Multivariate selection under adverse genetic correlations: impacts of population sizes and selection strategies on gains and coancestry in forest tree breeding

We examined gene models for two traits with and without antagonistic pleiotropy using a locus-based simulation model to investigate the effects of different population sizes, heritabilities and economic weights, using index selection, and index selection with optimum selection (OS), over 10 generations. Gene models included additive and dominance gene action, with equal and varying initial allele frequencies with and without pleiotropy for a fixed level of resources (i.e. founder sizes each generation of 40, 80 and 160 with progeny arrays that totaled 800 per generation). Pleiotropy (with an initial r _g of −0.5), reduced gain by ~8–10% when heritabilities for both traits were the same (0.2), relative to non-pleiotropic cases. When traits had different heritabilities (i.e. 0.2 and 0.4), gains in the lower heritability trait were substantially lower, especially with pleiotropy present. In general, OS with slightly larger population sizes could offset losses in gain, but rarely overrode the large effects of different heritabilities or economic weights. Pleiotropy increased response variance among traits, which was magnified when heritabilities were different. Identifying an appropriate weight on relatedness in the OS process is important to manage coancestry expectations around the loss of alleles (or fixation of recessive alleles) and to minimise response variance. The dynamics of selection intensity, drift, rate of coancestry build-up, response variance, etc. are complex for multi-trait selection; however, a few economically viable strategies could reduce the adverse effects of selecting against genetic correlations without drastically impairing gain.     

Effects of Mutation on Selection Limits in Finite Populations with Multiple Alleles

The ultimate response to directional selection (i.e., the selection limit) under recurrent mutation is analyzed by a diffusion approximation for a population in which there are k possible alleles at a locus. The limit mainly depends on two scaled parameters S (= 4Ns sigma a) and theta (= 4Nu) and k, the number of alleles, where N is the effective population size, u is the mutation rate, s is the selection coefficient, and sigma 2a is the variance of allelic effects. When the selection pressure is weak (S less than or equal to 0.5), the limit is given approximately by 2S sigma a[1 - (1 + c2)/k]/(theta + 1) for additive effects of alleles, where c is the coefficient of variation of the mutation rates among alleles. For strong selection, other approximations are devised to analyze the limit in different parameter regions. The effect of mutation on selection limits largely relies on the potential of mutation to introduce new and better alleles into the population. This effect is, however, bounded under the present model. Unequal mutation rates among alleles tend to reduce the selection limit, and can have a substantial effect only for small numbers of alleles and weak selection. The selection limit decreases as the mutation rate increases.     

The conditional ancestral selection graph with strong balancing selection

Using a heuristic separation-of-time-scales argument, we describe the behavior of the conditional ancestral selection graph with very strong balancing selection between a pair of alleles. In the limit as the strength of selection tends to infinity, we find that the ancestral process converges to a neutral structured coalescent, with two subpopulations representing the two alleles and mutation playing the role of migration. This agrees with a previous result of Kaplan et al., obtained using a different approach. We present the results of computer simulations to support our heuristic mathematical results. We also present a more rigorous demonstration that the neutral conditional ancestral process converges to the Kingman coalescent in the limit as the mutation rate tends to infinity.     

Correlation of heterozygosity and the number of alleles in different frequency classes

Analytic expressions for the expectations and variance of the number of alleles with gene frequencies in a specified class are derived in the entire population as well as in a random sample of genes drawn from the population. The correlation of this quantity with heterozygosity at the locus is also obtained. The derivations are given in details for a steady state population of finite size under the infinite allele model of selectively neutral alleles. The results are extended to include weak selection pressures and non-stationarity of the population. The relevance of the correlation of heterozygosity and the number of rare alleles in connection with the neutralist-selectionist controversy is also discussed.     

Maintenance of Genetic Variability under the Joint Effect of Mutation, Selection and Random Drift

Formulae are developed for the distribution of allele frequencies (the frequency spectrum), the mean number of alleles in a sample, and the mean and variance of heterozygosity under mutation pressure and under either genic or recessive selection. Numerical computations are carried out by using these formulae and Watterson's (1977) formula for the distribution of allele frequencies under overdominant selection. The following properties are observed: (1) The effect of selection on the distribution of allele frequencies is slight when 4Ns 相似文献   

Allelic Spectra of Risk SNPs Are Different for Environment/Lifestyle Dependent versus Independent Diseases

Genome-wide association studies (GWAS) have generated sufficient data to assess the role of selection in shaping allelic diversity of disease-associated SNPs. Negative selection against disease risk variants is expected to reduce their frequencies making them overrepresented in the group of minor (<50%) alleles. Indeed, we found that the overall proportion of risk alleles was higher among alleles with frequency <50% (minor alleles) compared to that in the group of major alleles. We hypothesized that negative selection may have different effects on environment (or lifestyle)-dependent versus environment (or lifestyle)-independent diseases. We used an environment/lifestyle index (ELI) to assess influence of environmental/lifestyle factors on disease etiology. ELI was defined as the number of publications mentioning “environment” or “lifestyle” AND disease per 1,000 disease-mentioning publications. We found that the frequency distributions of the risk alleles for the diseases with strong environmental/lifestyle components follow the distribution expected under a selectively neutral model, while frequency distributions of the risk alleles for the diseases with weak environmental/lifestyle influences is shifted to the lower values indicating effects of negative selection. We hypothesized that previously selectively neutral variants become risk alleles when environment changes. The hypothesis of ancestrally neutral, currently disadvantageous risk-associated alleles predicts that the distribution of risk alleles for the environment/lifestyle dependent diseases will follow a neutral model since natural selection has not had enough time to influence allele frequencies. The results of our analysis suggest that prediction of SNP functionality based on the level of evolutionary conservation may not be useful for SNPs associated with environment/lifestyle dependent diseases.     

Maintenance of Genetic Variability under the Pressure of Neutral and Deleterious Mutations in a Finite Population

In order to assess the effect of deleterious mutations on various measures of genic variation, approximate formulas have been developed for the frequency spectrum, the mean number of alleles in a sample, and the mean homozygosity; in some particular cases, exact formulas have been obtained. The assumptions made are that two classes of mutations exist, neutral and deleterious, and that selection is strong enough to keep deleterious alleles in low frequencies, the mode of selection being either genic or recessive. The main findings are: (1) If the expected value (q) of the sum of the frequencies of deleterious alleles is about 10% or less, then the presence of deleterious alleles causes only a minor reduction in the mean number of neutral alleles in a sample, as compared to the case of q = 0. Also, the low- and intermediate-frequency parts of the frequency spectrum of neutral alleles are little affected by the presence of deleterious alleles, though the high-frequency part may be changed drastically. (2) The contribution of deleterious mutations to the expected total number of alleles in a sample can be quite large even if q is only 1 or 2%. (3) The mean homozygosity is roughly equal to (1--2q)/(1 + theta 1), where theta 1 is twice the number of new neutral mutations occurring in each generation in the total population. Thus, deleterious mutations increase the mean heterozygosity by about 2q/(1 + theta 1). The present results have been applied to study the controversial problem of how deleterious mutations may affect the testing of the neutral mutation hypothesis.     

The Coalescent Process in Models with Selection

Statistical properties of the process describing the genealogical history of a random sample of genes are obtained for a class of population genetics models with selection. For models with selection, in contrast to models without selection, the distribution of this process, the coalescent process, depends on the distribution of the frequencies of alleles in the ancestral generations. If the ancestral frequency process can be approximated by a diffusion, then the mean and the variance of the number of segregating sites due to selectively neutral mutations in random samples can be numerically calculated. The calculations are greatly simplified if the frequencies of the alleles are tightly regulated. If the mutation rates between alleles maintained by balancing selection are low, then the number of selectively neutral segregating sites in a random sample of genes is expected to substantially exceed the number predicted under a neutral model.     

How Informative Is Wright's Estimator of the Number of Genes Affecting a Quantitative Character?

S. Wright suggested an estimator, m, of the number of loci, m, contributing to the difference in a quantitative character between two differentiated populations, which is calculated from the phenotypic means and variances in the two parental populations and their F1 and F2 hybrids. The same method can also be used to estimate m contributing to the genetic variance within a single population, by using divergent selection to create differentiated lines from the base population. In this paper we systematically examine the utility and problems of this technique under the influences of unequal allelic effects and initial allele frequencies, and linkage, which are known to lead m to underestimate m. In addition, we examine the effects of population size and selection intensity during the generations of selection. During selection, the estimator m rapidly approaches its expected value at the selection limit. With reasonable assumptions about unequal allelic effects and initial allele frequencies, the expected value of m without linkage is likely to be on the order of one-third of the number of genes. The estimates suffer most seriously from linkage. The practical maximum expectation of m is just about the number of chromosomes, considerably less than the "recombination index" which has been assumed to be the upper limit. The estimates are also associated with large sampling variances. An estimator of the variance of m derived by R. Lande substantially underestimates the actual variance. Modifications to the method can ameliorate some of the problems. These include using F3 or later generation variances or the genetic variance in the base population, and replicating the experiments and estimation procedure. However, even in the best of circumstances, information from m is very limited and can be misleading.     

Natural selection affects multiple aspects of genetic variation at putatively neutral sites across the human genome

A major question in evolutionary biology is how natural selection has shaped patterns of genetic variation across the human genome. Previous work has documented a reduction in genetic diversity in regions of the genome with low recombination rates. However, it is unclear whether other summaries of genetic variation, like allele frequencies, are also correlated with recombination rate and whether these correlations can be explained solely by negative selection against deleterious mutations or whether positive selection acting on favorable alleles is also required. Here we attempt to address these questions by analyzing three different genome-wide resequencing datasets from European individuals. We document several significant correlations between different genomic features. In particular, we find that average minor allele frequency and diversity are reduced in regions of low recombination and that human diversity, human-chimp divergence, and average minor allele frequency are reduced near genes. Population genetic simulations show that either positive natural selection acting on favorable mutations or negative natural selection acting against deleterious mutations can explain these correlations. However, models with strong positive selection on nonsynonymous mutations and little negative selection predict a stronger negative correlation between neutral diversity and nonsynonymous divergence than observed in the actual data, supporting the importance of negative, rather than positive, selection throughout the genome. Further, we show that the widespread presence of weakly deleterious alleles, rather than a small number of strongly positively selected mutations, is responsible for the correlation between neutral genetic diversity and recombination rate. This work suggests that natural selection has affected multiple aspects of linked neutral variation throughout the human genome and that positive selection is not required to explain these observations.     

Gametic Disequilibrium Measures: Proceed with Caution

Five different measures of gametic disequilibrium in current use and a new one based on R. C. Lewontin's D', are examined and compared. All of them, except the measure based on Lewontin's D', are highly dependent upon allelic frequencies, including four measures that are normalized in some manner. In addition, the measures suggested by A. H. D. Brown, M. F. Feldman and E. Nevo, and T. Ohta can have negative values when there is maximum disequilibrium and have rates of decay in infinite populations that are a function of the initial gametic array. The variances were large for all the measures in samples taken from populations at equilibrium under neutrality, with the measure based on D' having the lowest variance. In these samples, three of the measures were highly correlated, D2, D (equal to the correlation coefficient when there are two alleles at each locus) and the measure X(2) of Brown et al. Using frequency-dependent measures may result in mistaken conclusions, a fact illustrated by discussion of studies inferring recombinational hot spots and the effects of population bottlenecks from disequilibrium values.     

A finite locus effect diffusion model for the evolution of a quantitative trait

A diffusion model is constructed for the joint distribution of absolute locus effect sizes and allele frequencies for loci contributing to an additive quantitative trait under selection in a haploid, panmictic population. The model is designed to approximate a discrete model exactly in the limit as both population size and the number of loci affecting the trait tend to infinity. For the case when all loci have the same absolute effect size, formal multiple-timescale asymptotics are used to predict the long-time response of the population trait mean to selection. For the case where loci can take on either of two distinct effect sizes, not necessarily with equal probability, numerical solutions of the system indicate that response to selection of a quantitative trait is insensitive to the variability of the distribution of effect sizes when mutation is negligible.     

Genetic variance in the F2 generation of divergently selected parents

 Either by selective breeding for population divergence or by using natural population differences, F₂ and advanced generation hybrids can be developed with high variances. We relate the size of the genetic variance to the population divergence based on a forward and backward mutation model at a locus with two alleles with additive gene action. The effects of population size and initial gene frequency are also explored. Larger parental population sizes increase the F₂ genetic variance if the initial probability distribution is uniform or U-shaped. However, population size has the opposite effect if the initial distribution of gene frequencies is skewed such as it would be with newly arriving alleles. These alleles contribute to the genetic variance sooner when the selection pressure is higher or when the effective population size is smaller. Received: 5 April 1998 / Accepted: 22 April 1998     

The effect of linkage and population size on inbreeding depression due to mutational load.

Using a stochastic model of a finite population in which there is mutation to partially recessive detrimental alleles at many loci, we study the effects of population size and linkage between the loci on the population mean fitness and inbreeding depression values. Although linkage between the selected loci decreases the amount of inbreeding depression, neither population size nor recombination rate have strong effects on these quantities, unless extremely small values are assumed. We also investigate how partial linkage between the loci that determine fitness affects the invasion of populations by alleles at a modifier locus that controls the selfing rate. In most of the cases studied, the direction of selection on modifiers was consistent with that found in our previous deterministic calculations. However, there was some evidence that linkage between the modifier locus and the selected loci makes outcrossing less likely to evolve; more losses of alleles promoting outcrossing occurred in runs with linkage than in runs with free recombination. We also studied the fate of neutral alleles introduced into populations carrying detrimental mutations. The times to loss of neutral alleles introduced at low frequency were shorter than those predicted for alleles in the absence of selected loci, taking into account the reduction of the effective population size due to inbreeding. Previous studies have been confined to outbreeding populations, and to alleles at frequencies close to one-half, and have found an effect in the opposite direction. It therefore appears that associations between neutral and selected loci may produce effects that differ according to the initial frequencies of the neutral alleles.     

Predictions of patterns of response to artificial selection in lines derived from natural populations

The pattern of response to artificial selection on quantitative traits in laboratory populations can tell us something of the genetic architecture in the natural population from which they were derived. We modeled artificial selection in samples drawn from natural populations in which variation had been maintained by recurrent mutation, with genes having an effect on the trait, which was subject to real stabilizing selection, and a pleitropic effect on fitness (the joint-effect model). Natural selection leads to an inverse correlation between effects and frequencies of genes, such that the frequency distribution of genes increasing the trait has an extreme U-shape. In contrast to the classical infinitesimal model, an early accelerated response and a larger variance of response among replicates were predicted. However, these are reduced if the base population has been maintained in the laboratory for some generations by random sampling prior to artificial selection. When multiple loci and linkage are also taken into account, the gametic disequilibria generated by the Bulmer and Hill-Robertson effects are such that little or no increase in variance and acceleration of response in early generations of artificial selection are predicted; further, the patterns of predicted responses for the joint-effect model now become close to those of the infinitesimal model. Comparison with data from laboratory selection experiments shows that, overall, the analysis did not provide clear support for the joint-effect model or a clear case for rejection.     

ANTAGONISTIC VERSUS NONANTAGONISTIC MODELS OF BALANCING SELECTION: CHARACTERIZING THE RELATIVE TIMESCALES AND HITCHHIKING EFFECTS OF PARTIAL SELECTIVE SWEEPS

Antagonistically selected alleles‐–those with opposing fitness effects between sexes, environments, or fitness components‐–represent an important component of additive genetic variance in fitness‐related traits, with stably balanced polymorphisms often hypothesized to contribute to observed quantitative genetic variation. Balancing selection hypotheses imply that intermediate‐frequency alleles disproportionately contribute to genetic variance of life‐history traits and fitness. Such alleles may also associate with population genetic footprints of recent selection, including reduced genetic diversity and inflated linkage disequilibrium at linked, neutral sites. Here, we compare the evolutionary dynamics of different balancing selection models, and characterize the evolutionary timescale and hitchhiking effects of partial selective sweeps generated under antagonistic versus nonantagonistic (e.g., overdominant and frequency‐dependent selection) processes. We show that the evolutionary timescales of partial sweeps tend to be much longer, and hitchhiking effects are drastically weaker, under scenarios of antagonistic selection. These results predict an interesting mismatch between molecular population genetic and quantitative genetic patterns of variation. Balanced, antagonistically selected alleles are expected to contribute more to additive genetic variance for fitness than alleles maintained by classic, nonantagonistic mechanisms. Nevertheless, classical mechanisms of balancing selection are much more likely to generate strong population genetic signatures of recent balancing selection.     

Perturbation-Reperturbation Test of Selection Vs. Hitchhiking of the Two Major Alleles of Esterase-5 in Drosophila Pseudoobscura

A perturbation-reperturbation tests selective neutrality of 100/100/100/100/100 and 106/100/100/100/100, the two most common alleles at the highly polymorphic X-linked locus Esterase-5 in Drosophila pseudoobscura. A total of 22 replicate populations are set up in cages, 11 start at a high frequency of 76% (U) and 11 at a low frequency of 21% (N) of the 106 allele. Allele frequencies change directionally and decrease in both U and N populations as groups and reach equilibria of 60 and 14%, respectively, after 200-300 days. These changes suggest natural selection. A hypothesis of balancing selection accounts for the pattern and predicts a dynamic equilibrium. A rival neutral hypothesis accounts for the pattern equally well by postulating hitchhiking and breakup of linkage leaving the Est-5 variants to drift at neutral equilibria. A reperturbation of allele frequencies in each population, creating 22 additional reperturbed populations EN and EU, with the original populations as controls, directly addresses the question of balancing selection or hitchhiking and breakup of linkage effects. Allele frequencies do not change directionally among the reperturbed populations as a group. The hypothesis of balancing selection is rejected in favor of the hypothesis of initial hitchhiking and dissipated linkage effects. The power of the experimental design to detect selection is studied by simulation. Within the limits of power set by the design, it is concluded that the 100 and 106 are iso-fitness alleles of Est-5 under the environmental conditions of the laboratory populations. The requirements of a method of perturbation and reperturbation are discussed.     

Allele frequencies with genic selection

The structure of the limit point process of the ordered allele frequencies in the stationary distribution of a K-allele diffusion model with mutation and genic selection is studied. This leads to a formula for expectations of functions of the allele frequencies in terms of expectations in the neutral infinite alleles model.     

Patterns of neutral diversity under general models of selective sweeps

Two major sources of stochasticity in the dynamics of neutral alleles result from resampling of finite populations (genetic drift) and the random genetic background of nearby selected alleles on which the neutral alleles are found (linked selection). There is now good evidence that linked selection plays an important role in shaping polymorphism levels in a number of species. One of the best-investigated models of linked selection is the recurrent full-sweep model, in which newly arisen selected alleles fix rapidly. However, the bulk of selected alleles that sweep into the population may not be destined for rapid fixation. Here we develop a general model of recurrent selective sweeps in a coalescent framework, one that generalizes the recurrent full-sweep model to the case where selected alleles do not sweep to fixation. We show that in a large population, only the initial rapid increase of a selected allele affects the genealogy at partially linked sites, which under fairly general assumptions are unaffected by the subsequent fate of the selected allele. We also apply the theory to a simple model to investigate the impact of recurrent partial sweeps on levels of neutral diversity and find that for a given reduction in diversity, the impact of recurrent partial sweeps on the frequency spectrum at neutral sites is determined primarily by the frequencies rapidly achieved by the selected alleles. Consequently, recurrent sweeps of selected alleles to low frequencies can have a profound effect on levels of diversity but can leave the frequency spectrum relatively unperturbed. In fact, the limiting coalescent model under a high rate of sweeps to low frequency is identical to the standard neutral model. The general model of selective sweeps we describe goes some way toward providing a more flexible framework to describe genomic patterns of diversity than is currently available.     

Adaptation of Drosophila to a novel laboratory environment reveals temporally heterogeneous trajectories of selected alleles

The genomic basis of adaptation to novel environments is a fundamental problem in evolutionary biology that has gained additional importance in the light of the recent global change discussion. Here, we combined laboratory natural selection (experimental evolution) in Drosophila melanogaster with genome‐wide next generation sequencing of DNA pools (Pool‐Seq) to identify alleles that are favourable in a novel laboratory environment and traced their trajectories during the adaptive process. Already after 15 generations, we identified a pronounced genomic response to selection, with almost 5000 single nucleotide polymorphisms (SNP; genome‐wide false discovery rates < 0.005%) deviating from neutral expectation. Importantly, the evolutionary trajectories of the selected alleles were heterogeneous, with the alleles falling into two distinct classes: (i) alleles that continuously rise in frequency; and (ii) alleles that at first increase rapidly but whose frequencies then reach a plateau. Our data thus suggest that the genomic response to selection can involve a large number of selected SNPs that show unexpectedly complex evolutionary trajectories, possibly due to nonadditive effects.