The evolution of traits that determine ability in competitive contests

Summary We analyse mathematical models of the evolution of a trait that determines ability in contest competition. We assume that the value of the competitive trait affects two different components of fitness, one measuring the benefit of winning contests and the other measuring the cost of developing the competitive trait. Unlike previous analyses, we include the population dynamical consequences of larger competitive trait values. Exaggeration of the competitive trait reduces the mean probability of survival during the non-competitive stage of the life cycle. The resulting lower population density reduces competition and, therefore, reduces the advantages of greater competitive ability. Models without population dynamics often predict dimorphism in the competitive trait when resource possession is decided by interactions with many other individuals. If the competition involves a contest with a single other individual, models without population dynamics often predict cycles of increase and collapse in the trait or a continual increase, possibly resulting in extinction. When population dynamics are included, both of these results become less likely and a single stable trait value becomes more likely. Population dynamics also make it possible to have dimorphism when individuals have a single pairwise contest and alternative stable trait values when an individual has many contests. Increases in the value of the resource being contested may increase or decrease the evolutionarily stable size of the trait. Competition between very differently sized species will often decrease size in the larger species (character convergence).     

Phenotypic variation,sexual reproduction and evolutionary population dynamics

I studied the effects of introducing phenotypic variation into a well-known single species model for a population with discrete, non-overlapping generations. The phenotypes differed in their dynamic behaviour. The analysis was made under the assumption that the population was in an evolutionary stable state. Differences in the timing of the competitive impacts of the phenotypes on each other had a strong simplifying effect on the dynamics. This result could also be applied to competition between species. The effect of sexual reproduction on the dynamics of the population was analysed by assuming the simplest genetic model of one locus with two alleles. Sexual reproduction made the system much more stable in the (mathematical) sense that the number of attractors was reduced and their basins of attraction enlarged. In a dominant system sex tended to increase the frequency of the recessive allele, and in an overdominant system it induced gene frequencies of 1/2. Whether the attractors in the dominant system tended to be simpler or more complex than the attractors in the asexual system depended on the phenotype of the recessive homozygote. The overdominant sexual system tended to have simpler dynamics than the corresponding asexual population. A 2-locus model was used to study whether sexuals can invade an asexual population and vice versa. One locus coded for sexual and asexual reproduction, while the other coded for the dynamics. Enhanced stability through sexual reproduction seemed to be the reason why there was a clear asymmetry favouring sex in this evolutionary context.     

The joint evolution of seed dormancy and flowering time in annual plants living in variable environments

In annual plants, both seed germination (as opposed to dormancy) and delayed flowering are assumed to confer both greater and more variable reproduction. With this assumption, a simple model of these two characters, together with a reparameterization of survival and reproductive rates and a general approximation, leads to several predictions based on maximizing geometric growth rates. Each character optimum is a ratio of mean to variance of future reproduction, and the two optimums are interdependent, with compensation by one favored if the other changes. Optimal character variances, possible with prediction of future reproduction, are roughly squared correlations of characters with future reproduction, divided by variances of future reproduction. The optimal mean of each character is more sensitive to the other character's variance than to its own variance, and the optimal variance of each character is more sensitive to the other character's mean than to its own mean. Optimal germination is increased with better correlation between flowering time and future reproduction. A diffusion approximation for the single locus, single character genetic analog of the phenotypic model showed fluctuating natural selection to favor, in expectation and under suitable conditions, the allele frequency maximizing the geometric population growth rate. Conditions for a protected polymorphism at a second locus, controlling the other character, show genetic variation at the first locus favors alleles at the second locus adapted to greater environmental variability. Computer simulations check some results, and the general predictions should be relevant for studies of correlated life history characters.     

Effects of genetic architecture on the evolution of assortative mating under frequency-dependent disruptive selection

We consider a model of sympatric speciation due to frequency-dependent competition, in which it was previously assumed that the evolving traits have a very simple genetic architecture. In the present study, we numerically analyze the consequences of relaxing this assumption. First, previous models assumed that assortative mating evolves in infinitesimal steps. Here, we show that the range of parameters for which speciation is possible increases when mutational steps are large. Second, it was assumed that the trait under frequency-dependent selection is determined by a single locus with two alleles and additive effects. As a consequence, the resultant intermediate phenotype is always heterozygous and can never breed true. To relax this assumption, here we add a second locus influencing the trait. We find three new possible evolutionary outcomes: evolution of three reproductively isolated species, a monomorphic equilibrium with only the intermediate phenotype, and a randomly mating population with a steep unimodal distribution of phenotypes. Both extensions of the original model thus increase the likelihood of competitive speciation.     

Dynamic modeling of cooperative protein secretion in microorganism populations

Interactions between microorganisms can have a crucial effect on their population dynamics. Typically, interactions are mediated through the environment by molecules and proteins that are products of cell metabolism and physiology; they therefore reflect the internal dynamics of the single cell. In this work we aim to integrate single-cell properties of gene expression that affect indirect interactions between microorganisms under challenging conditions, into a quantitative model of population dynamics. Specifically we address the problem of a microbial population secreting a protein that can actively extract a growth-limiting resource, such as a simple sugar or iron, from the environment. The genes coding for the protein can undergo random epigenetic transitions between active and silenced states, and can be repressed by the product of their reaction. We model cooperative and competitive interactions between protein producing and non-producing phenotypes by nonlinear dynamical systems and analyze them both in terms of asymptotic states and of transient dynamics. Our model shows that phenotypic transitions allow a stable coexistence of the two phenotypes, and enables us to make predictions regarding the conditions required for such coexistence and the typical timescales of transient dynamics. It also shows how repression by the reaction product induces a feedback at the population-environment level that can result in limit cycle dynamics. The relation of these results to experiments are discussed.     

Gene interactions from maternal effects

Theoretical analyses have demonstrated a potential role for epistasis in many of the most important processes in evolution. These analyses generally assume that an individual's genes map directly to its phenotype and epistasis results from interactions among loci that contribute to the same biochemical or developmental pathways (termed physiological, or within-genotype, epistasis). For many characters, particularly those expressed early in life, an individual's phenotype may also be affected by genes expressed by its parents. The presence of these parental effects allows for interactions between the genes present in the parental and offspring genomes. When the phenotypic effect of a locus in the offspring depends on the alleles possessed by its parents, genotype-by-genotype, or among-genotype, epistasis occurs. The among-genotype epistasis resulting from parental effects may contribute to ruggedness of adaptive landscapes because early mortality often accounts for much of the variance in fitness in populations. To demonstrate how parent-offspring interactions can result in among-genotype epistasis, I use a two-locus model, with one maternal effect locus and one direct effect locus, each with two alleles. Dynamical equations are presented for the two-locus model and are directly contrasted with the dynamical equations derived for a model for physiological epistasis. The relationship between the evolutionary dynamics resulting from these two forms of epistasis is discussed. Three scenarios are presented to illustrate systems in which maternal-offspring, genotype-by-genotype epistasis may occur. The implications of maternal-offspring epistasis for quantitative-trait-loci studies are also discussed.     

具脉冲扩散效应的单种群动力学模型

讨论了两斑块间脉冲扩散的单种群动力学模型,利用离散动力系统频闪映射理论,得到了种群持续生存的充分条件．结论31,1~了现实的生物种群动力学性质,也丰富了脉冲微分方程理论．     

Genetic modelling: an analysis of a colour polymorphism in the Snow Goose (Anser caerulescens)

Previous studies of colour polymorphism in the Snow Goose [ Anser caerulescens ; failed to consider and reject alternative hypotheses to that of a single locus with incomplete dominance. Utilizing data from a long-term study of a wild population, we test the validity of these earlier results by considering two alternatives: (1) a single locus with multiple allelism and (2) a threshold polygenic system. Our analyses corroborate the original model, but emphasize the importance of testing all plausible hypotheses.     

Analytical framework for identifying and differentiating recent hitchhiking and severe bottleneck effects from multi-locus DNA sequence data

Hitchhiking and severe bottleneck effects have impact on the dynamics of genetic diversity of a population by inducing homogenization at a single locus and at the genome-wide scale, respectively. As a result, identification and differentiation of the signatures of such events from DNA sequence data at a single locus is challenging. This paper develops an analytical framework for identifying and differentiating recent homogenization events at multiple neutral loci in low recombination regions. The dynamics of genetic diversity at a locus after a recent homogenization event is modeled according to the infinite-sites mutation model and the Wright-Fisher model of reproduction with constant population size. In this setting, I derive analytical expressions for the distribution, mean, and variance of the number of polymorphic sites in a random sample of DNA sequences from a locus affected by a recent homogenization event. Based on this framework, three likelihood-ratio based tests are presented for identifying and differentiating recent homogenization events at multiple loci. Lastly, I apply the framework to two data sets. First, I consider human DNA sequences from four non-coding loci on different chromosomes for inferring evolutionary history of modern human populations. The results suggest, in particular, that recent homogenization events at the loci are identifiable when the effective human population size is 50,000 or greater in contrast to 10,000, and the estimates of the recent homogenization events are agree with the "Out of Africa" hypothesis. Second, I use HIV DNA sequences from HIV-1-infected patients to infer the times of HIV seroconversions. The estimates are contrasted with other estimates derived as the mid-time point between the last HIV-negative and first HIV-positive screening tests. The results show that significant discrepancies can exist between the estimates.     

A multilocus-multiallele analysis of frequency-dependent selection induced by intraspecific competition

The study of the mechanisms that maintain genetic variation has a long history in population genetics. We analyze a multilocus-multiallele model of frequency- and density-dependent selection in a large randomly mating population. The number of loci and the number of alleles per locus are arbitrary. The n loci are assumed to contribute additively to a quantitative character under stabilizing or directional selection as well as under frequency-dependent selection caused by intraspecific competition. We assume the strength of stabilizing selection to be weak, whereas the strength of frequency dependence may be arbitrary. Density-dependence is induced by population regulation. Our main result is a characterization of the equilibrium structure and its stability properties in terms of all parameters. It turns out that no equilibrium exists with more than two alleles segregating per locus. We give necessary and sufficient conditions on the strength of frequency dependence to ensure the maintenance of multilocus polymorphism. We also give explicit formulas on the number of polymorphic loci maintained at equilibrium. These results are based on the assumption that selection is sufficiently weak compared with recombination, so that linkage equilibrium can be assumed. If additionally the population size is assumed to be constant, we prove that the dynamics of the model form a generalized gradient system. For the model in its general form we are able to derive necessary and sufficient conditions for the stability of the monomorphic equilibria. Furthermore, we briefly analyze a special symmetric two-locus two-allele model for a constant population size but allowing for linkage disequilibrium. Finally, we analyze a single diallelic locus with dominance to illustrate the complications that can occur if the assumption of additivity is relaxed.     

FITNESS VARIATION DUE TO SEXUAL ANTAGONISM AND LINKAGE DISEQUILIBRIUM

Extensive fitness variation for sexually antagonistic characters has been detected in nature. However, current population genetic theory suggests that sexual antagonism is unlikely to play a major role in the maintenance of variation. We present a two‐locus model of sexual antagonism that is capable of explaining greater fitness variance at equilibrium than previous single‐locus models. The second genetic locus provides additional fitness variance in two complementary ways. First, linked loci can maintain gene variants that are lost in single‐locus models of evolution, expanding the opportunity for polymorphism. Second, linkage disequilibrium results between any two sexually antagonistic genes, producing an excess of high‐ and low‐fitness haplotypes. Our results uncover a unique contribution of conflicting selection pressures to the maintenance of variation, which simpler models that neglect genetic architecture overlook.     

Adaptation to slow environmental change, with apparent anticipation of selection

We investigate a genetic model of a large population of sexual organisms in a changing environment. The organisms are subject to stabilising selection on a quantitative trait, with environmental change causing the fitness optimum to move. When the fitness optimum moves slowly, adaptation to the changing environment occurs by means of reasonably well-separated substitutions at the loci controlling the trait. In this way, the trait generally tracks the moving optimum, but in such a case, the population may exhibit periods of time where the mean trait value overshoots the moving optimal trait value, thereby exhibiting an apparent anticipation of selection. The mechanism underlying this phenomenon is determined from consideration of a simpler model that correctly captures the observed dynamical behaviour. We note that very slow rates of changes of traits are seen in the fossil record and the present work may be relevant to this topic.     

季节性和综合害虫管理策略实施时间对害虫控制的影响(英文)

通过建立具有季节变化和综合脉冲控制效应的非自治捕食与被捕食模型,我们得到了保证害虫根除的临界条件,即得到了保证害虫根除周期解全局稳定的充分条件.进而我们讨论了季节性变化以及最优的害虫控制策略实施时间对临界条件的影响.结论显示当害虫种群数量具有季节波动时,系统存在使得临界值达到最小的最优控制策略实施时间.     

Does competitive divergence occur if assortative mating is costly?

Most models of sympatric speciation have assumed that assortative mating has no costs. A few studies, however, have shown that the costs for being choosy can prevent such speciation. Here, we investigate the role of the strength of assortment and of the costs for being choosy for a simple genetic model of a single ('magic') trait that mediates both intraspecific competition for a continuum of resources and assortative mating, which is induced by choosy females who preferentially mate with males of similar phenotype. Choosiness may be costly if it is difficult to find a mating partner. Such magic trait models are considered to be most conducive of sympatric speciation. We consider a sexually reproducing population of haploid individuals that is density regulated. The trait is determined by a single locus with multiple alleles. The strength of stabilizing selection (caused by a unimodal resource distribution), the strength of competition, the degree of assortment and the costs for being choosy are independent parameters. We investigate analytically and numerically how these parameters determine the equilibrium and stability structure. In particular, we identify conditions under which no polymorphism at all is maintained as well as conditions under which strong competitive divergence occurs, or the population even splits into two reproductively isolated classes of highly diverse phenotypes. If costs are absent or moderate, genetic variability tends to be minimized at intermediate strengths of assortment, and reproductively isolated classes of phenotypes are a likely result of evolution only for intermediate or strong competition and for very strong assortment. The likelihood of divergence depends relatively weakly on the costs as long as they are not high. With high costs, however, increasingly strong assortment rapidly depletes all genetic variation, and strong competitive divergence is prevented.     

Density-dependent birth rate, birth pulses and their population dynamic consequences

 In most models of population dynamics, increases in population due to birth are assumed to be time-independent, but many species reproduce only during a single period of the year. We propose a single-species model with stage structure for the dynamics in a wild animal population for which births occur in a single pulse once per time period. Using the discrete dynamical system determined by the stroboscopic map, we obtain an exact periodic solution of systems which are with Ricker functions or Beverton-Holt functions, and obtain the threshold conditions for their stability. Above this threshold, there is a characteristic sequence of bifurcations, leading to chaotic dynamics, which implies that the dynamical behaviors of the single species model with birth pulses are very complex, including small-amplitude annual oscillations, large-amplitude multi-annual cycles, and chaos. This suggests that birth pulse, in effect, provides a natural period or cyclicity that allows for a period-doubling route to chaos. Received: 13 June 2001 / Revised version: 7 September 2001 / Published online: 8 February 2002     

Convergence to constant equilibrium for a density-dependent selection model with diffusion

We consider the classical single locus two alleles selection model with diffusion where the fitnesses of the genotypes are density dependent. Using a theorem of Peter Brown, we show that in a bounded domain with homogeneous Neumann boundary conditions, the allele frequency and population density converge to a constant equilibrium lying on the zero population mean fitness curve. The results agree with the case without diffusion obtained by Selgrade and Namkoong. Frequency and density dependent selection is also considered.Research partially supported by NSF grant DMS-8601585     

Delayed maturation in temporally structured populations with non-equilibrium dynamics

In this paper we study the evolutionary dynamics of delayed maturation in semelparous individuals. We model this in a two-stage clonally reproducing population subject to density-dependent fertility. The population dynamical model allows multiple — cyclic and/or chaotic — attractors, thus allowing us to illustrate how (i) evolutionary stability is primarily a property of a population dynamical system as a whole, and (ii) that the evolutionary stability of a demographic strategy by necessity derives from the evolutionary stability of the stationary population dynamical systems it can engender, i.e., its associated population dynamical attractors. Our approach is based on numerically estimating invasion exponents or “mutant fitnesses”. The invasion exponent is defined as the theoretical long-term average relative growth rate of a population of mutants in the stationary environment defined by a resident population system. For some combinations of resident and mutant trait values, we have to consider multi-valued invasion exponents, which makes the evolutionary argument more complicated (and more interesting) than is usually envisaged. Multi-valuedness occurs (i) when more than one attractor is associated with the values of the residents' demographic parameters, or (ii) when the setting of the mutant parameters makes the descendants of a single mutant reproduce exclusively either in even or in odd years, so that a mutant population is affected by either subsequence of the fluctuating resident densities only. Non-equilibrium population dynamics or random environmental noise selects for strategists with a non-zero probability to delay maturation. When there is an evolutionarily attracting pair of such a strategy and a population dynamical attractor engendered by it, this delaying probability is a Continuously Stable Strategy, that is an Evolutionarily Unbeatable Strategy which is also Stable in a long term evolutionary sense. Population dynamical coexistence of delaying and non-delaying strategists is possible with non-equilibrium dynamics, but adding random environmental noise to the model destroys this coexistence. Adding random noise also shifts the CSS towards a higher probability of delaying maturation.     

Dependence of expected heterozygosity on locus number with stabilizing selection and drift

I determine expected levels of heterozygosity in two allele multilocus models with mutation, stabilizing selection and drift. In the range 2 to 32 loci, the per locus heterozygosity can depend on the locus number. The per locus heterozygosity for ten loci can be as low as three fourths of the per locus heterozygosity in the limit, as the number of loci gets large. Simulations indicate that this dependence on locus number is not due to the population approaching equilibria at which the mean differs from the optimum, but is due to changes in the substitution rate as a function of the number of loci.