Framework Of Adaptive Dynamics Research Articles

Virulence evolution of Toxoplasma gondii within a multi-host system.

Current research on the virulence evolution of Toxoplasma gondii is mainly conducted via experiments, and studies using mathematical models are still limited. Here, we constructed a complex cycle model of T. gondii in a multi-host system considering multiple transmission routes and cat-mouse interaction. Based on this model, we studied how the virulence of T. gondii evolves with the factors related to transmission routes and the regulation of infection on host behavior under an adaptive dynamics framework. The study shows that all factors that enhance the role of mice favored decreased virulence of T. gondii, except the decay rate of oocysts that led to different evolutionary trajectories under different vertical transmission. The same was true of the environmental infection rate of cats, whose effect was different under different vertical transmission. The effect of the regulation factor on the virulence evolution of T. gondii was the same as that of the inherent predation rate depending on its net effect on direct and vertical transmissions. The global sensitivity analysis on the evolutionary outcome suggests that changing the vertical infection rate and decay rate was most effective in regulating the virulence of T. gondii. Furthermore, the presence of coinfection would favor virulent T. gondii and make evolutionary bifurcation easy to occur. The results reveal that the virulence evolution of T. gondii had a compromise between adapting to different transmission routes and maintaining the cat-mouse interaction thereby leading to different evolutionary scenarios. This highlights the significance of evolutionary ecological feedback to evolution. In addition, the qualitative verification of T. gondii virulence evolution in different areas by the present framework will provide a new perspective for the study of evolution.

Adaptive Evolution Analysis of a Predator-Prey Model With Group Defense

Based on the theoretical framework of adaptive dynamics, the evolution of predator-prey model with functional response of group defense effect on predator handing time was investigated. Firstly, considering the interaction of predator populations with interspecific competition, the evolutionary conditions for a single predator population to split into two populations with different strategies through evolutionary branching were given. Secondly, when the ecological equilibrium of the model is unstable and the system exists a limit cycle, the population could have strong coexistence under large mutation, but this coexistence is evolutionarily unstable. Finally, the conclusions for the model with Holling-Ⅱ type functional response were compared. The results indicate that, with a sufficiently large prey carrying capacity, group defense effects can evolutionarily lead to the extinction of predators.

Study on the virulence evolution of SARS-CoV-2 and the trend of the epidemics of COVID-19.

This is the first attempt to investigate the effects of the factors related to non‐pharmaceutical interventions (NPIs) and the physical condition of the public on virulence evolution of SARS‐CoV‐2 and the trend of the epidemics of COVID‐19 under an adaptive dynamics framework. Qualitative agreement of the prediction on the epidemics of COVID‐19 with the actual situations convinced the rationality of the present model. The study showed that enhancing both NPIs (including public vigilance, quarantine measures, and hospitalization) and the physical condition of the public (including susceptibility and recovery speed) contributed to decreasing the prevalence of COVID‐19 but only increasing public vigilance and decreasing the susceptibility of the public could also reduce the virulence of SARS‐CoV‐2. Therefore, controlling the contact rate and infection rate was the key to control not only the epidemic scale of COVID‐19 but also the extent of its harm. On the other hand, the best way to control the epidemics was to increase the public vigilance and physical condition because both of them could reduce the prevalence and case fatality rate (CFR) of COVID‐19. In addition, the enhancement of quarantine measures and hospitalization could bring the (slight) increase in the CFR of COVID‐19.

Spatial social dilemmas promote diversity

Cooperative investments in social dilemmas can spontaneously diversify into stably coexisting high and low contributors in well-mixed populations. Here we extend the analysis to emerging diversity in (spatially) structured populations. Using pair approximation, we derive analytical expressions for the invasion fitness of rare mutants in structured populations, which then yields a spatial adaptive dynamics framework. This allows us to predict changes arising from population structures in terms of existence and location of singular strategies, as well as their convergence and evolutionary stability as compared to well-mixed populations. Based on spatial adaptive dynamics and extensive individual-based simulations, we find that spatial structure has significant and varied impacts on evolutionary diversification in continuous social dilemmas. More specifically, spatial adaptive dynamics suggests that spontaneous diversification through evolutionary branching is suppressed, but simulations show that spatial dimensions offer new modes of diversification that are driven by an interplay of finite-size mutations and population structures. Even though spatial adaptive dynamics is unable to capture these new modes, they can still be understood based on an invasion analysis. In particular, population structures alter invasion fitness and can open up new regions in trait space where mutants can invade, but that may not be accessible to small mutational steps. Instead, stochastically appearing larger mutations or sequences of smaller mutations in a particular direction are required to bridge regions of unfavorable traits. The net effect is that spatial structure tends to promote diversification, especially when selection is strong.

How does feedback from phage infections influence the evolution of phase variation in Campylobacter?

Campylobacter jejuni (C. jejuni) causes gastroenteritis following the consumption of contaminated poultry meat, resulting in a large health and economic burden worldwide. Phage therapy is a promising technique for eradicating C. jejuni from poultry flocks and chicken carcasses. However, C. jejuni can resist infections by some phages through stochastic, phase-variable ON/OFF switching of the phage receptors mediated by simple sequence repeats (SSR). While selection strength and exposure time influence the evolution of SSR-mediated phase variation (PV), phages offer a more complex evolutionary environment as phage replication depends on having a permissive host organism. Here, we build and explore several continuous culture bacteria-phage computational models, each analysing different phase-variable scenarios calibrated to the experimental SSR rates of C. jejuni loci and replication parameters for the F336 phage. We simulate the evolution of PV rates via the adaptive dynamics framework for varying levels of selective pressures that act on the phage-resistant state. Our results indicate that growth reducing counter-selection on a single PV locus results in the stable maintenance of the phage, while compensatory selection between bacterial states affects the evolutionary stable mutation rates (i.e. very high and very low mutation rates are evolutionarily disadvantageous), whereas, in the absence of either selective pressure the evolution of PV rates results in mutation rates below the basal values. Contrastingly, a biologically-relevant model with two phase-variable loci resulted in phage extinction and locking of the bacteria into a phage-resistant state suggesting that another counter-selective pressure is required, instance, the use of a distinct phage whose receptor is an F336-phage-resistant state. We conclude that a delicate balance between counter-selection and phage-attack can result in both the evolution of phase-variable phage receptors and persistence of PV-receptor-specific phage.

Evolution of Specialization in Heterogeneous Environments: Equilibrium Between Selection, Mutation and Migration.

Adaptation in spatially heterogeneous environments results from the balance between local selection, mutation, and migration. We study the interplay among these different evolutionary forces and demography in a classical two-habitat scenario with asexual reproduction. We develop a new theoretical approach that goes beyond the Adaptive Dynamics framework, and allows us to explore the effect of high mutation rates on the stationary phenotypic distribution. We show that this approach improves the classical Gaussian approximation, and captures accurately the shape of this equilibrium phenotypic distribution in one- and two-population scenarios. We examine the evolutionary equilibrium under general conditions where demography and selection may be nonsymmetric between the two habitats. In particular, we show how migration may increase differentiation in a source-sink scenario. We discuss the implications of these analytic results for the adaptation of organisms with large mutation rates, such as RNA viruses.

MATHEMATICAL MODEL FOR THE EVOLUTIONARY DYNAMIC OF INNOVATION IN CITY PUBLIC TRANSPORT SYSTEMS

In this study, a mathematical model is formulated and studied from the perspective of adaptive dynamics (evolutionary processes), in order to describe the interaction dynamics between two city public transport systems: one of which is established and one of which is innovative. Each system is to be influenced by a characteristic attribute; in this case, the number of assumed passengers per unit it that can transport. The model considers the proportion of users in each transport system, as well as the proportion of the budget destined for their expansion among new users, to be state variables. Model analysis allows for the determination of the conditions under which an innovative transportation system can expand and establish itself in a market which is initially dominated by an established transport system. Through use of the adaptive dynamics framework, the expected long-term behavior of the characteristic attribute which defines transport systems is examined. This long-term study allows for the establishment of the conditions under which certain values of the characteristic attribute configure coexistence, divergence, or both kinds of scenarios. The latter case is reported as the occurrence of evolutionary ramifications, conditions that guarantee the viability of an innovative transport system. Consequently, this phenomenon is referred to as the origin of diversity.

Cyclic prey evolution with cannibalistic predators

We investigate the evolution of timidity in a prey species whose predator has cannibalistic tendencies. The ecological model is derived from individual-level processes, in which the prey seeks refuge after detecting a predator, and the predator cannibalises on the conspecific juveniles. Bifurcation analysis of the model reveals ecological bistability between equilibrium and periodic attractors. Using the framework of adaptive dynamics, we classify ten qualitatively different evolutionary scenarios induced by the ecological bistability. These scenarios include ecological attractor switching through catastrophic bifurcations, which can reverse the direction of evolution. We show that such reversals often result in evolutionary cycling of the level of timidity. In the absence of cannibalism, the model never exhibits ecological bistability nor evolutionary cycling. We conclude that cannibalistic predator behaviour can completely change both the ecological dynamics and the evolution of prey.

Modelling evolution of virulence in populations with a distributed parasite load

Modelling evolution of virulence in host-parasite systems is an actively developing area of research with ever-growing literature. However, most of the existing studies overlook the fact that individuals within an infected population may have a variable infection load, i.e. infected populations are naturally structured with respect to the parasite burden. Empirical data suggests that the mortality and infectiousness of individuals can strongly depend on their infection load; moreover, the shape of distribution of infection load may vary on ecological and evolutionary time scales. Here we show that distributed infection load may have important consequences for the eventual evolution of virulence as compared to a similar model without structuring. Mathematically, we consider an SI model, where the dynamics of the infected subpopulation is described by a von Förster-type equation, in which the infection load plays the role of age. We implement the adaptive dynamics framework to predict evolutionary outcomes in this model. We demonstrate that for simple trade-off functions between virulence, disease transmission and parasite growth rates, multiple evolutionary attractors are possible. Interestingly, unlike in the case of unstructured models, achieving an evolutionary stable strategy becomes possible even for a variation of a single ecological parameter (the parasite growth rate) and keeping the other parameters constant. We conclude that evolution in disease-structured populations is strongly mediated by alterations in the overall shape of the parasite load distribution.

Adaptive dynamics of hematopoietic stem cells and their supporting stroma: a model and mathematical analysis.

We propose a mathematical model to describe the evolution of hematopoietic stem cells (HSCs) and stromal cells in considering the bi-directional interaction between them. Cancerous cells are also taken into account in our model. HSCs are structured by a continuous phenotype characterising the population heterogeneity in a way relevant to the question at stake while stromal cells are structured by another continuous phenotype representing their capacity of support to HSCs. We then analyse the model in the framework of adaptive dynamics. More precisely, we study single Dirac mass steady states, their linear stability and we investigate the role of parameters in the model on the nature of the evolutionary stable distributions (ESDs) such as monomorphism, dimorphism and the uniqueness properties. We also study the dominant phenotypes by an asymptotic approach and we obtain the equation for dominant phenotypes. Numerical simulations are employed to illustrate our analytical results. In particular, we represent the case of the invasion of malignant cells as well as the case of co-existence of cancerous cells and healthy HSCs.

Mathematical model for the evolutionary dynamics of innovation in city public transport systems

In this study, a mathematical model is formulated and studied from the perspective of adaptive dynamics (evolutionary processes), in order to describe the interaction dynamics between two city public transport systems: one of which is established and one of which is innovative. Each system is to be influenced by a characteristic attribute; in this case, the number of assumed passengers per unit it that can transport. The model considers the proportion of users in each transport system, as well as the proportion of the budget destined for their expansion among new users, to be state variables. Model analysis allows for the determination of the conditions under which an innovative transportation system can expand and establish itself in a market which is initially dominated by an established transport system. Through use of the adaptive dynamics framework, the expected long-term behavior of the characteristic attribute which defines transport systems is examined. This long-term study allows for the establishment of the conditions under which certain values of the characteristic attribute configure coexistence, divergence, or both kinds of scenarios. The latter case is reported as the occurrence of evolutionary ramifications, conditions that guarantee the viability of an innovative transport system. Consequently, this phenomenon is referred to as the origin of diversity.

Large-amplitude consumer-resource cycles allow for the evolution of ontogenetic niche shifts in consumer life history

In many size-structured populations individuals change resources during the course of their ontogenetic development. Different resources often require different adaptations to be effectively exploited. This leads to a trade-off between small and large individuals in direct developing species. Specialization on the resource used later in life turns out to be hardly possible in case of equilibrium dynamics. However, size-structured populations often exhibit population cycles. Non-equilibrium dynamics can change evolutionary behavior when compared with equilibrium dynamics. Here, we study the evolution of specialization on a secondary resource that is available only to large individuals, using the framework of adaptive dynamics. We show that in case of small-amplitude cycles, specialization on a secondary resource is hardly possible. Specialization will either decrease the resource intake of large individuals or severely increase competition among small individuals such that they cannot mature. Specialization on a secondary resource is often possible in case the population exhibits large-amplitude cycles. Specialization in that case increases the resource intake of large individuals and therefore prevents starvation. While specialization on a secondary resource increases competition among small individuals, maturation is still possible in case of large-amplitude cycles. We furthermore show that there is ecological bistability where small- and large-amplitude cycles coexist, giving rise to evolutionary bistability.

Dirac-concentrations in an integro-pde model from evolutionary game theory

<p style='text-indent:20px;'>Nonlocal Lotka-Volterra models have the property that solutions concentrate as Dirac masses in the limit of small diffusion. Motivated by the existence of moving Dirac-concentrations in the time-dependent problem, we study the qualitative properties of steady states in the limit of small diffusion. Under different conditions on the growth rate and interaction kernel as motivated by the framework of adaptive dynamics, we will show that as the diffusion rate tends to zero the steady state concentrates (ⅰ) at a single location; (ⅱ) at two locations simultaneously; or (ⅲ) at one of two alternative locations. The third result in particular shows that solutions need not be unique. This marks an important difference of the non-local equation with its local counterpart.

Coevolution of virulence and immunosuppression in multiple infections.

Many components of host-parasite interactions have been shown to affect the way virulence (i.e. parasite-induced harm to the host) evolves. However, coevolution of multiple parasite traits is often neglected. We explore how an immunosuppressive adaptation of parasites affects and coevolves with virulence in multiple infections. Applying the adaptive dynamics framework to epidemiological models with coinfection, we show that immunosuppression is a double-edged sword for the evolution of virulence. On one hand, it amplifies the adaptive benefit of virulence by increasing the abundance of coinfections through epidemiological feedbacks. On the other hand, immunosuppression hinders host recovery, prolonging the duration of infection and elevating the cost of killing the host (as more opportunities for transmission will be forgone if the host dies). The balance between the cost and benefit of immunosuppression varies across different background mortality rates of hosts. In addition, we find that immunosuppression evolution is influenced considerably by the precise trade-off shape determining the effect of immunosuppression on host recovery and susceptibility to further infection. These results demonstrate that the evolution of virulence is shaped by immunosuppression while highlighting that the evolution of immune evasion mechanisms deserves further research attention.

Conditional Reproductive Strategies Under Variable Environmental Conditions

Within the framework of adaptive dynamics we consider the evolution by natural selection of reproductive strategies in which individuals may adjust their reproductive behaviour in response to changing environmental conditions. As a specific example we considered a discrete-time model in which possible fluctuations in the environmental conditions are caused by predator—prey interaction. Our main findings include: (1) Coexistence between two fixed strategies (i.e., strategies that do not adjust to changing environmental conditions) is impossible; there exists a best fixed strategy, which invades and ousts all other fixed strategies. (2) A necessary condition for conditional (adjustable) strategies to evolve is that there are fluctuations in the environmental conditions. Predator—prey interactions may cause such fluctuations and under natural assumptions there exists an optimal conditional strategy which is uninvadable and invades and ousts all other strategies.

The social diversification of fashion

ABSTRACTWe propose a model to investigate the dynamics of fashion traits purely driven by social interactions. We assume that people adapt their style to maximize social success, and we describe the interaction as a repeated group game in which the payoffs reflect the social norms dictated by fashion. On one hand, the tendency to imitate the trendy stereotypes opposed to the tendency to diverge from them to proclaim identity; on the other hand, the exploitation of sex appeal for dating success opposed to the moral principles of the society. These opposing forces promote diversity in fashion traits, as predicted by the modeling framework of adaptive dynamics. Our results link the so-called horizontal dynamics—the primary driver of fashion evolution, compared with the vertical dynamics accounting for interclass and economic drivers—to style variety.

Evolutionary response of plant interaction traits to nutrient enrichment modifies the assembly and structure of antagonistic‐mutualistic communities

Summary Nutrient enrichment is one of the major threats acting on natural communities. The ecological consequences of this disturbance for ecosystems have been largely studied, but we still have little knowledge on its evolutionary effects at community scale. We are interested in the evolutionary consequences of nutrient enrichment for plant interaction traits, embedded in complex communities made of antagonistic and mutualistic interactions. We built a mathematical model of a plant–pollinator–herbivore community confronted by nutrient enrichment. Plants have an interaction trait that is involved in an ecological trade‐off. An increase in this trait, leading to more attractive phenotypes, increases the strength of both interactions with pollinators and herbivores. A lower value of this trait leads to defensive phenotypes with weak interactions with both herbivores and pollinators. We use the framework of adaptive dynamics to study the evolutionary dynamics of this kind of traits and the consequences for community dynamics. We found that evolutionary dynamics of plants modify the assembly of the community along a nutrient enrichment gradient. Due to top‐down controls, herbivory leads to priority effects when only ecological dynamics are considered. Evolution of the plant interaction trait alleviates this priority effect and facilitates community assembly. In the three‐species community, we find that nutrient enrichment leads to more defended phenotypes of plants, at the expense of pollinator attraction. We find that, when the ecological trade‐off between pollination and herbivory is convex, evolution of interaction trait may lead to plant diversification. Two plant phenotypes then coexist in the community, one which is highly attractive and one which is highly defensive. Synthesis. Our results suggest that accounting for evolutionary dynamics will profoundly modify the dynamics of communities in the face of nutrient enrichment. Both community assembly and equilibrium dynamics are altered and enrichment may even lead to diversification. These results advocate for the development of an eco‐evolutionary theory of nutrient enrichment and may be particularly important in agro‐ecosystems relying on fertilization.

Modes of competition and the fitness of evolved populations.

Competition between individuals drives the evolution of whole species. Although the fittest individuals survive the longest and produce the most offspring, in some circumstances the resulting species may not be optimally fit. Here, using theoretical analysis and stochastic simulations of a simple model ecology, we show how the mode of competition can profoundly affect the fitness of evolved species. When individuals compete directly with one another, the adaptive dynamics framework provides accurate predictions for the number and distribution of species, which occupy positions of maximal fitness. By contrast, if competition is mediated by the consumption of a common resource, then demographic noise leads to the stabilization of species with near minimal fitness.

Adaptive dynamics on an environmental gradient that changes over a geological time-scale

The standard adaptive dynamics framework assumes two timescales, i.e. fast population dynamics and slow evolutionary dynamics. We further assume a third timescale, which is even slower than the evolutionary timescale. We call this the geological timescale and we assume that slow climatic change occurs within this timescale. We study the evolution of our model population over this very slow geological timescale with bifurcation plots of the standard adaptive dynamics framework. The bifurcation parameter being varied describes the abiotic environment that changes over the geological timescale. We construct evolutionary trees over the geological timescale and observe both gradual phenotypic evolution and punctuated branching events. We concur with the established notion that branching of a monomorphic population on an environmental gradient only happens when the gradient is not too shallow and not too steep. However, we show that evolution within the habitat can produce polymorphic populations that inhabit steep gradients. What is necessary is that the environmental gradient at some point in time is such that the initial branching of the monomorphic population can occur. We also find that phenotypes adapted to environments in the middle of the existing environmental range are more likely to branch than phenotypes adapted to extreme environments.

Evolution, the loss of diversity and the role of trade-offs

We investigate how the loss of previously evolved diversity in host resistance to disease is dependent on the complexity of the underlying evolutionary trade-off. Working within the adaptive dynamics framework, using graphical tools (pairwise invasion plots, PIPs; trait evolution plots, TEPs) and algebraic analysis we consider polynomial trade-offs of increasing degree. Our focus is on the evolutionary trajectory of the dimorphic population after it has been attracted to an evolutionary branching point. We show that for sufficiently complex trade-offs (here, polynomials of degree three or higher) the resulting invasion boundaries can form closed ‘oval’ areas of invadability and strategy coexistence. If no attracting singular strategies exist within this region, then the population is destined to evolve outside of the region of coexistence, resulting in the loss of one strain. In particular, the loss of diversity in this model always occurs in such a way that the remaining strain is not attracted back to the branching point but to an extreme of the trade-off, meaning the diversity is lost forever. We also show similar results for a non-polynomial but complex trade-off, and for a different eco-evolutionary model. Our work further highlights the importance of trade-offs to evolutionary behaviour.