Evolutionary responses to harvesting in ungulates

1. We investigate the evolutionary responses to harvesting in ungulates using a state-dependent, stochastic, density-dependent individual-based model of red deer Cervus elaphus (L.) females subject to different harvesting regimes. 2. The population's mean weight at first reproduction shifts towards light weights as harvesting increases, and its distribution changes from a single peak distribution under very low or high harvest rates, to a bimodal distribution under intermediate harvest rates. 3. These results suggest that, consistent with previous studies on aquatic species, harvesting-induced mortality may drive adaptive responses in ungulates by reducing the fitness benefits from adult survival and growth in favour of early and lightweight reproduction. 4. Selective harvesting for heavy animals has no additional effect on the evolutionarily stable strategy, suggesting that harvest rate is more important than the degree of selectivity in driving adaptive responses. However, selective harvesting of light females is positively associated with maturation weights even higher than those of a nonharvested population, probably due to the reduction in the fitness value of the offspring. 5. The average number of weight at maturation strategies in the population declines but the total number of strategies across all simulations increases with harvest rate, suggesting that harvesting-induced selection on weight at maturity overcomes the increase in strategy diversity expected from density-dependent release. 6. Yield initially increases with harvesting due to enhanced productivity of light females experiencing density-dependent release. However, it crashes under intense harvesting resulting in a population skewed to light, young and, therefore, less reproductive animals.     

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.     

Fluctuations in numbers in box populations of Drosophila and selective genetic mechanism of their regulation

Box populations of Drosophila melanogaster are characterized by two types of periodical fluctuations of numbers: with low and high frequency. High frequency fluctuations are determined by existence of preimago and imago stages and subsequent delay in density-dependent limitation of imago reproduction, duration of which is determined by time of preimago stage. The period of these fluctuations should be limited within two generation, that is confirmed by experimental data. Low frequency fluctuations with the period of 13-15 generations are the result of ecological density-dependent effect. In this case during pick density one can observe continuous degradation of population (i.e. decrease in fecundity and life time of imago) and following decrease in numbers. Temporary changes in fecundity of females and their offspring of the second generation are positively correlated with low frequency fluctuations in numbers. Such relationships show the possibility of density-dependent, cyclic, genetic changes in fecundity connected with fluctuations in numbers. It means that at the phase of growth in numbers when the density is still low, the selection is directed to the individuals with high fecundity sensible to overpopulation. The phase of decline in numbers is connected with high density and selection directed to the individuals with low fecundity in low density populations. The changes in genetic structure of fluctuating population lead to the weakening of this fluctuations and to the maintaining of population under such conditions.     

Frequency- and density-dependent selection on a quantitative character

The equilibrium distribution of a quantitative character subject to frequency- and density-dependent selection is found under different assumptions about the genetical basis of the character that lead to a normal distribution in a population. Three types of models are considered: (1) one-locus models, in which a single locus has an additive effect on the character, (2) continuous genotype models, in which one locus or several loci contribute additively to a character, and there is an effectively infinite range of values of the genotypic contributions from each locus, and (3) correlation models, in which the mean and variance of the character can change only through selection at modifier loci. It is shown that the second and third models lead to the same equilibrium values of the total population size and the mean and variance of the character. One-locus models lead to different equilibrium values because of constraints on the relationship between the mean and variance imposed by the assumptions of those models.——The main conclusion is that, at the equilibrium reached under frequency- and density-dependent selection, the distribution of a normally distributed quantitative character does not depend on the underlying genetic model as long as the model imposes no constraints on the mean and variance.     

Natural selection and density-dependent population growth

Natural selection was studied in the context of density-dependent population growth using a single locus, continuous time model for the rates of change of population size and allele frequency. The maximization principle of density-dependent selection was applied to a class of fitness expressions with explicit recruitment and mortality terms. Three general results were obtained: First, at low population densities, the genetic basis of selection is the difference between the mean recruitment rate and the mean mortality rate. Second, at densities much higher than the equilibrium population size, selection is expected to act to minimize the mean mortality rate. Third, as the population approaches its equilibrium density, selection is predicted to maximize the ratio of the mean recruitment rate to the mean mortality rate.     

Selection in populations with overlapping generations. VI. Rates of change of gene frequency and population growth rate

Two methods (Methods 1 and 2) are used to derive approximate equations describing the rates of change of gene frequency and population growth rate in an age-structured population which is not subject to density-dependent limitation of numbers. Method 2 gives equations which are closely related to Fisher's Malthusian parameter equations, and are good approximations even with quite strong selection (30% selection coefficients) in the case of a single autosomal locus. When there is strong heterotic selection, however, Method 2 gives a bad fit to the population's behaviour in the neighbourhood of equilibrium, but a good fit elsewhere. Method 1 gives a good fit near equilibrium, but a bad fit when gene frequencies change rapidly. With strong heterotic selection, therefore, no single set of selection parameters is adequate, but in other single locus cases, the genotypic intrinsic rates of increases may be used, except when selection is very intense. In multilocus situations it is shown that further specializing assumptions have to be made for this to be true. The asymptotic states of populations under various selection regimes are determined for the case of a single locus with two alleles, when the direction of selective differences remains constant throughout the life-span of an individual.     

Separation of time scales, fixation probabilities and convergence to evolutionary stable states under isolation by distance

To a first order of approximation, selection is frequency independent in a wide range of family structured models and in populations following an island model of dispersal, provided the number of families or demes is large and the population is haploid or diploid but allelic effects on phenotype are semidominant. This result underlies the way the evolutionary stability of traits is computed in games with continuous strategy sets. In this paper similar results are derived under isolation by distance. The first-order effect on expected change in allele frequency is given in terms of a measure of local genetic diversity, and of measures of genetic structure which are almost independent of allele frequency in the total population when the number of demes is large. Hence, when the number of demes increases the response to selection becomes of constant sign. This result holds because the relevant neutral measures of population structure converge to equilibrium at a rate faster than the rate of allele frequency changes in the total population. In the same conditions and in the absence of demographic fluctuations, the results also provide a simple way to compute the fixation probability of mutants affecting various ecological traits, such as sex ratio, dispersal, life-history, or cooperation, under isolation by distance. This result is illustrated and tested against simulations for mutants affecting the dispersal probability under a stepping-stone model.     

Regular and chaotic cycling in models of ecological genetics

A model of density-dependent selection is investigated for the cyclical behavior associated with the analogous nonlinear models of population growth. If the population size regulating mechanism reacts too sharply to perturbations in population size, regular and chaotic limit cycles may result. It is established analytically that the population may converge to fixation or an invariant polymorphic gene frequency while the population size undergoes regular or chaotic oscillations. The possibility of joint limit cycles in both the population size and gene frequency is demonstrated and investigated numerically. Such cycles may occur even though one or both fixation equilibria are locally stable. In the context of equilibrium cycles it is found that overdominance in carrying capacity is not necessary for the maintenance of genetic variation in the population. Furthermore, the genetic system appears able to exert a stabilizing influence on the overall system.     

A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative trait

The equilibrium structure of an additive, diallelic multilocus model of a quantitative trait under frequency- and density-dependent selection is derived. The trait is under stabilizing selection and mediates intraspecific competition as induced, for instance, by differential resource utilization. It is assumed that stabilizing selection is weak, but the strength of competition may be arbitrary relative to it. Density dependence is caused by population regulation, which may be of a very general kind. The number and effects of loci are arbitrary, and stabilizing selection is not necessarily symmetric with respect to the range of phenotypic values. All previously studied models of intraspecific competition for a continuum of resources known to the author reduce to a special case of the present model if overall selection is weak. Therefore, in this case our results are applicable as approximations to all these models. Our central result is the (nearly) complete characterization of the equilibrium and stability structure in terms of all parameters. It is derived under the sole assumption that selection is weak enough relative to recombination to ignore linkage disequilibrium. In particular, necessary and sufficient conditions on the strength of competition relative to stabilizing selection are found that ensure the maintenance of multilocus polymorphism and the occurrence of disruptive selection. In this case, explicit formulas for the number of polymorphic loci at equilibrium, the allele frequencies, the genetic variance, and the strength of disruptive selection are obtained. For two loci, the effects of linkage are investigated analytically; for several loci, they are studied numerically.     

Separation of time scales, fixation probabilities and convergence to evolutionarily stable states under isolation by distance

To a first order of approximation, selection is frequency independent in a wide range of family structured models and in populations following an island model of dispersal, provided the number of families or demes is large and the population is haploid or diploid but allelic effects on phenotype are semidominant. This result underlies the way the evolutionary stability of traits is computed in games with continuous strategy sets. In this paper similar results are derived under isolation by distance. The first-order effect on expected change in allele frequency is given in terms of a measure of local genetic diversity, and of measures of genetic structure which are almost independent of allele frequency in the total population when the number of demes is large. Hence, when the number of demes increases the response to selection becomes of constant sign. This result holds because the relevant neutral measures of population structure converge to equilibrium at a rate faster than the rate of allele frequency changes in the total population. In the same conditions and in the absence of demographic fluctuations, the results also provide a simple way to compute the fixation probability of mutants affecting various ecological traits, such as sex ratio, dispersal, life-history, or cooperation, under isolation by distance. This result is illustrated and tested against simulations for mutants affecting the dispersal probability under a stepping-stone model.     

Insight into the genetic bases of climatic adaptation in experimentally evolving wheat populations

Experimental populations evolving under natural selection represent an interesting tool to study genetic bases of adaptation. Evolution of genes possibly involved in adaptive response can be followed together with the corresponding phenotypic traits. Using experimental populations of hexaploid wheat, we studied the evolution of flowering time, a major adaptive trait that synchronizes the initiation of reproduction and the occurrence of favourable environmental conditions. During 12 generations, three populations were grown in contrasted environments (Vervins North France, Le Moulon near Paris, Toulouse South France) under the influence of natural selection, drift, mutation and recombination. Evolution of diversity at the major gene VRN-1 involved in wheat vernalization response has been analysed jointly with earliness estimated in controlled conditions. Whatever the population, rapid phenotypic changes as well as parallel genotypic variations were observed in the first seven generations, probably as the result of selection acting on this major gene which explains 80% of the trait variation overall. Different allelic combinations at physically unlinked copies of VRN-1 located on distinct genomes (A, B and D) were selected between populations. As theoretically expected, due to population differentiation, a high level of genetic diversity was maintained overall in generation 12. Surprisingly, in two populations out of three, the emergence of new alleles by mutation or migration, coupled with temporal variable selection or frequency-dependent selection, allowed to maintain within-population diversity despite local genetic drift and natural selection. This result may plead for an evolutionary approach of wheat genetic resource conservation.     

Molecular ecological approaches to studying the evolutionary impact of selective harvesting in wildlife

Harvesting of wildlife populations by humans is usually targeted by sex, age or phenotypic criteria, and is therefore selective. Selective harvesting has the potential to elicit a genetic response from the target populations in several ways. First, selective harvesting may affect population demographic structure (age structure, sex ratio), which in turn may have consequences for effective population size and hence genetic diversity. Second, wildlife-harvesting regimes that use selective criteria based on phenotypic characteristics (e.g. minimum body size, horn length or antler size) have the potential to impose artificial selection on harvested populations. If there is heritable genetic variation for the target characteristic and harvesting occurs before the age of maturity, then an evolutionary response over time may ensue. Molecular ecological techniques offer ways to predict and detect genetic change in harvested populations, and therefore have great utility for effective wildlife management. Molecular markers can be used to assess the genetic structure of wildlife populations, and thereby assist in the prediction of genetic impacts by delineating evolutionarily meaningful management units. Genetic markers can be used for monitoring genetic diversity and changes in effective population size and breeding systems. Tracking evolutionary change at the phenotypic level in the wild through quantitative genetic analysis can be made possible by genetically determined pedigrees. Finally, advances in genome sequencing and bioinformatics offer the opportunity to study the molecular basis of phenotypic variation through trait mapping and candidate gene approaches. With this understanding, it could be possible to monitor the selective impacts of harvesting at a molecular level in the future. Effective wildlife management practice needs to consider more than the direct impact of harvesting on population dynamics. Programs that utilize molecular genetic tools will be better positioned to assess the long-term evolutionary impact of artificial selection on the evolutionary trajectory and viability of harvested populations.     

Vicious circles: positive feedback in major evolutionary and ecological transitions

Evolutionary biologists and ecologists often focus on equilibrium states that are subject to forms of negative feedback, such as optima for phenotypic traits or regulation of population sizes. However, recent theoretical and empirical studies show how positive feedback can be instrumental in driving many of the most important and spectacular processes in evolutionary ecology, including the evolution of sex and genetic systems, mating systems, life histories, complex cooperation in insects and humans, ecological specialization, species diversity, species ranges, speciation and extinction. Taken together, this work suggests that positive feedback is more common than is generally appreciated, and that its self-reinforcing dynamics generate the conditions for changes that might otherwise be difficult or impossible for selection or other mechanisms to achieve. Testing for positive feedback requires analysing each causal link in feedback loops, tracking genetic, character and population-dynamic changes across generations, and elucidating the conditions that can result in self-reinforcing change.     

Density-Dependent Selection Incorporating Intraspecific Competition. II. a Diploid Model

A diploid model is introduced and analyzed in which intraspecific competition is incorporated within the context of density-regulated selection. It is assumed that each genotype has a unique carrying capacity corresponding to the equilibrium population size when only that type is present. Each genotypic fitness at a single diallelic autosomal locus is a decreasing function of a distinctive effective population size perceived as a result of intraspecific competition. The resulting fitnesses are both density and frequency dependent with selective advantage determined by a balance between genotypic carrying capacity and sensitivity to intraspecific competition. A major finding is that intergenotypic interactions may allow genetic variation to be more easily maintained than in the corresponding model of purely density-dependent selection. In addition, numerical study confirms the possible existence of multiple interior equilibria and that neither overdominance in fitness nor carrying capacity is necessary for stability. The magnitude of the equilibrium population size and optimization principles are also discussed.     

The equilibrium and stability for n alleles under the density-dependent selection

The problem of the equilibrium under the density-dependent selection for n-alleles belonging to one locus is considered. The new “measure of quality” of the population φ is introduced and it is shown that the equilibrium points are the constrained stationary points of the function φ and all locally stable equilibriums are its local maximum points. The analoque of the Fisher theorem for density-dependent selection is considered.     

Invasive species management in two-patch environments: agricultural damage control in the raccoon (<Emphasis Type="Italic">Procyon lotor</Emphasis>) problem,Hokkaido, Japan

We develop discrete-time models for analyzing the long-run equilibrium outcomes on invasive species management in two-patch environments with migration. In particular, the focus is on a situation where removal operations for invasive species are implemented only in one patch (controlled patch). The new features of the model are that (1) asymmetry in density-dependent migration is considered, which may originate from impact of harvesting as well as heterogeneous habitat conditions, and (2) the effect of density-dependent catchability accounts for the fact that the required effort level to remove one individual may rise as the existing population decreases. The model is applied to agricultural damage control in the raccoon (Procyon lotor) problem that has occurred in Hokkaido, Japan. Numerical illustrations demonstrate that the long-run equilibrium outcomes largely depend on the degree of asymmetry in migration as well as the sensitivity of catchability in response to a change in the population size of the invasive species. Furthermore, we characterize the conditions under which the economically optimal effort levels are qualitatively affected by the above two factors, and conclude that aiming at local extermination of invasive species in the controlled patch is justified. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

不同水分条件下春小麦种群中个体大小不整齐性及遗传学分析不同水分条件下春小麦种群中个体大小不整齐性及遗传学分析

 种群内个体大小不整齐性是种群数量结构的主要指标。本文研究了不同水分条件下,3个品种春小麦种群个体大小不整齐性的建立及变化规律。对春小麦种群不整齐性的遗传学分析表明：遗传结构与随机环境修饰对种群数量结构形成的相对重要性,因水分条件不同而异。种群不整齐性在自然选择中的作用可用下列简单模型表示：CSo＝SH×hSH2 CSo：自然选择强度;SH：大小不整齐性;hSH2：不整齐性的遗传力。     

The effect of optimal harvesting on the dynamics of size and genetic composition of a two-age population

The effect of optimal stationary harvesting at a constant harvest rate on the dynamics of a two-age population is considered. It has been shown analytically that harvesting a fixed rate of the population size of only one age cohort is optimal. As has been observed, the maximum of revenue function is unattainable in the case of concurrent harvesting of both age cohorts. It has been demonstrated that the direction of natural selection does not explicitly change when unselectively harvesting individuals; however, the adaptive genetic diversity of an unharvested population can be lost due to harvesting.     

Fluctuations in the Size of Isolated Single-Species Populations and Natural Selection

This paper discusses the basic types of dynamical behavior of populations obtained in discrete models, such as monotonous dynamics, stable limited cycles, and chaotic variations. All these modes are shown to have possibly arisen in the evolution of limited populations under the effect of density-independent selection. This effect together with that of density-dependent non-selective factors has been termed F-selection, which is characterized by independence of relative fitnesses from population density, whereas populations may be ecologically limited; in other words, absolute fitnesses prove to be a function of population size. The characteristic of F-selection is to be not sensitive to changes in population size but to lead to fluctuations, that create conditions for achieving density-dependent selection.     

Frequency and density-dependent selection on life-history strategies--a field experiment

Negative frequency-dependence, which favors rare genotypes, promotes the maintenance of genetic variability and is of interest as a potential explanation for genetic differentiation. Density-dependent selection may also promote cyclic changes in frequencies of genotypes. Here we show evidence for both density-dependent and negative frequency-dependent selection on opposite life-history tactics (low or high reproductive effort, RE) in the bank vole (Myodes glareolus). Density-dependent selection was evident among the females with low RE, which were especially favored in low densities. Instead, both negative frequency-dependent and density-dependent selection were shown in females with high RE, which were most successful when they were rare in high densities. Furthermore, selection at the individual level affected the frequencies of tactics at the population level, so that the frequency of the rare high RE tactic increased significantly at high densities. We hypothesize that these two selection mechanisms (density- and negative frequency-dependent selection) may promote genetic variability in cyclic mammal populations. Nevertheless, it remains to be determined whether the origin of genetic variance in life-history traits is causally related to density variation (e.g. population cycles).