theory's success rests, in part, on the scope of its applicability. A great deal of this theory focuses on a relatively small subset of the space of potential genotypes, chosen largely based on historical or contemporary patterns, and then predicts the evolutionary dynamics within this pre-defined set. To what extent can such an approach be pushed to a broader perspective that accounts for the potential open-endedness of evolutionary diversification? There have been a number of significant theoretical developments along these lines but the question of how far such theory can be pushed has not been addressed. Here a theorem is proven demonstrating that, because of the digital nature of inheritance, there are inherent limits on the kinds of questions that can be answered using such an approach. In particular, even in extremely simple evolutionary systems, a complete theory accounting for the potential open-endedness of evolution is unattainable unless evolution is progressive. The theorem is closely related to Gödel's incompleteness theorem, and to the halting problem from computability theory.

Despite much debate and numerous studies, the question of how to most effectively administer antiviral treatment during an influenza pandemic is still unanswered. We present some basic models, coupled with simple geometric arguments, to provide insight into this topic. Specifically, we address the question of how best to administer treatment to minimize the outbreak size. Furthermore we consider how a limited supply of drugs and the occurrence of de novo resistance can affect this solution. INSETS: Box A: Geometric Interpretation of Result 1;Box B: Geometric Interpretation of Result 2. [ABSTRACT FROM AUTHOR]

Evolutionary invasion analysis is a powerful technique for modelling in evolutionary biology. The general approach is to derive an expression for the growth rate of a mutant allele encoding some novel phenotype, and then to use this expression to predict long-term evolutionary outcomes. Mathematically, such ‘invasion fitness’ expressions are most often derived using standard linear stability analyses from dynamical systems theory. Interestingly, there is a mathematically equivalent approach to such stability analyses that is often employed in mathematical epidemiology, and that is based on so-called ‘next-generation’ matrices. Although this next-generation matrix approach has sometimes also been used in evolutionary invasion analyses, it is not yet common in this area despite the fact that it can sometimes greatly simplify calculations. The aim of this article is to bring the approach to a wider evolutionary audience in two ways. First, we review the next-generation matrix approach and provide a novel, and easily intuited, interpretation of how this approach relates to more standard techniques. Second, we illustrate next-generation methods in evolutionary invasion analysis through a series of informative examples. Although focusing primarily on evolutionary invasion analysis, we provide several insights that apply to biological modelling in general.

Vaccination leads to dramatic perturbations of the environment of parasite populations and this can have both demographic and evolutionary consequences. We present a theoretical framework for modelling the short- and long-term epidemiological and evolutionary consequences of vaccination. This framework integrates previous theoretical studies of vaccine-induced parasite evolution, and it allows one to make some useful qualitative predictions regarding the outcome of the competition between different types of vaccine-favoured variants. It can also be used to make quantitative predictions about the speed of such evolutionary processes. This work may help define the relevant parameters that need to be measured in specific parasite populations in order to evaluate the potential evolutionary consequences of vaccination. In particular, we argue that more work should be done evaluating the nature and magnitude of parasite fitness costs associated with adaptation to vaccinated hosts.

We begin by providing an operational definition of sexual conflict that applies to both inter- and intralocus conflict. Using this definition, we examine a series of simple coevolutionary models to elucidate fruitful approaches for detecting interlocus sexual conflict and resultant sexually antagonistic coevolution. We then use published empirical examples to illustrate the utility of these approaches. Three relevant attributes emerge. First, the dynamics of sexually antagonistic coevolution may obscure the conflict itself. Second, competing models of inter-sexual coevolution may yield similar population patterns near equilibria. Third, a variety of evolutionary forces underlying competing models may be acting simultaneously near equilibria. One main conclusion is that studies of emergent patterns in extant populations (e.g. studies of population and/or female fitness) are unlikely to allow us to distinguish among competing coevolutionary models. Instead, we need more research aimed at identifying the forces of selection acting on shared traits and sexually antagonistic traits. More specifically, we need a greater number of functional studies of female traits as well as studies of the consequences of both male and female traits for female fitness. A mix of selection and manipulative studies on these is likely the most promising route.

The hypothesis that females prefer older males because they have higher mean fitness than younger males has been the centre of recent controversy. These discussions have focused on the success of a female who prefers males of a particular age class when age cues, but not quality cues, are available. Thus, if the distribution of male quality changes with age, such that older males have on average genotypes with higher fitness than younger males, then a female who mates with older males has fitter offspring, which allows the female preference to spread through a genetic correlation. We develop a general model for male display in a species with multiple reproductive bouts that allows us to identify the conditions that promote reliable signalling within an age class. Because males have opportunities for future reproduction, they will reduce their levels of advertising compared with a semelparous species. In addition, because higher–quality males have more future reproduction, they will reduce their advertising more than low–quality males. Thus, the conditions for reliable signalling in a semelparous organism are generally not sufficient to produce reliable signalling in species with multiple reproductive bouts. This result is due to the possibility of future reproduction so that, as individuals age and the opportunities for future reproduction fade, signalling becomes more reliable. This provides a novel rationale for female preference for older mates; older males reveal more information in their sexual displays.

Smallpox causes roughly 20 mortality whereas chickenpox causes less than 0.1. Most ‘verbal’ (i.e. non–mathematical) discussions using a mortality definition of virulence would therefore label smallpox as more virulent. Indeed, the virulence of many diseases is measured using such case mortalities, , or related measures such as expected host lifespan, T, or lethal dose, LDx. But , Tand LDxare only indirectly related to parasite–induced instantaneous mortality rate, α, which is the mortality measure used in much of the theory developed to explain virulence evolution. Here I point out that relatively deadly pathogens can actually have lower values of αthan benign pathogens, demonstrating that αdoes not, by itself, reflect the extent to which a parasite causes host mortality. I present mathematical relationships between αand , Tand LDx, and use these to demonstrate that predictions about virulence evolution can be qualitatively altered depending upon which measure is used as the definition of virulence. Two simple examples are presented to illustrate this point, one of which demonstrates that the well–cited prediction that virulence should evolve to be higher when disease–independent host mortality increases need not hold. This prediction has been made in terms of parasite–induced instantaneous mortality, α, but if virulence is measured using case mortality (or Tor LDx) then this prediction can easily be reversed. Theoretical and empirical researchers must use compatible mortality measures before a productive exchange between the two can take place, and it is suggested that case mortality (or lethal dose) is best suited as a single (mortality) measure of parasite virulence.

A well–known result from the theory of the evolution of virulence is the prediction that the virulence of a pathogen (i.e. the rate of parasite–induced host mortality) always evolves to higher levels when host background mortality rates increase. This prediction, however, is derived from models that assume that host mortality sources combine additively to determine the overall host mortality rate. In this paper, we suggest that such additivity is probably rare for many host–pathogen systems, and explore how the predictions for the evolution of virulence are altered when interactions between host mortality sources are incorporated into the theory. Our results indicate that if mortality–source interactions are sufficiently strong then the evolutionarily stable level of virulence can actually decrease as the background mortality rate increases. Consequently, a detailed mechanistic description of how parasites and other mortality sources combine to cause host mortality is required before reliable predictions about virulence evolution can be made. Moreover, mortality–source interactions make empirical comparisons of the virulence of different parasites a much more subtle issue.

We present two theorems that generalize Pontryagin's maximum principle to the setting of dynamic evolutionary games between genetically related individuals. The two theorems correspond to two types of interactions among individuals: patch-structured populations in which individuals locally “play the field” and pairwise interactions. These generalizations can be used in the same way that Pontryagin's maximum principle is used and they are valid for diploid organisms under a single locus, diallelic genetic model. These generalizations involve an interesting, dynamic version of Hamilton's Rule from inclusive fitness theory. We illustrate how these theoretical results can be applied by modeling the evolution of lifetime resource allocation to growth and reproduction in an annual plant when there is competition for resources among related individuals.

A framework is presented for unifying single locus genetic and game theoretic models of continuous traits under frequency-dependent selection when there are interactions among relatives. This framework serves two purposes. First, it is used to determine how “games between relatives” must be modeled to be genetically valid. There are two commonly employed phenotypic approaches used in this setting, and we demonstrate that, although some of their predictions are always genetically valid, others are invalid in general, and this is true for both haploid asexual and diploid sexual organisms. In particular, we show that both approaches obtain the correct equilibrium and convergence stability conditions, but neither obtains the correct condition for evolutionary stability. Unlike earlier results for discrete trait matrix games (Hines & Maynard Smith, 1979), there is no simple correspondence between phenotypic and genetic predictions, and we provide two examples to illustrate this point. It is possible however, to obtain these earlier results within the present setting by restricting attention to a particular class of fitness functions. These results demonstrate that, even when selection is weak, phenotypic models can fail if fitness is frequency-dependent. The second purpose is to determine when population mean inclusive fitness effect provides an adaptive topography in games between relative. Our results show that the fitness function must have a special form for this to be true, and this form differs between haploid and diploid organisms.

Many biological characters of interest are temporal sequences of decisions. The evolution of such characters is often modelled using dynamic optimization methods such as the maximum principle. A quantity central to these analyses is the ‘Hamiltonian’ function, named after the mathematician William R. Hamilton. On the other hand, evolutionary models in which individuals interact with relatives are usually based on Hamilton's rule, named after the evolutionary biologist William D. Hamilton. In this article we present a generalized maximum principle that includes the effects of interactions among relatives and we show that a time–dependent (dynamic) version of Hamilton's rule holds involving the Hamiltonian. This result brings together the power and generality of both the maximum principle and Hamilton's rule thereby providing a natural framework for understanding the evolution of ‘dynamic’ characters under kin selection.

We conducted an experiment to assess the change in foraging efficiency resulting from diet-induced morphological and behavioural plasticity in a species of freshwater, threespine stickleback (Gasterosteus sp.). Different degrees of morphological and behavioural change were induced using two prey items commonly found in the diet of this species, allowing us to estimate the relative importance of each type of plasticity. The purpose of the experiment was twofold. First, earlier work had suggested that diet variability might be an important factor in the evolution of trophic morphological plasticity in sticklebacks. The present results extend this work by revealing the adaptive significance of morphological plasticity. The current experiment also qualitatively assessed the compatibility of the time scale of morphological change with that of the natural resource variability experienced by this species. The results indicate that diet-induced plasticity improves foraging efficiency continuously for up to 72 days of prey exposure. This is probably due in part to plasticity of the external trophic morphology but our results also suggest a complex interplay between morphology and behaviour. The time scale appears to be matched to that of natural diet variability although it is possible that some traits exhibit non-labile plasticity. Our discussion highlights the important distinction between conditions favouring the evolution of labile versus non-labile plasticity. The second objective of the experiment was to determine the relative importance of morphological and behavioural plasticity. Few studies have attempted to quantify the adaptive significance of morphological plasticity and no study to our knowledge has separated the effects of morphological and behavioural plasticity. Our experiment reveals that both behavioural and morphological plasticity are important and it also suggests a dichotomy between the two: behavioural plasticity predominately affects searching efficiency whereas morphological plasticity predominately affects handling efficiency.

The theory of life-history evolution provides a powerful framework to understand the evolutionary dynamics of pathogens. It assumes, however, that host populations are large and that one can neglect the effects of demographic stochasticity. Here, we expand the theory to account for the effects of finite population size on the evolution of pathogen virulence. We show that demographic stochasticity introduces additional evolutionary forces that can qualitatively affect the dynamics and the evolutionary outcome. We discuss the importance of the shape of the pathogen fitness landscape on the balance between mutation, selection and genetic drift. This analysis reconciles Adaptive Dynamics with population genetics in finite populations and provides a new theoretical toolbox to study life-history evolution in realistic ecological scenarios.

BACKGROUND: The use of neuraminidase inhibitors (oseltamivir and zanamivir) for the treatment of ill individuals has been an important intervention during the 2009 H1N1 pandemic. However, the emergence and spread of drug resistance remains a major concern and, therefore, optimizing antiviral strategies is crucial to retain the long-term effectiveness of these pharmaceutical interventions.METHODS: A dynamic model of disease transmission was developed to investigate optimal scenarios for the use of a secondary drug (eg, zanamivir). Considering both small and large stockpiles, attack rates were projected by simulating the model to identify ‘tipping points’ for switching to zanamivir as resistance to oseltamivir develops.RESULTS: The use of a limited stockpile of zanamivir can substantially reduce the overall attack rate during pandemic outbreaks. For a reasonably large stockpile of zanamivir, it is optimal to delay the use of this drug for a certain amount of time during which oseltamivir is used as the primary drug. For smaller stockpiles, however, earlier use of zanamivir will be most effective in reducing the overall attack rate. Given a limited stockpile of zanamivir (1.8% in the Canadian plan) without replenishment, and assuming that the fraction of ill individuals being treated is maintained below 60%, the results suggest that zanamivir should be dispensed as the primary drug for thresholds of the cumulative number of oseltamivir resistance below 20%.INTERPRETATION: Strategic use of a secondary drug becomes crucial for pandemic mitigation if vaccination and other interventions fail to sufficiently reduce disease transmission in the community. These findings highlight the importance of enhanced surveillance and clinical monitoring for rapid identification of resistance emergence and its population incidence, so that optimal timing for adaptation to the use of drugs can be achieved.