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.     

Arms races between and within species.

An adaptation in one lineage (e.g. predators) may change the selection pressure on another lineage (e.g. prey), giving rise to a counter-adaptation. If this occurs reciprocally, an unstable runaway escalation or 'arms race' may result. We discuss various factors which might give one side an advantage in an arms race. For example, a lineage under strong selection may out-evolve a weakly selected one (' the life-dinner principle'). We then classify arms races in two independent ways. They may be symmetric or asymmetric, and they may be interspecific or intraspecific. Our example of an asymmetric interspecific arms race is that between brood parasites and their hosts. The arms race concept may help to reduce the mystery of why cuckoo hosts are so good at detecting cuckoo eggs, but so bad at detecting cuckoo nestlings. The evolutionary contest between queen and worker ants over relative parental investment is a good example of an intraspecific asymmetric arms race. Such cases raise special problems because the participants share the same gene pool. Interspecific symmetric arms races are unlikely to be important, because competitors tend to diverge rather than escalate competitive adaptations. Intraspecific symmetric arms races, exemplified by adaptations for male-male competition, may underlie Cope's Rule and even the extinction of lineages. Finally we consider ways in which arms races can end. One lineage may drive the other to extinction; one may reach an optimum, thereby preventing the other from doing so; a particularly interesting possibility, exemplified by flower-bee coevolution, is that both sides may reach a mutual local optimum; lastly, arms races may have no stable and but may cycle continuously. We do not wish necessarily to suggest that all, or even most, evolutionary change results from arms races, but we do suggest that the arms race concept may help to resolve three long-standing questions in evolutionary theory.     

Scramble competitions can rescue endangered species subject to strong Allee effects

In this article, we study population dynamics of a general two-species discrete-time competition model where each species suffers from both strong Allee effects and scramble intra-specific competitions. We focus on how the combinations of the scramble intra-specific and inter-specific competition affect the extinction and coexistence of these two competing species where each species is subject to strong Allee effects. We derive sufficient conditions on the extinction, essential-like extinction and coexistence for such models. One of the most interesting findings is that scramble competitions can promote coexistence of these two species at their high densities. This is supported by the outcome of single species models with strong Allee effects. In addition, we apply theoretical results to a symmetric competition model with strong Allee effects induced by predator saturations where we give a completed study of its possible equilibria and attractors. Numerical simulations are performed to support our results.     

Allee effects can both conserve and create spatial heterogeneity in population densities

In order to determine conditions which allow the Allee effect (caused by biparental reproduction) to conserve and create spatial heterogeneity in population densities, we studied a deterministic model of a symmetric two-patch metapopulation. We proved that under certain conditions there exist stable equilibria with unequal population densities in the two patches, a situation which can be interpreted as conserved heterogeneity. Furthermore, the Allee effect can lead to instability of the equilibrium with equal population densities if some degree of competition is assumed to occur between the subpopulations (non-local competition). This indicates the potential of the Allee effect to create spatial heterogeneity. Neither of these effects appear under biologically realistic parameter values in a model where uniparental reproduction is assumed. We proved that both the between-patch migration intensity and the degree of non-local competition are decisive in determining boundaries between these types of behaviour of the spatial system with Allee effect. Therefore, we propose that the Allee effect, migration intensity, and non-local competition should be considered jointly in studies focusing on problems like pattern formation in space and invasions of spreading species.     

On evolution under asymmetric competition

The evolutionary consequences of asymmetric competition between species are poorly understood in comparison with symmetric competition. A model for evolution of body size under asymmetric competition within and between species is described. The model links processes operating at the scale of the individual to that of macroscopic evolution through a stochastic mutation–selection process. Phase portraits of evolution in a phenotype space characteristically show character convergence and parallel character shifts, with character divergence being relatively uncommon. The asymptotic states of evolution depend very much on the properties of asymmetric competition. Given relatively weak asymmetries between species, a single equilibrium point exists; this is a local attractor, and its position is determined by the intra- and interspecific asymmetries. When the asymmetries are made stronger, several fixed points may come about, creating further equilibrium points which are local attractors. It is also possible for periodic attractors to occur; such attractors comprise Red Queen dynamics with phenotype values that continue to change without ever settling down to constant values. From certain initial conditions, evolution leading to extinction of one of the species is also a likely outcome.     

Evolutionary games and two species population dynamics

Competition between species has long been modeled by population dynamics based on total numbers of each species. Recently, the evolution of strategy frequencies has been used successfully for competition models between individuals. In this paper, we illustrate that these two views of competition are compatible. It is shown that the rate of intra and interspecific competitions between individuals largely determines the population dynamics. Competition models over a single common resource and predator-prey models are developed from this individual competition approach. In particular, the equilibrium strategies in a co-evolving predator-prey system are shown to be more stable than the predicted strategy cycling of standard evolutionary game theory.     

Long-term evolution of polygenic traits under frequency-dependent intraspecific competition

We analytically investigate the long-term evolution of a continuously varying quantitative character in a diploid population that is determined additively by a finite number of loci. The trait is under a mixture of frequency-dependent disruptive selection induced by intraspecific competition and frequency-independent stabilizing selection. Moreover, the trait is restricted to a finite range by constraints on the particular loci. Our investigations are based on explicit analytical results (provided by Bürger [2005. A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative trait. J. Math. Biol. 50, 355-396]; Schneider [2006. A multilocus-multiallele analysis of frequency-dependent selection induced by intraspecific competition. J. Math. Biol. 52, 483-523]) on the short-term dynamics under the assumption of linkage equilibrium. We show that the population always reaches a long-term equilibrium (LTE), i.e., an equilibrium that is resistant against perturbations of mutations of sufficiently small effect. In general, several LTEs can coexist. They can be calculated explicitly, and we provide necessary and sufficient conditions for their existence. In the case that more than one LTE exists, we exemplify numerically that the evolutionary outcome depends crucially on the initial genetic architecture, on the joint distribution of mutational effects across loci, and on the particular realization of the mutation process. Therefore, long-term evolution cannot be predicted from the ecology alone. We further show that a partial order exists for the LTEs. The set of LTEs has a 'largest' element, an LTE which is reached during long-term evolution if the effects of the occurring mutant alleles are sufficiently large.     

Asymmetric competition between Rana clamitans and Hyla versicolor tadpoles

When two organisms interact over a potentially limiting resource, several outcomes are possible (e.g. neither affected, both equally affected, one affected more than the other). The outcome depends on a variety of factors, both internal and external to the organism. We performed a laboratory experiment to investigate the outcome of potential competitive interactions between tadpoles of the green frog ( Rana clamitans ) and the gray treefrog ( Hyla versicolor ), and to examine the factors that may explain the outcome of the interaction. We found that competition between these two species was asymmetric. Hyla versicolor tadpoles were more affected by intraspecific competition than interspecific competition (i.e. grew faster when grown with heterospecifics than conspecifics); whereas, R . clamitans tadpoles were more affected by interspecific competition than intraspecific competition (i.e. grew faster when grown with conspecifics than heterospecifics). Based on behavioral observations, this result could not be explained on the basis of activity levels, a trait previously linked to competitive ability in tadpoles. However, differences in initial body size may help explain the observed results; the gray treefrog tadpoles were larger than the green frog tadpoles.     

塔里木荒漠优势植物——胡杨种内、种间竞争研究

采用逐步扩大范围的方法确定影响对象木的邻体最佳竞争范围,利用Hegyi提出的单木竞争指数模型对塔里木荒漠优势植物———胡杨种内、种间竞争强度进行定量分析。结果表明,在胡杨群落中,对象木的最适竞争距离为6 m,胡杨种内、种间竞争强度随着植株径级的增大而逐渐减小,种内竞争较种间竞争剧烈。竞争强度与对象木胸径服从幂函数关系,从模型预测结果可知当胡杨胸径达30 cm以上时,竞争强度变化很小。因此,应在此前采取适当的人工疏伐措施来促进植株生长和增强生态系统的稳定性。     

Evolutionarily stable range limits set by interspecific competition

A combination of abiotic and biotic factors probably restricts the range of many species. Recent evolutionary models and tests of those models have asked how a gradual change in environmental conditions can set the range limit, with a prominent idea being that gene flow disrupts local adaptation. We investigate how biotic factors, explicitly competition for limited resources, result in evolutionarily stable range limits even in the absence of the disruptive effect of gene flow. We model two competing species occupying different segments of the resource spectrum. If one segment of the resource spectrum declines across space, a species that specializes on that segment can be driven to extinction, even though in the absence of competition it would evolve to exploit other abundant resources and so be saved. The result is that a species range limit is set in both evolutionary and ecological time, as the resources associated with its niche decline. Factors promoting this outcome include: (i) inherent gaps in the resource distribution, (ii) relatively high fitness of the species when in its own niche, and low fitness in the alternative niche, even when resource abundances are similar in each niche, (iii) strong interspecific competition, and (iv) asymmetric interspecific competition. We suggest that these features are likely to be common in multispecies communities, thereby setting evolutionarily stable range limits.     

Accounting for interspecific competition and age structure in demographic analyses of density dependence improves predictions of fluctuations in population size

Understanding species coexistence has long been a major goal of ecology. Coexistence theory for two competing species posits that intraspecific density dependence should be stronger than interspecific density dependence. Great tits and blue tits are two bird species that compete for food resources and nesting cavities. On the basis of long‐term monitoring of these two competing species at sites across Europe, combining observational and manipulative approaches, we show that the strength of density regulation is similar for both species, and that individuals have contrasting abilities to compete depending on their age. For great tits, density regulation is driven mainly by intraspecific competition. In contrast, for blue tits, interspecific competition contributes as much as intraspecific competition, consistent with asymmetric competition between the two species. In addition, including age‐specific effects of intra‐ and interspecific competition in density‐dependence models improves predictions of fluctuations in population size by up to three times.     

四川大头茶在其群落中的种内与种间竞争的初步研究

用Ｈｅｇｙｉ的单木竞争指数模型对不同演替阶段的四川大头茶群落内的四川大头茶种内,种间的竞争强度进行了定量分析,结果表明：四川大头茶种内竞争较与其伴生树种间的竞争剧烈,竞争木对对象木的竞争强度与对象木的个体大小服从幂函数关系,竞争强度随着对象木人体的增大页减小;对象木的生长速度与竞争指数之间有极显著的负相关关系。     

Competition between perch (Perca fluviatilis) and ruffe (Gymnocephalus cernuus): the advantage of turning night into day

1. The outcome of interspecific competition for food resources depends both on the competitors’ sensory abilities and on environmental conditions. In laboratory experiments we tested the influence of daylight and darkness on feeding behaviour and specific growth rate (SGR) of two species with different sensory abilities. 2. We used perch (Perca fluviatilis) as a visually orientated, and ruffe (Gymnocephalus cernuus) as a mechano‐sensory oriented predator and tested their growth rates and behaviour under conditions of interspecific and intraspecific competition. Three different foraging conditions were used: food supplied (i) only during the day, (ii) only during the night or (iii) during both day and night. 3. In perch neither SGR nor feeding behaviour were influenced substantially by interspecific competition during daylight. During darkness their foraging behaviour changed markedly and their access to the food source as well as their SGR were negatively affected by the presence of ruffe. 4. Ruffe's foraging behaviour did not change during either day or night with interspecific competition. During the night ruffe's SGR was higher with interspecific competition, probably because of a release from intraspecific competition and the competitive inferiority of perch during the night. 5. Because of its seonsory abilities ruffe feeds predominantly at night, thereby reducing competitive interference from perch.     

Evolutionary disarmament in interspecific competition.

Competitive asymmetry, which is the advantage of having a larger body or stronger weaponry than a contestant, drives spectacular evolutionary arms races in intraspecific competition. Similar asymmetries are well documented in interspecific competition, yet they seldom lead to exaggerated traits. Here we demonstrate that two species with substantially different size may undergo parallel coevolution towards a smaller size under the same ecological conditions where a single species would exhibit an evolutionary arms race. We show that disarmament occurs for a wide range of parameters in an ecologically explicit model of competition for a single shared resource; disarmament also occurs in a simple Lotka-Volterra competition model. A key property of both models is the interplay between evolutionary dynamics and population density. The mechanism does not rely on very specific features of the model. Thus, evolutionary disarmament may be widespread and may help to explain the lack of interspecific arms races.     

Equilibrium structure and stability in a frequency-dependent,two-population diploid model

We investigate the equilibrium structure for an evolutionary genetic model in discrete time involving two monoecious populations subject to intraspecific and interspecific random pairwise interactions. A characterization for local stability of an equilibrium is found, related to the proximity of this equilibrium with evolutionarily stable strategies (ESS). This extends to a multi-population framework a principle initially proposed for single populations, which states that the mean population strategy at a locally stable equilibrium is as close as possible to an ESS.     

Density dependent selection incorporating intraspecific competition 1. A haploid model

A haploid model is introduced and analyzed in which intraspecific competition is incorporated within a density dependent framework. It is assumed that each genotype has a unique carrying capacity corresponding to the equilibrium population size when fixed for that type. Each genotypic fitness at a single multi-allelic locus is a function of a distinctive effective population size formed by adding the numbers of each genotype present, weighted by an intraspecific competition coefficient. As a result, the fitnesses depend upon the relative frequencies of the various genotypes as well as the total population size. Intergenotypic interactions can have a profound effect upon the outcome of the population. In particular, when the density effect of one individual upon another depends upon their respective genotypes, a unique stable interior equilibrium is possible in which all alleles are present. This stands in contrast to the purely density dependent haploid system in which the only possible stable state corresponds to fixation for the type with the highest carrying capacity. In the present model selective advantage is determined by a balance between carrying capacity and sensitivity to density pressures from other genotypes. Fixation for the genotype with the highest carrying capacity, for instance, will not be stable if it exerts a sufficiently weak competitive effect upon the other genotypes. In the diallelic case, maintenance of both alleles at a stable equilibrium requires that the net intragenotypic competition between individuals of like genotype be stronger than that between unlike types. As for purely density regulated systems, there may be no stable equilibria and/or regular and chaotic cycling may occur. The results may also be interpreted in terms of a discrete time model of interspecific competition with each haplotype representing a different species.     

Competition and coexistence in plant communities: intraspecific competition is stronger than interspecific competition

Theory predicts that intraspecific competition should be stronger than interspecific competition for any pair of stably coexisting species, yet previous literature reviews found little support for this pattern. We screened over 5400 publications and identified 39 studies that quantified phenomenological intraspecific and interspecific interactions in terrestrial plant communities. Of the 67% of species pairs in which both intra‐ and interspecific effects were negative (competitive), intraspecific competition was, on average, four to five‐fold stronger than interspecific competition. Of the remaining pairs, 93% featured intraspecific competition and interspecific facilitation, a situation that stabilises coexistence. The difference between intra‐ and interspecific effects tended to be larger in observational than experimental data sets, in field than greenhouse studies, and in studies that quantified population growth over the full life cycle rather than single fitness components. Our results imply that processes promoting stable coexistence at local scales are common and consequential across terrestrial plant communities.     

Continuously stable strategies as evolutionary branching points

Evolutionary branching points are a paradigmatic feature of adaptive dynamics, because they are potential starting points for adaptive diversification. The antithesis to evolutionary branching points are continuously stable strategies (CSS's), which are convergent stable and evolutionarily stable equilibrium points of the adaptive dynamics and hence are thought to represent endpoints of adaptive processes. However, this assessment is based on situations in which the invasion fitness function determining the adaptive dynamics have non-zero second derivatives at CSS. Here we show that the scope of evolutionary branching can increase if the invasion fitness function vanishes to higher than first order at CSS. Using classical models for frequency-dependent competition, we show that if the invasion fitness vanishes to higher orders, a CSS may be the starting point for evolutionary branching. Thus, when invasion fitness functions vanish to higher than first order at equilibrium points of the adaptive dynamics, evolutionary diversification can occur even after convergence to an evolutionarily stable strategy.     

Competitive Interactions between Immature Stages of Bactrocera cucurbitae (Coquillett) and Bactrocera tau (Walker) (Diptera: Tephritidae) under Laboratory Conditions

The melon fly, Bactrocera cucurbitae (Coquillett), and the pumpkin fly, Bactrocera tau (Walker), are economically important pests that attack mainly cucurbitacean fruits. The two fruit fly species have similar natural distributions, host ranges, and population growth capacities. This study was designed to assess the asymmetrical competitions through resource exploitation between the larvae of B. cucurbitae and B. tau at different density levels and temperatures, and on different hosts by comparing the relative effects of interspecific and intraspecific interactions on four life history parameters: survival rate, puparial mass, puparial duration, and developmental duration. Our results showed that intraspecific and interspecific competitions occurred under some laboratory conditions, and B. cucurbitae took advantage over B. tau at the high-density level and at low and high temperatures on pumpkin, bitter gourd, and bottle gourd when interspecific competition took place. Intraspecific and interspecific competitions mainly affected the puparial mass and the survival rate of the two fruit fly species but had no marked effect on the puparial duration or development duration.     

A predator–prey refuge system: Evolutionary stability in ecological systems

A refuge model is developed for a single predator species and either one or two prey species where no predators are present in the prey refuge. An individual’s fitness depends on its strategy choice or ecotype (predators decide which prey species to pursue and prey decide what proportion of their time to spend in the refuge) as well as on the population sizes of all three species. It is shown that, when there is a single prey species with a refuge or two prey species with no refuge compete only indirectly (i.e. there is only apparent competition between prey species), that stable resident systems where all individuals in each species have the same ecotype cannot be destabilized by the introduction of mutant ecotypes that are initially selectively neutral. In game-theoretic terms, this means that stable monomorphic resident systems, with ecotypes given by a Nash equilibrium, are both ecologically and evolutionarily stable. However, we show that this is no longer the case when the two indirectly-competing prey species have a refuge. This illustrates theoretically that two ecological factors, that are separately stabilizing (apparent competition and refuge use), may have a combined destabilizing effect from the evolutionary perspective. These results generalize the concept of an evolutionarily stable strategy (ESS) to models in evolutionary ecology. Several biological examples of predator–prey systems are discussed from this perspective.