The average frequency of private alleles in a partially isolated population

An analytic model is developed to explore the relationship between gene flow, selection, and genetic drift. We assume that a single copy of a mutant allele appears in a finite, partially isolated population and allow for the effects of immigration, genic selection, and mutation on the frequency of the mutant. Our concern is with the distribution of the mutant's frequency before it either is lost from the population or emigrates. Before either of these events, the allele will be a “private allele” and would be found in only one of several populations in a larger collection. Slatkin [(1985) Evolution 39, 53–65] found several simple properties of private alleles in his simulations. We use the method developed by Karlin and Tavaré [(1980) Genet. Res. 37, 33–46; (1981a), Theor. Pop. Biol. 19, 187–214; (1981b) Theor. Pop. Biol. 19, 215–229] for a model similar to ours to obtain a diffusion equation with a “killing term” and obtain the mean and variance of the mutant's frequency and its expected frequency in samples of a specified size. There is only fair agreement between the analytic results from this model and those from Slatkin's (loc. cit.) simulations. The rescaling method used to obtain the results indicates that if emigration is relatively frequent, the distribution of rare alleles is governed largely by the balance between genetic drift and emigration, with selection, mutation, and immigration playing a lesser role.     

Statistical Mechanics and the Evolution of Polygenic Quantitative Traits

The evolution of quantitative characters depends on the frequencies of the alleles involved, yet these frequencies cannot usually be measured. Previous groups have proposed an approximation to the dynamics of quantitative traits, based on an analogy with statistical mechanics. We present a modified version of that approach, which makes the analogy more precise and applies quite generally to describe the evolution of allele frequencies. We calculate explicitly how the macroscopic quantities (i.e., quantities that depend on the quantitative trait) depend on evolutionary forces, in a way that is independent of the microscopic details. We first show that the stationary distribution of allele frequencies under drift, selection, and mutation maximizes a certain measure of entropy, subject to constraints on the expectation of observable quantities. We then approximate the dynamical changes in these expectations, assuming that the distribution of allele frequencies always maximizes entropy, conditional on the expected values. When applied to directional selection on an additive trait, this gives a very good approximation to the evolution of the trait mean and the genetic variance, when the number of mutations per generation is sufficiently high (4Nμ > 1). We show how the method can be modified for small mutation rates (4Nμ → 0). We outline how this method describes epistatic interactions as, for example, with stabilizing selection.     

Selection responses of means and inbreeding depression for female fecundity in Drosophila melanogaster suggest contributions from intermediate-frequency alleles to quantitative trait variation

The extent to which quantitative trait variability is caused by rare alleles maintained by mutation, versus intermediate-frequency alleles maintained by balancing selection, is an unsolved problem of evolutionary genetics. We describe the results of an experiment to examine the effects of selection on the mean and extent of inbreeding depression for early female fecundity in Drosophila melanogaster. Theory predicts that rare, partially recessive deleterious alleles should cause a much larger change in the effect of inbreeding than in the mean of the outbred population, with the change in inbreeding effect having an opposite sign to the change in mean. The present experiment fails to support this prediction, suggesting that intermediate-frequency alleles contribute substantially to genetic variation in early fecundity.     

Limited evidence that cancer susceptibility regions are preferential targets for somatic mutation

BackgroundGenome wide-association studies have successfully identified several hundred independent loci harboring common cancer susceptibility alleles that are distinct from the more than 110 cancer predisposition genes. The latter are generally characterized by disruptive mutations in coding genes that have been established as ‘drivers’ of cancer in large somatic sequencing studies. We set out to determine whether, similarly, common cancer susceptibility loci map to genes that have altered frequencies of mutation.ResultsIn our analysis of the intervals defined by the cancer susceptibility markers, we observed that cancer susceptibility regions have gene mutation frequencies comparable to background mutation frequencies. Restricting analyses to genes that have been determined to be pleiotropic across cancer types, genes affected by expression quantitative trait loci, or functional genes indicates that most cancer susceptibility genes classified into these subgroups do not display mutation frequencies that deviate from those expected. We observed limited evidence that cancer susceptibility regions that harbor common alleles with small estimated effect sizes are preferential targets for altered somatic mutation frequencies.ConclusionsOur findings suggest a complex interplay between germline susceptibility and somatic mutation, underscoring the cumulative effect of common variants on redundant pathways as opposed to driver genes. Complex biological pathways and networks likely link these genetic features of carcinogenesis, particularly as they relate to distinct polygenic models for each cancer type.     

The Evolution of Recombination: Removing the Limits to Natural Selection

One of the oldest hypotheses for the advantage of recombination is that recombination allows beneficial mutations that arise in different individuals to be placed together on the same chromosome. Unless recombination occurs, one of the beneficial alleles is doomed to extinction, slowing the rate at which adaptive mutations are incorporated within a population. We model the effects of a modifier of recombination on the fixation probability of beneficial mutations when beneficial alleles are segregating at other loci. We find that modifier alleles that increase recombination do increase the fixation probability of beneficial mutants and subsequently hitchhike along as the mutants rise in frequency. The strength of selection favoring a modifier that increases recombination is proportional to λ(2)Sδr/r when linkage is tight and λ(2)S(3)δ r/N when linkage is loose, where λ is the beneficial mutation rate per genome per generation throughout a population of size N, S is the average mutant effect, r is the average recombination rate, and δr is the amount that recombination is modified. We conclude that selection for recombination will be substantial only if there is tight linkage within the genome or if many loci are subject to directional selection as during periods of rapid evolutionary change.     

Selection against genetic defects in conservation schemes while controlling inbreeding

We studied different genetic models and evaluation systems to select against a genetic disease with additive, recessive or polygenic inheritance in genetic conservation schemes. When using optimum contribution selection with a restriction on the rate of inbreeding (ΔF) to select against a disease allele, selection directly on DNA-genotypes is, as expected, the most efficient strategy. Selection for BLUP or segregation analysis breeding value estimates both need 1–2 generations more to halve the frequency of the disease allele, while these methods do not require knowledge of the disease mutation at the DNA level. BLUP and segregation analysis methods were equally efficient when selecting against a disease with single gene or complex polygene inheritance, i.e. knowledge about the mode of inheritance of the disease was not needed for efficient selection against the disease. Smaller schemes or schemes with a more stringent restriction on ΔF needed more generations to halve the frequency of the disease alleles or the fraction of diseased animals. Optimum contribution selection maintained ΔF at its predefined level, even when selection of females was at random. It is argued that in the investigated small conservation schemes with selection against a genetic defect, control of ΔF is very important.     

Mutating away from your enemies: The evolution of mutation rate in a host–parasite system

The rate at which mutations occur in nature is itself under natural selection. While a general reduction of mutation rates is advantageous for species inhabiting constant environments, higher mutation rates can be advantageous for those inhabiting fluctuating environments that impose on-going directional selection. Analogously, species involved in antagonistic co-evolutionary arms races, such as hosts and parasites, can also benefit from higher mutation rates. We use modifier theory, combined with simulations, to investigate the evolution of mutation rate in such a host–parasite system. We derive an expression for the evolutionary stable mutation rate between two alleles, each of whose fitness depends on the current genetic composition of the other species. Recombination has been shown to weaken the strength of selection acting on mutation modifiers, and accordingly, we find that the evolutionarily attracting mutation rate is lower when recombination between the selected and the modifier locus is high. Cyclical dynamics are potentially commonplace for loci governing antagonistic species interactions. We characterize the parameter space where such cyclical dynamics occur and show that the evolution of large mutation rates tends to inhibit cycling and thus eliminates further selection on modifiers of the mutation rate. We then find using computer simulations that stochastic fluctuations in finite populations can increase the size of the region where cycles occur, creating selection for higher mutation rates. We finally use simulations to investigate the model behaviour when there are more than two alleles, finding that the region where cycling occurs becomes smaller and the evolutionarily attracting mutation rate lower when there are more alleles.     

Identification of rare alleles and their carriers using compressed se(que)nsing

Identification of rare variants by resequencing is important both for detecting novel variations and for screening individuals for known disease alleles. New technologies enable low-cost resequencing of target regions, although it is still prohibitive to test more than a few individuals. We propose a novel pooling design that enables the recovery of novel or known rare alleles and their carriers in groups of individuals. The method is based on a Compressed Sensing (CS) approach, which is general, simple and efficient. CS allows the use of generic algorithmic tools for simultaneous identification of multiple variants and their carriers. We model the experimental procedure and show via computer simulations that it enables the recovery of rare alleles and their carriers in larger groups than were possible before. Our approach can also be combined with barcoding techniques to provide a feasible solution based on current resequencing costs. For example, when targeting a small enough genomic region (∼100 bp) and using only ∼10 sequencing lanes and ∼10 distinct barcodes per lane, one recovers the identity of 4 rare allele carriers out of a population of over 4000 individuals. We demonstrate the performance of our approach over several publicly available experimental data sets.     

The Pattern of Neutral Molecular Variation under the Background Selection Model

Stochastic simulations of the infinite sites model were used to study the behavior of genetic diversity at a neutral locus in a genomic region without recombination, but subject to selection against deleterious alleles maintained by recurrent mutation (background selection). In large populations, the effect of background selection on the number of segregating sites approaches the effct on nucleotide site diversity, i.e., the reduction in genetic variability caused by background selection resembles that caused by a simple reduction in effective population size. We examined, by coalescence-based methods, the power of several tests for the departure from neutral expectation of the frequency spectra of alleles in samples from randomly mating populations (TAJIMA's, FU and LI's, and WATTERSON's tests). All of the tests have low power unless the selection against mutant alleles is extremely weak. In Drosophila, significant TAJIMA's tests are usually not obtained with empirical data sets from loci in genomic regions with restricted recombination frequencies and that exhibit low genetic diversity. This is consistent with the operation of background selection as opposed to selective sweeps. It remains to be decided whether background selection is sufficient to explain the observed extent of reduction in diversity in regions of restricted recombination.     

Detection and quantification of in vitro-culture induced chimerism using simple sequence repeat (SSR) analysis in <Emphasis Type="Italic">Theobroma cacao</Emphasis> (L.)

Mutation rates are often elevated in plants regenerated from in vitro culture, giving rise to so-called somaclonal variation. Detailed characterisation of mutation profiles that arise during culture should improve our understanding of processes influencing mutation and allow the selection of protocols yielding the fewest/least severe changes. Somatic mutations will usually produce genetic chimeras where unchanged alleles are retained by some cells. Such chimeras are difficult to detect but likely to form a significant proportion of any regenerant population. We present a simple protocol that enables the provisional diagnosis of both homogenous and chimeric mutants among large regenerant populations, together with a semi-quantitative means of estimating the proportion of mutant cells. The assay exploits consistent differential amplification of alternate simple sequence repeat alleles at heterozygous loci. Calibration of the relative amplification of alleles from two genotypes—and the synthetic chimeras created from them—revealed a strong linear relationship between peak heights representing alternate alleles following capillary electrophoresis. The assay predicts chimeric composition to a reasonable level of confidence (±5%) so long as the infrequent allele exceeds 15% of the template. The system was applied to 233 regenerants of cocoa somatic embryogenesis and identified 72 (31%) putative chimeric mutants for slippage mutation or allele loss across two loci.     

Persistence of Common Alleles in Two Related Populations or Species

Mathematical studies are conducted on three problems that arise in molecular population genetics. (1) The time required for a particular allele to become extinct in a population under the effects of mutation, selection, and random genetic drift is studied. In the absence of selection, the mean extinction time of an allele with an initial frequency close to 1 is of the order of the reciprocal of the mutation rate when 4Nv << 1, where N is the effective population size and v is the mutation rate per generation. Advantageous mutations reduce the extinction time considerably, whereas deleterious mutations increase it tremendously even if the effect on fitness is very slight. (2) Mathematical formulae are derived for the distribution and the moments of extinction time of a particular allele from one or both of two related populations or species under the assumption of no selection. When 4Nv << 1, the mean extinction time is about half that for a single population, if the two populations are descended from a common original stock. (3) The expected number as well as the proportion of common neutral alleles shared by two related species at the tth generation after their separation are studied. It is shown that if 4Nv is small, the two species are expected to share a high proportion of common alleles even 4N generations after separation. In addition to the above mathematical studies, the implications of our results for the common alleles at protein loci in related Drosophila species and for the degeneration of unused characters in cave animals are discussed.     

Correcting Coalescent Analyses for Panel-Based SNP Ascertainment

Single-nucleotide polymorphism (SNP) data are routinely obtained by sequencing a region of interest in a small panel, constructing a chip with probes specific to sites found to vary in the panel, and using the chip to assay subsequent samples. The size of the chip is often reduced by removing low-frequency alleles from the set of SNPs. Using coalescent estimation of the scaled population size parameter, Θ, as a test case, we demonstrate the loss of information inherent in this procedure and develop corrections for coalescent analysis of SNPs obtained via a panel. We show that more accurate Θ-estimates can be recovered if the panel size is known, but at considerable computational cost as the panel individuals must be explicitly modeled in the analysis. We extend this technique to apply to the case where rare alleles have been omitted from the SNP panel. We find that when appropriate corrections for panel ascertainment and rare-allele omission are used, the biases introduced by ascertainment are largely correctable, but recovered estimates are less accurate than would be obtained with fully sequenced data. This method is then applied to recombinant multiple population data to investigate the effects of recombination and migration on the estimate of Θ.     

Populations adapt to fluctuating selection using derived and ancestral allelic diversity

Populations can adapt to changing environments by using allelic diversity, yet whether diversity is recently derived or ancestral is often debated. Although evolution could productively use both types of diversity in a changing environment, their relative frequency has not been quantified. We address this question experimentally using budding yeast strains that harbor a tandem repeat containing URA3 gene, which we expose to cyclical selection and counterselection. We characterize and quantify the dynamics of frameshift events in the URA3 gene in eight populations over 12 cycles of selection and find that ancestral alleles account for 10–20% of all adaptive events. Using a general model of fluctuating selection, we determine how these results depend on mutation rates, population sizes, and fluctuation timescales. We quantify the contribution of derived alleles to the adaptation process using the de novo mutation rate along the population's ancestral lineage, a novel measure that is applicable in a wide range of settings. We find that the adaptive dynamics undergoes a sharp transition from selection on ancestral alleles to selection on derived alleles as fluctuation timescales increase. Our results demonstrate that fluctuations can select between different modes of adaptation over evolutionary timescales.     

SOCIAL CAUSES OF CORRELATIONAL SELECTION AND THE RESOLUTION OF A HERITABLE THROAT COLOR POLYMORPHISM IN A LIZARD

Abstract When selection acts on social or behavioral traits, the fitness of an individual depends on the phenotypes of its competitors. Here, we describe methods and statistical inference for measuring natural selection in small social groups. We measured selection on throat color alleles that arises from microgeographic variation in allele frequency at natal sites of side‐blotched lizards (Uta stansburiana). Previous game‐theoretic analysis indicates that two color morphs of female side‐blotched lizards are engaged in an offspring quantity‐quality game that promotes a density‐and frequency‐dependent cycle. Orange‐throated females are r‐strategists. They lay large clutches of small progeny, which have poor survival at high density, but good survival at low density. In contrast, yellow‐throated females are K‐strategists. They lay small clutches of large progeny, which have good survival at high density. We tested three predictions of the female game: (1) orange progeny should have a fitness advantage at low density; (2) correlational selection acts to couple color alleles and progeny size; and (3) this correlational selection arises from frequency‐dependent selection in which large hatchling size confers an advantage, but only when yellow alleles are rare. We also confirmed the heritability of color, and therefore its genetic basis, by producing progeny from controlled matings. A parsimonious cause of the high heritability is that three alleles (o, b, y) segregate as one genetic factor. We review the physiology of color formation to explain the possible genetic architecture of the throat color trait. Heritability of color was nearly additive in our breeding study, allowing us to compute a genotypic value for each individual and thus predict the frequency of progeny alleles released on 116 plots. Rather than study the fitness of individual progeny, we studied how the fitness of their color alleles varied with allele frequency on plots. We confirmed prediction 1: When orange alleles are present in female progeny, they have higher fitness at low density when compared to other alleles. Even though the difference in egg size of the female morphs was small (0.02 g), it led to knife‐edged survival effects for their progeny depending on local social context. Selection on hatchling survival was not only dependent on color alleles, but on a fitness interaction between color alleles and hatchling size, which confirmed prediction 2. Sire effects, which are not confounded by maternal phenotype, allowed us to resolve the frequency dependence of correlational selection on egg size and color alleles and thereby confirmed prediction 3. Selection favored large size when yellow sire alleles were rare, but small size when they were common. Correlational selection promotes the formation of a self‐reinforcing genetic correlation between the morphs and life‐history variation, which causes selection in the next density and frequency cycle to be exacerbated. We discuss general conditions for the evolution of self‐reinforcing genetic correlations that arise from social selection associated with frequency‐dependent sexual and natural selection.     

Rapid HIV-1 Disease Progression in Individuals Infected with a Virus Adapted to Its Host Population

HIV-1 escape from CTL is predictable based on the Human Leukocyte Antigen (HLA) class I alleles expressed by the host. As such, HIV-1 sequences circulating in a population of hosts will harbor escape mutations specific to the HLA alleles of that population. In theory, this should increase the frequency of escape mutation transmission to persons expressing the restricting HLA allele, thereby compromising host immunity to the incoming HIV-1 strain. However, the clinical impact of infection with HIV-1 containing immune escape mutations has not conclusively been demonstrated. Japan’s population features limited HLA diversity which is driving population-level HIV adaptation: for example, >60% of Japanese express HLA-A*24:02 and its associated Nef-Y135F escape mutation represents the population consensus. As such, Japan is an ideal population in which to examine this phenomenon. Here, we combine genetic and immunological analyses to identify A*24:02-positive individuals likely to have been infected with Y135F-containing HIV-1. Over a ~5 year follow-up, these individuals exhibited significantly lower CD4 counts compared to individuals inferred to have been infected with wild-type HIV-1. Our results support a significant negative clinical impact of pathogen adaptation to host pressures at the population level.     

The effect of isozyme selection on metric characters in an interspecific backcross of tomato — basis of an early screening procedure

Summary The extent of correlation was estimated between isozyme genotypes and the four widely segregating characters — leaf segment W/L ratio, stigma exsertion, fruit weight, and seed weight — in the first backcross of F₁ Lycopersicon esculentum x Solanum pennellii to the former parent. The inbred parents differ in their alleles at the 12 tested isozymic loci, which are known to mark a minimum of eight of the twelve tomato chromosomes. Based on the isozyme data, a mean heterozygosity value, ¯H, was calculated which estimates the proportion of pennillii alleles in each individual. Correlations between mean heterozygosity and observed levels of each quantitative trait were highly significant and positive or negative as expected from the relative parental values. Plants with the lowest mean heterozygosity — i.e., closest to the esculentum zymotype also had mean values closest to those of this parent amongst the whole backcross population for each of the quantitative traits.Bivariate and multiple regression analysis was used to evaluate the ability of isozymes vs diagnostic morphological characters to estimate the portion of recurrent parent genes carried in each backcross individual. The results suggest that isozyme data gives better estimates than single diagnostic morphological characters and approach the level obtained by combinations of three morphological traits. Since electrophoretic determinations are made on small seedlings, selection at that stage can effect great savings of space and effort by greatly deminishing the size of the population needed at maturity. As such, isozyme selection would precede morphological selection but not replace it, thus the predictive value of these biochemical markers as well as diagnostic morphological characters could be obtained.     

Can Evidence from Genome-Wide Association Studies and Positive Natural Selection Surveys Be Used to Evaluate the Thrifty Gene Hypothesis in East Asians?

Body fat deposition and distribution differ between East Asians and Europeans, and for the same level of obesity, East Asians are at higher risks of Type 2 diabetes (T2D) and other metabolic disorders. This observation has prompted the reclassifications of body mass index thresholds for the definitions of “overweight” and “obese” in East Asians. However, the question remains over what evolutionary mechanisms have driven the differences in adiposity morphology between two population groups that shared a common ancestor less than 80,000 years ago. The Thrifty Gene hypothesis has been suggested as a possible explanation, where genetic factors that allowed for efficient food-energy conversion and storage are evolutionarily favoured by conferring increased chances of survival and fertility. Here, we leveraged on the existing findings from genome-wide association studies and large-scale surveys of positive natural selection to evaluate whether there is currently any evidence to support the Thrifty Gene hypothesis. We first assess whether the existing genetic associations with obesity and T2D are located in genomic regions that are reported to be under positive selection, and if so, whether the risk alleles sit on the extended haplotype forms. In addition, we interrogate whether these risk alleles are the derived forms that differ from the ancestral alleles, and whether there is significant evidence of population differentiation at these SNPs between East Asian and European populations. Our systematic survey did not yield conclusive evidence to support the Thrifty Gene hypothesis as a possible explanation for the differences observed between East Asians and Europeans.     

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.     

Competition Between the Sperm of a Single Male Can Increase the Evolutionary Rate of Haploid Expressed Genes

The population genetic behavior of mutations in sperm genes is theoretically investigated. We modeled the processes at two levels. One is the standard population genetic process, in which the population allele frequencies change generation by generation, depending on the difference in selective advantages. The other is the sperm competition during each genetic transmission from one generation to the next generation. For the sperm competition process, we formulate the situation where a huge number of sperm with alleles A and B, produced by a single heterozygous male, compete to fertilize a single egg. This “minimal model” demonstrates that a very slight difference in sperm performance amounts to quite a large difference between the alleles’ winning probabilities. By incorporating this effect of paternity-sharing sperm competition into the standard population genetic process, we show that fierce sperm competition can enhance the fixation probability of a mutation with a very small phenotypic effect at the single-sperm level, suggesting a contribution of sperm competition to rapid amino acid substitutions in haploid-expressed sperm genes. Considering recent genome-wide demonstrations that a substantial fraction of the mammalian sperm genes are haploid expressed, our model could provide a potential explanation of rapid evolution of sperm genes with a wide variety of functions (as long as they are expressed in the haploid phase). Another advantage of our model is that it is applicable to a wide range of species, irrespective of whether the species is externally fertilizing, polygamous, or monogamous. The theoretical result was applied to mammalian data to estimate the selection intensity on nonsynonymous mutations in sperm genes.     

MHC allele frequency distributions under parasite-driven selection: A simulation model

Background  

The extreme polymorphism that is observed in major histocompatibility complex (MHC) genes, which code for proteins involved in recognition of non-self oligopeptides, is thought to result from a pressure exerted by parasites because parasite antigens are more likely to be recognized by MHC heterozygotes (heterozygote advantage) and/or by rare MHC alleles (negative frequency-dependent selection). The Ewens-Watterson test (EW) is often used to detect selection acting on MHC genes over the recent history of a population. EW is based on the expectation that allele frequencies under balancing selection should be more even than under neutrality. We used computer simulations to investigate whether this expectation holds for selection exerted by parasites on host MHC genes under conditions of heterozygote advantage and negative frequency-dependent selection acting either simultaneously or separately.