Evolutionary branching and evolutionarily stable coexistence of predator species: Critical function analysis

On the ecological timescale, two predator species with linear functional responses can stably coexist on two competing prey species. In this paper, with the methods of adaptive dynamics and critical function analysis, we investigate under what conditions such a coexistence is also evolutionarily stable, and whether the two predator species may evolve from a single ancestor via evolutionary branching. We assume that predator strategies differ in capture rates and a predator with a high capture rate for one prey has a low capture rate for the other and vice versa. First, by using the method of critical function analysis, we identify the general properties of trade-off functions that allow for evolutionary branching in the predator strategy. It is found that if the trade-off curve is weakly convex in the vicinity of the singular strategy and the interspecific prey competition is not strong, then this singular strategy is an evolutionary branching point, near which the resident and mutant predator populations can coexist and diverge in their strategies. Second, we find that after branching has occurred in the predator phenotype, if the trade-off curve is globally convex, the predator population will eventually branch into two extreme specialists, each completely specializing on a particular prey species. However, in the case of smoothed step function-like trade-off, an interior dimorphic singular coalition becomes possible, the predator population will eventually evolve into two generalist species, each feeding on both of the two prey species. The algebraical analysis reveals that an evolutionarily stable dimorphism will always be attractive and that no further branching is possible under this model.     

Evolutionary branching and long-term coexistence of cycling predators: critical function analysis

It is well known that two predators with different functional responses can coexist on one prey when the system exhibits nonequilibrium dynamics. In this paper, we investigate under which conditions such coexistence is evolutionarily stable, and whether the two predators may evolve from a single ancestor via evolutionary branching. We assume that predator strategies differ in handling time, and hence in the shape of their Holling type II functional response. Longer handling times are costly in terms of lost foraging time, but allow the predator to extract more nutrients from the prey and therefore to produce more offspring per consumed prey. In the analysis, we apply a new method to accommodate arbitrary trade-off functions between handling time and offspring production. Contrary to previous results obtained assuming a particular trade-off [Kisdi, E. and Liu, S., 2006. J. Evol. Biol. 19, 49-58], we find that evolutionary branching of handling time is possible, although it does not appear to be very likely and can be excluded for a class of trade-offs. Evolutionarily stable coexistence of two predators occurs under less restrictive conditions, which are always satisfied when the trade-off function has two strongly concave parts connected by a convex piece.     

Adaptive dynamics of Lotka-Volterra systems with trade-offs: the role of interspecific parameter dependence in branching

We determine the adaptive dynamics of a general Lotka-Volterra system containing an intraspecific parameter dependency--in the form of an explicit functional trade-off between evolving parameters--and interspecific parameter dependencies--arising from modelling species interactions. We develop expressions for the fitness of a mutant strategy in a multi-species resident environment, the position of the singular strategy in such systems and the non-mixed second-order partial derivatives of the mutant fitness. These expressions can be used to determine the evolutionary behaviour of the system. The type of behaviour expected depends on the curvature of the trade-off function and can be interpreted in a biologically intuitive manner using the rate of acceleration/deceleration of the costs implicit in the trade-off function. We show that for evolutionary branching to occur we require that one (or both) of the traded-off parameters includes an interspecific parameter dependency and that the trade-off function has weakly accelerating costs. This could have important implications for understanding the type of mechanisms that cause speciation. The general theory is motivated by using adaptive dynamics to examine evolution in a predator-prey system. The applicability of the general theory as a tool for examining specific systems is highlighted by calculating the evolutionary behaviour in a three species (prey-predator-predator) system.     

Adaptive evolution of foraging-related traits in a predator-prey community

In this paper, with the method of adaptive dynamics and geometric technique, we investigate the adaptive evolution of foraging-related phenotypic traits in a predator-prey community with trade-off structure. Specialization on one prey type is assumed to go at the expense of specialization on another. First, we identify the ecological and evolutionary conditions that allow for evolutionary branching in predator phenotype. Generally, if there is a small switching cost near the singular strategy, then this singular strategy is an evolutionary branching point, in which predator population will change from monomorphism to dimorphism. Second, we find that if the trade-off curve is globally convex, predator population eventually branches into two extreme specialists, each completely specializing on a particular prey species. However, if the trade-off curve is concave-convex-concave, after branching in predator phenotype, the two predator species will evolve to an evolutionarily stable dimorphism at which they can continue to coexist. The analysis reveals that an attractive dimorphism will always be evolutionarily stable and that no further branching is possible under this model.     

Spatially structured superinfection and the evolution of disease virulence

When pathogen strains differing in virulence compete for hosts, spatial structuring of disease transmission can govern both evolved levels of virulence and patterns in strain coexistence. We develop a spatially detailed model of superinfection, a form of contest competition between pathogen strains; the probability of superinfection depends explicitly on the difference in levels of virulence. We apply methods of adaptive dynamics to address the interplay of spatial dynamics and evolution. The mean-field approximation predicts evolution to criticality; any small increase in virulence capable of dynamical persistence is favored. Both pair approximation and simulation of the detailed model indicate that spatial structure constrains disease virulence. Increased spatial clustering reduces the maximal virulence capable of single-strain persistence and, more importantly, reduces the convergent-stable virulence level under strain competition. The spatially detailed model predicts that increasing the probability of superinfection, for given difference in virulence, increases the likelihood of between-strain coexistence. When strains differing in virulence can coexist ecologically, our results may suggest policies for managing diseases with localized transmission. Comparing equilibrium densities from the pair approximation, we find that introducing a more virulent strain into a host population infected by a less virulent strain can sometimes reduce total host mortality and increase global host density.     

Emergence of asymmetry in evolution

We investigate symmetry-breaking bifurcation patterns in evolution in the framework of adaptive dynamics (AD). We define weak and strong symmetry. The former applies for populations where only the simultaneous reflection of all individuals is an invariant transformation. The symmetry is strong in populations where reflection of some, but not all, individuals leaves the situation unchanged. We show that in case of weak symmetry evolutionary branching can lead to the emergence of two asymmetric variants, which are mirror images of each other, and the loss of the symmetric ancestor. We also show that in case of strong symmetry, evolutionary branching can occur into a symmetric and an asymmetric variant, both of which survive. The latter, asymmetric branching differs from the generic branching patterns of AD, which is always symmetric. We discuss biological examples for weak and strong symmetries and a specific model producing the new kind of branching.     

Adaptive evolution of anti-predator ability promotes the diversity of prey species: critical function analysis

In this paper, with the method of adaptive dynamics and critical function analysis, we investigate the evolutionary diversification of prey species. We assume that prey species can evolve safer strategies such that it can reduce the predation risk, but this has a cost in terms of its reproduction. First, by using the method of critical function analysis, we identify the general properties of trade-off functions that allow for continuously stable strategy and evolutionary branching in the prey strategy. It is found that if the trade-off curve is globally concave, then the evolutionarily singular strategy is continuously stable. However, if the trade-off curve is concave-convex-concave and the prey's sensitivity to crowding is not strong, then the evolutionarily singular strategy may be an evolutionary branching point, near which the resident and mutant prey can coexist and diverge in their strategies. Second, we find that after branching has occurred in the prey strategy, if the trade-off curve is concave-convex-concave, the prey population will eventually evolve into two different types, which can coexist on the long-term evolutionary timescale. The algebraical analysis reveals that an attractive dimorphism will always be evolutionarily stable and that no further branching is possible for the concave-convex-concave trade-off relationship.     

The evolution of phenotypic traits in a predator-prey system subject to Allee effect

This paper considers the evolution of phenotypic traits in a community comprising the populations of predators and prey subject to Allee effect. The evolutionary model is constructed from a deterministic approximation of the stochastic process of mutation and selection. Firstly, we investigate the ecological and evolutionary conditions that allow for continuously stable strategy and evolutionary branching. We find that the strong Allee effect of prey facilitates the formation of continuously stable strategy in the case that prey population undergoes evolutionary branching if the Allee effect of prey is not strong enough. Secondly, we show that evolutionary suicide is impossible for prey population when the intraspecific competition of prey is symmetric about the origin. However, evolutionary suicide can occur deterministically on prey population if prey individuals undergo strong asymmetric competition and are subject to Allee effect. Thirdly, we show that the evolutionary model with symmetric interactions admits a stable limit cycle if the Allee effect of prey is weak. Evolutionary cycle is a likely outcome of the process, which depends on the strength of Allee effect and the mutation rates of predators and prey.     

Dispersal and the evolution of specialisation in a two-habitat type metapopulation

Metapopulation theory for the evolution of specialisation is virtually absent. In this article, therefore, we study a metapopulation model for consumers with a fitness trade-off between two habitats. We focus on effects of habitat abundance, dispersal rate and trade-off strength on the evolution of specialisation under two types of trade-off. Adaptation affects either the intrinsic growth rates r or the carrying capacities K. Depending on dispersal rate and trade-off strength, evolution can result in one generalist, one specialist or two specialist types. Higher dispersal rate and a weaker trade-off favour the evolution of a generalist, for both trade-off structures. However, we also find differences between the two trade-off structures. Our results are qualitatively similar to analyses of two-patch models, suggesting that insights from such simpler models can be extrapolated to metapopulation models. Additional effects, however, occur because in classical metapopulations patch lifetime depends on extinction rate. Counterintuitively, this favours the evolution of specialisation when the trade-off affects r.     

A model for the evolutionary dynamics of cross-feeding polymorphisms in microorganisms

 Understanding mechanisms of evolutionary diversification is central to evolutionary biology. Microbes constitute promising model systems for observing processes of diversification directly in the laboratory. One of the main existing paradigms for microbial diversification is the evolution of cross-feeding polymorphisms, in which a strain specializing on a primary resource coexists with a cross-feeding strain that specializes on a waste product resulting from consumption of the primary resource. Here I propose a theoretical model for the evolutionary dynamics through which cross-feeding polymorphisms can gradually emerge from a single ancestral strain. The model is based on the framework of adaptive dynamics, which has proved to be very useful for studying adaptive processes of divergence under sympatric conditions. In particular, the phenomenon of evolutionary branching serves as a general paradigm for diversification. I show that evolutionary branching naturally occurs in evolutionary models of cross-feeding if (1) there is a trade-off between uptake efficiencies on the primary and secondary resources, and (2) this trade-off has positive curvature. The model also suggests that the evolution of cross-feeding should be more likely in chemostat cultures than in serial batch cultures, which conforms with empirical observations. Overall, the model provides a theoretical metaphor for the evolution of cross-feeding polymorphisms. Received: February 19, 2002 / Accepted: May 8, 2002     

Studies on a murine model for evaluation of virulence of Streptococcus suis capsular type 2 isolates

Five different parameters, time of incubation of the culture, type of culture medium, inoculum, strain of inbred mice, and age of mice, were tested using the LD50 technique to standardize a murine model for the evaluation of the virulence of Streptococcus suis capsular type 2 isolates. A model using 28 day-old mice belonging to CF1 strain appeared to give the best results. The inoculum size was the parameter most influencing the 50% lethal dose obtained with mice. Inoculation with 1-ml volume of a bacterial suspension instead of 0.1 or 0.5 ml decreased the LD50. The standardized model was used to evaluate the virulence of some isolates of known pathogenicity for pigs. The minimum lethal dose was used in the model and it appeared that the virulence of Streptococcus suis capsular type 2 isolates can be measured from highly virulent to totally avirulent.     

Evolutionary escape from the prisoner's dilemma

The classic prisoner's dilemma model of game theory is modified by introducing occasional variations on the options available to players. Mutation and selection of game options reliably change the game matrix, gradually, from a prisoner's dilemma game into a byproduct mutualism one, in which cooperation is stable, and "temptation to defect" is replaced by temptation to cooperate. This result suggests that when there are many different potential ways of interacting, exploring those possibilities may make escape from prisoner's dilemmas a common outcome in the world. A consequence is that persistent prisoner's dilemma structures may be less common than one might otherwise expect.     

Superinfections can induce evolutionarily stable coexistence of pathogens

Parasites reproduce and are subject to natural selection at several different, but intertwined, levels. In the recent paper, Gilchrist and Coombs (Theor. Popul. Biol. 69:145–153, 2006) relate the between-host transmission in the context of an SI model to the dynamics within a host. They demonstrate that within-host selection may lead to an outcome that differs from the outcome of selection at the host population level. In this paper we combine the two levels of reproduction by considering the possibility of superinfection and study the evolution of the pathogen’s within-host reproduction rate p. We introduce a superinfection function φ = φ(p,q), giving the probability with which pathogens with trait q, upon transmission to a host that is already infected by pathogens with trait p, “take over” the host. We consider three cases according to whether the function q → φ(p,q) (i) has a discontinuity, (ii) is continuous, but not differentiable, or (iii) is differentiable in q = p. We find that in case (i) the within-host selection dominates in the sense that the outcome of evolution at the host population level coincides with the outcome of evolution in a single infected host. In case (iii), it is the transmission to susceptible hosts that dominates the evolution to the extent that the singular strategies are the same as when the possibility of superinfections is ignored. In the biologically most relevant case (ii), both forms of reproduction contribute to the value of a singular trait. We show that when φ is derived from a branching process variant of the submodel for the within-host interaction of pathogens and target cells, the superinfection functions fall under case (ii). We furthermore demonstrate that the superinfection model allows for steady coexistence of pathogen traits at the host population level, both on the ecological, as well as on the evolutionary time scale.      

Actin filament branching and protrusion velocity in a simple 1D model of a motile cell

We formulate and analyse a 1D model for the spatial distribution of actin density at the leading edge of a motile cell. The model incorporates nucleation, capping, growth and decay of actin filaments, as well as retrograde flow of the actin meshwork and known parameter values based on the literature. Using a simplified geometry, and reasonable assumptions about the biochemical processes, we derive PDEs for the density of actin filaments and their tips. Analytic travelling wave solutions are used to predict how the speed of the cell depends on rates of nucleation, capping, polymerization and membrane resistance. Analysis and simulations agree with experimental profiles for measured actin distributions. Extended versions of the model are studied numerically. We find that our model produces stable travelling wave solutions with reasonable cell speeds. Increasing the rate of nucleation of filaments (by the actin related protein Arp2/3) or the rate of actin polymerization leads to faster cell speed, whereas increasing the rate of capping or the membrane resistance reduces cell speed. We consider several variants of nucleation (spontaneous, tip, and side branching) and find best agreement with experimentally measured spatial profiles of filament and tip density in the side branching case.     

Evolution of cell motility in an individual-based model of tumour growth

Tumour invasion is driven by proliferation and importantly migration into the surrounding tissue. Cancer cell motility is also critical in the formation of metastases and is therefore a fundamental issue in cancer research. In this paper we investigate the emergence of cancer cell motility in an evolving tumour population using an individual-based modelling approach. In this model of tumour growth each cell is equipped with a micro-environment response network that determines the behaviour or phenotype of the cell based on the local environment. The response network is modelled using a feed-forward neural network, which is subject to mutations when the cells divide. With this model we have investigated the impact of the micro-environment on the emergence of a motile invasive phenotype. The results show that when a motile phenotype emerges the dynamics of the model are radically changed and we observe faster growing tumours exhibiting diffuse morphologies. Further we observe that the emergence of a motile subclone can occur in a wide range of micro-environmental growth conditions. Iterated simulations showed that in identical growth conditions the evolutionary dynamics either converge to a proliferating or migratory phenotype, which suggests that the introduction of cell motility into the model changes the shape of fitness landscape on which the cancer cell population evolves and that it now contains several local maxima. This could have important implications for cancer treatments which focus on the gene level, as our results show that several distinct genotypes and critically distinct phenotypes can emerge and become dominant in the same micro-environment.     

Evolutionary genomics of C4 photosynthesis in grasses requires a large species sampling

Recent advances in genomics open promising opportunities to investigate adaptive trait evolution at the molecular level. However, the accuracy of comparative genomic studies strongly relies on the taxonomic coverage, which can be insufficient when based solely on a few completely sequenced genomes. In particular, when distantly-related genomes are compared, orthology of some genes can be misidentified and long branches of the phylogenetic reconstructions make inappropriate positive selection tests, as recently exemplified with investigations on the evolution of the C₄ photosynthetic pathway in grasses. Complementary studies addressing the diversification of multigene families in a broad taxonomic sample can help circumvent these issues.     

裸子植物psbA基因分子进化式样的研究

为阐明裸子植物对陆生生境生态响应的分子机制,以新近的裸子植物分类系统为指导,基于psb A基因编码全序列对4亚纲53种代表植物进行分子进化分析。首先,依据"放松分子钟"模型重建裸子植物在时间尺度下系统发育关系;其次,采用6个模型(MEC/JTT、MEC/cp REV、M5、M7、M8、M8a)估测氨基酸位点ω值,并对各模型结果进行统计检测;随后,利用Bootstrap方法检PSBA蛋白内部氨基酸位点的共进化动态。结果表明,系统树提示的物种分化历程支持前期分类结果;光合系统反应中心核心PSBA蛋白有3个氨基酸位点(13、19和243)曾经受正选择压力;PSBA蛋白内部有多对氨基酸位点间构成了共进化网络。因此,psb A基因编码序列具有作为描绘裸子植物系统发育关系标记的潜力,PSBA蛋白部分位点经历了适应性进化,通过位点间共进化网络协同作用方式辅助裸子植物响应陆生生境。     

Evolutionary syndromes linking dispersal and mating system: the effect of autocorrelation in pollination conditions

Self-fertilization is classically thought to be associated with propagule dispersal because self-fertilization is a boon to colonizers entering environments devoid of pollinators or potential mates. Yet, it has been theoretically shown that random fluctuations in pollination conditions select for the opposite association of traits. In nature, however, various ecological factors may deviate from random variations, and thus create temporal correlation in pollination conditions. Here, we develop a model to assess the effects of pollination condition autocorrelation on the joint evolution of dispersal and self-fertilization. Basically, two syndromes are found: dispersing outcrossers and nondispersing (partial) selfers. Importantly, (1) selfers are never associated with dispersal, whereas complete outcrossers are, and (2) the disperser/outcrosser syndrome is favored (resp. disfavored) by negative (resp. positive) autocorrelation in pollination conditions. Our results suggest that observed dispersal/mating system syndromes may depend heavily on the regime of pollination condition fluctuations. We also point out potential negative evolutionary effects of anthropic management of the environment on outcrossing species.     

On the evolution of specialization with a mechanistic underpinning in structured metapopulations

We analyze the evolution of specialization in resource utilization in a discrete-time metapopulation model using the adaptive dynamics approach. The local dynamics in the metapopulation are based on the Beverton-Holt model with mechanistic underpinnings. The consumer faces a trade-off in the abilities to consume two resources that are spatially heterogeneously distributed to patches that are prone to local catastrophes. We explore the factors favoring the spread of generalist or specialist strategies. Increasing fecundity or decreasing catastrophe probability favors the spread of the generalist strategy and increasing environmental heterogeneity enlarges the parameter domain where the evolutionary branching is possible. When there are no catastrophes, increasing emigration diminishes the parameter domain where the evolutionary branching may occur. Otherwise, the effect of emigration on evolutionary dynamics is non-monotonous: both small and large values of emigration probability favor the spread of the specialist strategies whereas the parameter domain where evolutionary branching may occur is largest when the emigration probability has intermediate values. We compare how different forms of spatial heterogeneity and different models of local growth affect the evolutionary dynamics. We show that even small changes in the resource dynamics may have outstanding evolutionary effects to the consumers.     

The influence of immune cross-reaction on phase structure in resonant solutions of a multi-strain seasonal SIR model

Resonance in seasonally forced SIR epidemiological models may lead to stable solutions in which the epidemic period is an integer multiple of the forcing period. We examine the influence of immune cross-protection and cross-enhancement on the epidemic phase relationship of resonance solutions in an annually forced two-strain SIR model. Solutions with epidemics of the two strains in-phase commonly occur for wide ranges of cross-reaction intensity. Solutions with epidemics out-of-phase are less common and limited to narrow ranges of cross-reaction intensity. This is broadly as predicted by the two natural periods of the system. The natural period corresponding to out-of-phase solutions is sensitive to changes in the cross-reaction parameter but the natural period corresponding to in-phase solutions is constant. Bifurcation analysis indicates that the stability of in-phase orbits is controlled by pitchfork and period doubling bifurcations while out-of-phase orbits may also be influenced by Andronov-Hopf bifurcations. In order to develop an intuitive understanding of the epidemiological factors governing the occurrence of different solutions we consider how the susceptible, infected and removed components of the system must interact to form a stable solution. This shows that the impact of cross-reaction is moderated by in-phase structures but amplified by out-of-phase structures. Although the average infection rate over long time periods is not affected by phase structure, this analysis indicates that in-phase epidemic patterns are likely to be more consistent and thus allow more effective health care management.