Effect of harvesting on the genetic diversity and dynamic behavior of a limited mendelian population

A mathematical model of the changes in the size and genetic diversity of a harvested, single-locus Mendelian population under the conditions of density-dependent selection is analyzed, with a special emphasis on the possibility of conserving or loosing polymorphism as a result of equilibrium harvesting. It is demonstrated that harvesting leads to changes in intrapopulation parameters under the conditions of density-dependent selection; as a result, the genotypes that were the least fit in an unharvested population will prove more fit, the genetic composition of the population at equilibrium being changed accordingly. Thus, harvesting may, under different conditions, either conserve or reduce the genetic diversity of the population.     

On the fixation process of a beneficial mutation in a variable environment

A population that adapts to gradual environmental change will typically experience temporal variation in its population size and the selection pressure. On the basis of the mathematical theory of inhomogeneous branching processes, we present a framework to describe the fixation process of a single beneficial allele under these conditions. The approach allows for arbitrary time-dependence of the selection coefficient s(t) and the population size N(t), as may result from an underlying ecological model. We derive compact analytical approximations for the fixation probability and the distribution of passage times for the beneficial allele to reach a given intermediate frequency. We apply the formalism to several biologically relevant scenarios, such as linear or cyclic changes in the selection coefficient, and logistic population growth. Comparison with computer simulations shows that the analytical results are accurate for a large parameter range, as long as selection is not very weak.     

Analytical results on the neutral non-equilibrium allele frequency spectrum based on diffusion theory

The allele frequency spectrum has attracted considerable interest for the simultaneous inference of the demographic and adaptive history of populations. In a recent study, Evans et al. (2007) developed a forward diffusion equation describing the allele frequency spectrum, when the population is subject to size changes, selection and mutation. From the diffusion equation, the authors derived a system of ordinary differential equations (ODEs) for the moments in a Wright–Fisher diffusion with varying population size and constant selection. Here, we present an explicit solution for this system of ODEs with variable population size, but without selection, and apply this result to derive the expected spectrum of a sample for time-varying population size. We use this forward-in-time-solution of the allele frequency spectrum to obtain the backward-in-time-solution previously derived via coalescent theory by Griffiths and Tavaré (1998). Finally, we discuss the applicability of the theoretical results to the analysis of nucleotide polymorphism data.     

Selection on laying date is connected to breeding density in the pied flycatcher

Timing of reproduction and clutch size are important determinants of breeding success, especially in seasonal environments. Several recent bird population studies have shown changes in breeding time and in natural selection on it. These changes have often been linked with climate change, but few studies have investigated how the traits or natural selection are actually connected with climatic factors. Furthermore, the effect of population density on selection has been rarely considered, despite the potential importance of density in demographic processes. We studied variation in natural selection on laying date and on clutch size in relation to measures of spring phenology and population density in a long-term study of pied flycatchers in SW Finland. The phenological stage of the environment at mean egg-laying did not affect the direction of selection on either laying date or on clutch size. There was, however, stronger selection for earlier laying date when the breeding density of the population was high, suggesting that early breeding is not necessarily beneficial as such, but that its importance is emphasized when high population density increases competition. In addition, early breeding was favoured when the pre-breeding period was cool, which may indicate an increased advantage for the fittest individuals in harsher conditions. In the middle of the twentieth century, there was selection for large clutch size, which subsequently ceased, along with an overall decrease in recruit production. Our results indicate that attention should be paid to demographic factors such as breeding density when studying natural selection and temporal changes in it.     

The Impact of Purifying and Background Selection on the Inference of Population History: Problems and Prospects

Current procedures for inferring population history generally assume complete neutrality—that is, they neglect both direct selection and the effects of selection on linked sites. We here examine how the presence of direct purifying selection and background selection may bias demographic inference by evaluating two commonly-used methods (MSMC and fastsimcoal2), specifically studying how the underlying shape of the distribution of fitness effects and the fraction of directly selected sites interact with demographic parameter estimation. The results show that, even after masking functional genomic regions, background selection may cause the mis-inference of population growth under models of both constant population size and decline. This effect is amplified as the strength of purifying selection and the density of directly selected sites increases, as indicated by the distortion of the site frequency spectrum and levels of nucleotide diversity at linked neutral sites. We also show how simulated changes in background selection effects caused by population size changes can be predicted analytically. We propose a potential method for correcting for the mis-inference of population growth caused by selection. By treating the distribution of fitness effect as a nuisance parameter and averaging across all potential realizations, we demonstrate that even directly selected sites can be used to infer demographic histories with reasonable accuracy.     

Cultural niche construction of repertoire size and learning strategies in songbirds

Birdsong is a complex cultural and biological system, and the selective forces driving evolutionary changes in aspects of song learning vary considerably among species. The extent to which repertoire size, the number of syllables or song types sung by a bird, is subject to sexual selection is unknown, and studies to date have provided inconsistent evidence. Here, we propose that selection pressure on the size and complexity of birdsong repertoires may facilitate the construction of a niche in which learning, sexual selection, and song-based homophily may co-evolve. We show, using a review of the birdsong literature and mathematical modeling, that learning mode (open-ended or closed-ended learning) is correlated with the size of birdsong repertoires. Underpinning this correlation may be a form of cultural niche construction in which a costly biological trait (for example, open-ended learning) can spread in a population (or be lost) as a result of direct selection on an associated cultural trait (for example, song repertoire size).     

Very slightly deleterious mutations and the molecular clock

Summary The model of very slightly deleterious mutations was examined from the standpoint of population genetics in relation to the molecular evolutionary clock. The distribution of selection coefficients of mutants (in terms of amino acid changes) with small effect is thought to be continuous around zero, with an average negative value. The variance of selection coefficients depends upon environmental diversity and hence on total population size of a species. By considering various examples of amino acid substitutions, the average and standard error of selection coefficients and the reciprocal of population size are assumed to have similar values. The model predicts negative correlation between evolutionary rate and population size. This effect is expected to be partially cancelled with the generation time effect of intrinsic mutation rate. Implications of this prediction on the molecular evolutionary clock are discussed.     

DNA evolution under weak selection

Some DNA data show patterns of variation not expected under the neutral theory. Here, the independent multicodon (IMC) model, a nearly neutral mutation model assuming no interaction among codons, was studied when population size changes using computer simulation. Patterns of variation expected under the model were investigated using statistics for the neutrality tests. The average dispersion index is more than one when population size changes slowly but it never becomes large. The diversity at linked silent site decreases when the strength of selection is intermediate and the reduction is larger when population size changes slowly. Tajima's (1989. Genetics 123, 585-595) D is generally negative. Rejections by the Tajima's test occur more frequently if population size changes quickly but the effect of selection is confounded with the size change itself in this case. If we apply the test of McDonald and Kreitman (1991. Nature 351, 652-654), the rejection is always in the direction of excess replacement polymorphisms. The rejection probability decreases as the rate of population size changes decreases. These results show that the predictions of the IMC model are consistent with the pattern observed in mitochondrial DNA data but not consistent with some data of nuclear DNA. Interaction among codons or variable selection would be necessary to explain such cases.     

Strong artificial selection in the wild results in predicted small evolutionary change

Estimates of genetic variation and selection allow for quantitative predictions of evolutionary change, at least in controlled laboratory experiments. Natural populations are, however, different in many ways, and natural selection on heritable traits does not always result in phenotypic change. To test whether we were able to predict the evolutionary dynamics of a complex trait measured in a natural, heterogeneous environment, we performed, over an 8-year period, a two-way selection experiment on clutch size in a subdivided island population of great tits (Parus major). Despite strong artificial selection, there was no clear evidence for evolutionary change at the phenotypic level. Environmentally induced differences in clutch size among years are, however, large and can mask evolutionary changes. Indeed, genetic changes in clutch size, inferred from a statistical model, did not deviate systematically from those predicted. Although this shows that estimates of genetic variation and selection can indeed provide quantitative predictions of evolutionary change, also in the wild, it also emphasizes that demonstrating evolution in wild populations is difficult, and that the interpretation of phenotypic trends requires great care.     

Transition Densities and Sample Frequency Spectra of Diffusion Processes with Selection and Variable Population Size

Advances in empirical population genetics have made apparent the need for models that simultaneously account for selection and demography. To address this need, we here study the Wright–Fisher diffusion under selection and variable effective population size. In the case of genic selection and piecewise-constant effective population sizes, we obtain the transition density by extending a recently developed method for computing an accurate spectral representation for a constant population size. Utilizing this extension, we show how to compute the sample frequency spectrum in the presence of genic selection and an arbitrary number of instantaneous changes in the effective population size. We also develop an alternate, efficient algorithm for computing the sample frequency spectrum using a moment-based approach. We apply these methods to answer the following questions: If neutrality is incorrectly assumed when there is selection, what effects does it have on demographic parameter estimation? Can the impact of negative selection be observed in populations that undergo strong exponential growth?     

Second-order moments of segregating sites under variable population size

The identification of genomic regions that have been exposed to positive selection is a major challenge in population genetics. Since selective sweeps are expected to occur during environmental changes or when populations are colonizing a new habitat, statistical tests constructed on the assumption of constant population size are biased by the co-occurrence of population size changes and selection. To delimit this problem and gain better insights into demographic factors, theoretical results regarding the second-order moments of segregating sites, such as the variance of segregating sites, have been derived. Driven by emerging genomewide surveys, which allow the estimation of demographic parameters, a generalized version of Tajima's D has been derived that takes into account a previously estimated demographic scenario to test single loci for traces of selection against the null hypothesis of neutral evolution under variable population size.     

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.     

Evolutionary consequences of habitat fragmentation: population size and density affect selection on inflorescence size in a perennial herb

Habitat fragmentation is considered to be one of the major threats to biological diversity worldwide. To date, however, its consequences have mainly been studied in an ecological context, while little is known about its effects on evolutionary processes. In this study we examined whether habitat fragmentation affects selection on plant phenotypic traits via changes in plant-pollinator interactions, using the self-incompatible perennial herb Phyteuma spicatum. Specifically, we hypothesized that limited pollination service in small or low-density populations leads to increased selection for traits that attract pollinators. We recorded mean seed production per capsule and per plant as a measure of pollination intensity and assessed selection gradients (i.e., trait-fitness relationships) in 16 natural populations of varying size and density over 2 years. Mean seed production was not related to population size or density, except for a marginal significant effect of density on the mean number of seeds per capsule in 1 year. Linear selection for flowering time and synchrony was consistent across populations; relative fitness was higher in earlier flowering plants and in plants flowering synchronously with others. Selection on inflorescence size, however, varied among populations, and linear selection gradients for inflorescence size were negatively related to plant population size and density in 1 year. Selection for increased inflorescence size decreased with increasing population size and density. Contrary to our expectation this appeared not to be related to changes in pollination intensity (mean seed production was not related to population size or density in this year), but was rather likely linked to differences in some other component of the abiotic or biotic environment. In summary, our results show that habitat fragmentation may influence selection on plant phenotypic traits, thereby highlighting potential evolutionary consequences of human-induced environmental change.     

Reports of the Death of Extrinsic Mortality Moulding Senescence Have Been Greatly Exaggerated

The classic evolutionary theory of aging posits that senescence evolves because the weakening of selection with age allows mutations with late-acting deleterious effects to accumulate. Because extrinsic mortality is an important cause of weakening selection, the central prediction of the theory has been that higher extrinsic mortality should lead to the evolution of a higher rate of senescence. However, the validity of this prediction has been questioned, even to the extent of suggesting that it is not a prediction of the theory at all, primarily on the basis that changes in population growth rate will compensate for changes in extrinsic mortality. The implication is that empiricists have been using the wrong prediction to test the theory. This claim is misleading, however, because it does not apply on an evolutionary timescale, when population size must be roughly constant. With a constant population size, Hamilton’s fitness sensitivities show that extrinsic mortality determines the rate at which the strength of selection declines with age, and thus determines the rate of senescence. The central prediction has been confirmed in the few controlled experiments with model organisms that have been conducted, but clearly this is an area ripe for further investigation.     

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 evolution of sexual size dimorphism in the house finch. IV. Population divergence in ontogeny

Differences among taxa in sexual size dimorphism of adults can be produced by changes in distinct developmental processes and thus may reflect different evolutionary histories. Here we examine whether divergence in sexual dimorphism of adults between recently established Montana and Alabama populations of the house finch (Carpodacus mexicanus) can be attributed to population differences in growth of males and females. In both populations, males and females were similar at hatching, but as a result of sex-specific growth attained sexual size dimorphism by the time of independence. Timing and extent of growth varied between the sexes: Females maintained maximum rates of growth for a longer time than males, whereas males had higher initial growth rates and achieved maximum growth earlier and at smaller sizes than females. Ontogeny of sexual dimorphism differed between populations, but in each population, sexual dimorphism in growth parameters and sexual dimorphism at the time of nest leaving were similar to sexual dimorphism of adults. Variation in growth of females contributed more to population divergence than did growth of males. In each population, we found close correspondence between patterns of sexual dimorphism in growth and population divergence in morphology of adults: Traits that were the most sexually dimorphic in growth in each population contributed the most to population divergence in both sexes. We suggest that sex-specific expression of phenotypic and genetic variation throughout the ontogeny of house finches can result in different responses to selection between males and females of the same age, and thus produce fast population divergence in the sexual size dimorphism.     

Effects of resource distribution on sexual selection and the cost of reproduction in sandgobies

I describe the results of an experimental manipulation of resource availability (nest substrate) and distribution (nest size), leading to effects on the opportunity for sexual selection and the survival of male sandgobies Pomatoschistus minutus competing for these resources. This study represents one of few such experimental manipulations. It shows a clear-cut effect of male-male competition on the survival of males, and it shows temporal variation in the opportunity for sexual selection, suggesting that short-term assessment of sexual selection could be misleading. Males breeding under male-male competition for nest sites lived on average 18 d less than males in the high-nest-availability treatment. This considerable cost of reproduction probably stems from increased stress levels as a result of higher levels of aggression. The opportunity for sexual selection was high throughout the 2-mo experiment in the low-nest-availability treatment, while in the high nest availability, it changed in a complex manner over the season. In the latter case, sexual selection was initially low but increased during midseason to values nearly as high as in the nest-site-limited environment and then decreased again toward the end of the season. Previous studies have shown that temporal variation in sexual selection follows variation in population density and sex ratio. This study demonstrates that there can be considerable temporal variation in the opportunity for sexual selection without changes in population parameters.     

Mutators, population size, adaptive landscape and the adaptation of asexual populations of bacteria.

Selection of mutator alleles, increasing the mutation rate up to 10, 000-fold, has been observed during in vitro experimental evolution. This spread is ascribed to the hitchhiking of mutator alleles with favorable mutations, as demonstrated by a theoretical model using selective parameters corresponding to such experiments. Observations of unexpectedly high frequencies of mutators in natural isolates suggest that the same phenomenon could occur in the wild. But it remains questionable whether realistic in natura parameter values could also result in selection of mutators. In particular, the main parameters of adaptation, the size of the adapting population and the height and steepness of the adaptive peak characterizing adaptation, are very variable in nature. By simulation approach, we studied the effect of these parameters on the selection of mutators in asexual populations, assuming additive fitness. We show that the larger the population size, the more likely the fixation of mutator alleles. At a large population size, at least four adaptive mutations are needed for mutator fixation; moreover, under stronger selection stronger mutators are selected. We propose a model based on multiple mutations to illustrate how second-order selection can optimize population fitness when few favorable mutations are required for adaptation.     

Egg size evolution and energetic constraints on population dynamics.

We use population models that are based on dynamic energy budget models for individuals in order to study the evolution of offspring size and its relationship to the evolution of population dynamics. We show the existence of alternative evolutionarily stable strategies for offspring investment strategy resulting from a trade off between offspring number and time-to-maturity. The model predicts egg energy in Daphnia magna well, and suggests that the observed egg energy in D. magna is the result of selection for minimal egg investment constrained by minimum viable egg energy, combined with selection for a juvenile energy reserve. The selection for minimal egg size pushes populations toward chaotic dynamics. However, the minimum viable egg size combined with low efficiency of conversion of energy to new biomass is sufficient to keep population dynamics out of chaos.     

The maintenance of phenotypic and genetic variation in threshold traits by frequency-dependent selection

Many traits are phenotypically dimorphic but determined by the action of many loci, the phenotype being a result of a threshold of sensitivity. Quantitative genetic analysis has shown that generally there is considerable additive genetic variation for the trait, the average heritability being 0.52. In numerous cases threshold traits have been shown, or are assumed, to be under frequency-dependent selection; examples include satellite-territorial behaviour, sex-determination, wing dimorphism and trophic dimorphism. In this paper I investigate the potential for frequency-dependent selection to maintain both phenotypic and additive genetic variation in threshold traits. The qualitative results are robust to the particular form of the frequency-dependent selection function. The equilibrium proportion is more or less independent of population size but the heritability increases with population size, typically approaching its maximal value at a population size of 5000, when the mutation rate is 10^?4. A tenfold decrease in the mutation rate requires an approximate doubling of the population size before an asymptotic value is approached. Thus frequency-dependent selection can account for both the existence of two morphs in a population and the observed levels of heritability. It is also shown, both via simulation and theory, that the quantitative genetic model and a simple phenotypic analysis predict the same equilibrium morph proportion.