Ages,extinction times,and first passage probabilities for a multiallele diffusion model with irreversible mutation

We derive some new results for diffusion models in population genetics of the “infinite-alleles” type. Assuming present allelic frequencies known, we find expected values for times which may be interpreted either as the age of the kth oldest allele or the time to extinction of the “kth-to-last” allele to be lost. We also find some conditional expectations and probabilities related to the order of extinction or creation of the alleles. Computations illustrate the dependence of the expected times on the mutation rate.     

Determination of protein complex stoichiometry through multisignal sedimentation velocity experiments

Determination of the stoichiometry of macromolecular assemblies is fundamental to an understanding of how they function. Many different biophysical methodologies may be used to determine stoichiometry. In the past, both sedimentation equilibrium and sedimentation velocity analytical ultracentrifugation have been employed to determine component stoichiometries. Recently, a method of globally analyzing multisignal sedimentation velocity data was introduced by Schuck and coworkers. This global analysis removes some of the experimental inconveniences and inaccuracies that could occur in the previously used strategies. This method uses spectral differences between the macromolecular components to decompose the well-known c(s) distribution into component distributions c_k(s); that is, each component k has its own c_k(s) distribution. Integration of these distributions allows the calculation of the populations of each component in cosedimenting complexes, yielding their stoichiometry. In our laboratories, we have used this method extensively to determine the component stoichiometries of several protein-protein complexes involved in cytoskeletal remodeling, sugar metabolism, and host-pathogen interactions. The overall method is described in detail in this work, as are experimental examples and caveats.     

The Effects of Overdominance on Linkage in a Multilocus System

Computer simulations were performed with overdominant multiple alleles among tightly linked multiple loci under a multiplicative fitness model. The quantity X²/N(n — 1) was introduced as a new measure of linkage disequilibrium which, unlike previously available measures, can be applied to multiple allele models, where N is the sample size, and n is the number of alleles at the locus possessing fewest alleles. Simulations showed that (1) With multiple (three or four) alleles, the approach to stable disequilibrium is slower and the amount of disequilibrium established is weaker than in a two allele system. (2) The number of complementary chromosomes is a function of number of alleles and of population size. (3) As population size increases, the rate of the approach to stable disequilibrium is slower. (4) There is an optimum selection coefficient which minimizes the transient fixation probability of alleles when linkage is present. (5) The absence of linkage disequilibrium is in most cases not a practical method of testing the hypothesis of balancing selection of genetic polymorphisms because it depends strongly on population size in determining linkage disequilibria.     

A deterministic model of admixture and genetic introgression: the case of Neanderthal and Cro-Magnon

There is an ongoing debate in the field of human evolution about the possible contribution of Neanderthals to the modern human gene pool. To study how the Neanderthal private alleles may have spread over the genes of Homo sapiens, we propose a deterministic model based on recursive equations and ordinary differential equations. If the Neanderthal population was large compared to the Homo sapiens population at the beginning of the contact period, we show that genetic introgression should have been fast and complete meaning that most of the Neanderthal private alleles should be found in the modern human gene pool in case of ancient admixture. In order to test/reject ancient admixture from genome-wide data, we incorporate the model of genetic introgression into a statistical hypothesis-testing framework. We show that the power to reject ancient admixture increases as the ratio, at the time of putative admixture, of the population size of Homo sapiens over that of Neanderthal decreases. We find that the power to reject ancient admixture might be particularly low if the population size of Homo sapiens was comparable to the Neanderthal population size.     

Soft Selective Sweeps in Complex Demographic Scenarios

Adaptation from de novo mutation can produce so-called soft selective sweeps, where adaptive alleles of independent mutational origin sweep through the population at the same time. Population genetic theory predicts that such soft sweeps should be likely if the product of the population size and the mutation rate toward the adaptive allele is sufficiently large, such that multiple adaptive mutations can establish before one has reached fixation; however, it remains unclear how demographic processes affect the probability of observing soft sweeps. Here we extend the theory of soft selective sweeps to realistic demographic scenarios that allow for changes in population size over time. We first show that population bottlenecks can lead to the removal of all but one adaptive lineage from an initially soft selective sweep. The parameter regime under which such “hardening” of soft selective sweeps is likely is determined by a simple heuristic condition. We further develop a generalized analytical framework, based on an extension of the coalescent process, for calculating the probability of soft sweeps under arbitrary demographic scenarios. Two important limits emerge within this analytical framework: In the limit where population-size fluctuations are fast compared to the duration of the sweep, the likelihood of soft sweeps is determined by the harmonic mean of the variance effective population size estimated over the duration of the sweep; in the opposing slow fluctuation limit, the likelihood of soft sweeps is determined by the instantaneous variance effective population size at the onset of the sweep. We show that as a consequence of this finding the probability of observing soft sweeps becomes a function of the strength of selection. Specifically, in species with sharply fluctuating population size, strong selection is more likely to produce soft sweeps than weak selection. Our results highlight the importance of accurate demographic estimates over short evolutionary timescales for understanding the population genetics of adaptation from de novo mutation.     

Pragmatic Perspective on Conservation Genetics and Demographic History of the Last Surviving Population of Kashmir Red Deer (Cervus elaphus hanglu) in India

The hangul (Cervus elaphus hanglu) is of great conservation concern because it represents the easternmost and only hope for an Asiatic survivor of the red deer species in the Indian subcontinent. Despite the rigorous conservation efforts of the Department of Wildlife Protection in Jammu & Kashmir, the hangul population has experienced a severe decline in numbers and range contraction in the past few decades. The hangul population once abundant in the past has largely become confined to the Dachigam landscape, with a recent population estimate of 218 individuals. We investigated the genetic variability and demographic history of the hangul population and found that it has shown a relatively low diversity estimates when compared to other red deer populations of the world. Neutrality tests, which are used to evaluate demographic effects, did not support population expansion, and the multimodal pattern of mismatch distribution indicated that the hangul population is under demographic equilibrium. Furthermore, the hangul population did not exhibit any signature of bottleneck footprints in the past, and Coalescent Bayesian Skyline plot analysis revealed that the population had not experienced any dramatic changes in the effective population size over the last several thousand years. We observed a strong evidence of sub-structuring in the population, wherein the majority of individuals were assigned to different clusters in Bayesian cluster analysis. Population viability analysis demonstrated insignificant changes in the mean population size, with a positive growth rate projected for the next hundred years. We discuss the phylogenetic status of hangul for the first time among the other red deer subspecies of the world and strongly recommend to upgrade hangul conservation status under IUCN that should be discrete from the other red deer subspecies of the world to draw more conservation attention from national and international bodies.     

Genome-wide population structure and evolutionary history of the Frizarta dairy sheep

In the present study, we used genomic data, generated with a medium density single nucleotide polymorphisms (SNP) array, to acquire more information on the population structure and evolutionary history of the synthetic Frizarta dairy sheep. First, two typical measures of linkage disequilibrium (LD) were estimated at various physical distances that were then used to make inferences on the effective population size at key past time points. Population structure was also assessed by both multidimensional scaling analysis and k-means clustering on the distance matrix obtained from the animals’ genomic relationships. The Wright’s fixation F_ST index was also employed to assess herds’ genetic homogeneity and to indirectly estimate past migration rates. The Wright’s fixation F_IS index and genomic inbreeding coefficients based on the genomic relationship matrix as well as on runs of homozygosity were also estimated. The Frizarta breed displays relatively low LD levels with r² and |Dʹ| equal to 0.18 and 0.50, respectively, at an average inter-marker distance of 31 kb. Linkage disequilibrium decayed rapidly by distance and persisted over just a few thousand base pairs. Rate of LD decay (β) varied widely among the 26 autosomes with larger values estimated for shorter chromosomes (e.g. β=0.057, for OAR6) and smaller values for longer ones (e.g. β=0.022, for OAR2). The inferred effective population size at the beginning of the breed’s formation was as high as 549, was then reduced to 463 in 1981 (end of the breed’s formation) and further declined to 187, one generation ago. Multidimensional scaling analysis and k-means clustering suggested a genetically homogenous population, F_ST estimates indicated relatively low genetic differentiation between herds, whereas a heat map of the animals’ genomic kinship relationships revealed a stratified population, at a herd level. Estimates of genomic inbreeding coefficients suggested that most recent parental relatedness may have been a major determinant of the current effective population size. A denser than the 50k SNP panel may be more beneficial when performing genome wide association studies in the breed.     

Allele frequency of VNTR locus D1S80 observed in Hb D-Los Angeles carrires

One of our previous studies presented the allele frequencies of D1S80 VNTR locus in province Denizli including the high frequencies of allele 24 and 18. In Denizli province of Turkey, the most common abnormal variant is Hb D-Los Angeles with a frequency of 57.8?% of the total abnormal Hbs. The aim of this study is to identify the allele frequencies of D1S80 VNTR locus in Hb D-Los Angeles carriers in Denizli province of Turkey. We studied unrelated 36 Hb D-Los Angeles carriers residing in Denizli province of Turkey. The size range of the D1S80 VNTR locus PCR products was determined first by agarose gel electrophoresis and then by a capillary electrophoresis system. For all subjects, DNA sequencing was performed. Allele frequency, theta (k) value, and observed and expected heterozygosity were calculated using Arlequin Software version 3.11. The most common alleles were the 24 (32?%), 18 (18.1?%) and 29 (16.7?%) alleles, and frequencies of these alleles were 0.329, 0.186 and 0.171 respectively. Other observed alleles percentages were 33, 2?%. We did not observe alleles 6, 15, 27 and 35, but we observed alleles 20 and 33. Results were in Hardy–Weinberg linkage disequilibrium. Observed heterozygosity was 0.889, and expected heterozygosity was 0.847. Theta (k) value was 4.91 (95?% confidence interval limits). According to our results, we concluded that Hb D-Los Angeles carriers have different allele frequencies in D1S80 VNTR and also have their own D1S80 VNTR locus divergence.     

Local selection of human populations shapes complex evolution patterns of CXCL10 gene

CXC motif chemokine 10 (CXCL10) is a small cytokine belonging to the CXC chemokine family, and it is secreted by several cell types in response to IFN-γ and regulates immune responses through the recruitment and activation of lymphocytes. As CXCL10 is very important in T-cell immunity and infectious diseases, we studied the effect of natural selection on the CXCL10 locus. By sequencing 74 individuals from three human populations, we found a complex pattern of natural selection acting on the CXCL10 locus. We discovered a signature of balancing selection in the European population with a significant positive Tajima’s D value (2.57, P?=?0.005) and an excess of intermediate frequency alleles. However, we observed an excess of high frequency-derived alleles and a significant Fay and Wu’s test statistics (P?=?0.015) in the Chinese population, which suggests that recent selective sweeps under positive selection had occurred. Also, there are a lot of alleles showing great frequency difference among populations. These results demonstrate that local selection has shaped CXCL10 evolution and indicates that there exist different actions of natural selection on the CXCL10 locus in different populations. This study provides insights into the likely relative roles of natural selection and population history in shaping today’s genetic variation at the CXCL10 locus, indicates the relationship between adaptation to past infection and predisposition to autoimmunity in modern populations, improves our understanding of CXCL10 evolution, and motivates further investigations of the role of CXCL10 in infectious diseases and autoimmune diseases.     

Geographical patterns of turnover and nestedness-resultant components of allelic diversity among populations

The analysis of geographical patterns in population divergence has always been a powerful way to infer microevolutionary processes involved in population differentiation, and several approaches have been used to investigate such patterns. Most frequently, multivariate spatial patterns of population differentiation are analyzed by computing pairwise genetic distances or F_ST (or related statistics, such as ?_ST from AMOVA), which are then correlated with geographical distances or landscape features. However, when calculating distances, especially based on presence-absence of alleles in local populations, there would be a confounding effect of allelic richness differences in the population differentiation. Moreover, the relative magnitude of these components and their spatial patterns can help identifying microevolutionary processes driving population differentiation. Here we show how recent methodological advances in ecological community analyses that allows partitioning dissimilarity into turnover (turnover) and richness differences, or nestedness-resultant dissimilarity, can be applied to allelic variation data, using an endemic Cerrado tree (Dipteryx alata) as a case study. Individuals from 15 local populations were genotyped for eight microsatellite loci, and pairwise dissimilarities were computed based on presence-absence of alleles. The turnover of alleles among populations represented 69?% of variation in dissimilarity, but only the richness difference component shows a clear spatial structure, appearing as a westward decrease of allelic richness. We show that decoupling richness difference and turnover components of allelic variation reveals more clearly how similarity among populations reflects geographical patterns in allelic diversity that can be interpreted in respect to historical range expansion in the species.     

A simple stochastic gene substitution model

If the fitnesses of n haploid alleles in a finite population are assigned at random and if the alleles can mutate to one another, and if the population is initially fixed for the kth most fit allele, then the mean number of substitutions that will occur before the most fit allele is fixed is shown to be

$\text{1}\text{2}\text{+}\text{1}\text{k}\text{+}\text{∑}\text{i=2}\text{k?1}\text{(i+3)}\text{(2i(i+1))}$

when selection is strong and mutation is weak. This result is independent of the parameters that went into the model. The result is used to provide a partial explanation for the large variance observed in the rates of molecular evolution.     

Diversity at two genetic loci associated with the major histocompatibility complex in the golden snub-nosed monkey (Rhinopithecus roxellana)

Habitat loss via human activity has fragmented populations of the golden snub-nosed monkey (Rhinopithecus roxellana), and thus affected patterns of gene flow. We investigated in-depth a single troop in the Qinling Mountains, central China, two major histocompatibility complex (MHC) class II loci, DQA1 and DQB1, and compared the resulting data with data from troops from the wider Qinling Mountains region. We found that a novel DQB1 allele was only present in the study troop and relatively few divergent alleles at the DQA1 and DQB1 loci were present compared with the wider population. The inbreeding coefficient (F_is) at the MHC region was lower than previous measurements, which may have reflected different sampling strategies. However, R. roxellana has relatively high diversity in MHC genes, even though it has probably experienced serious past population bottlenecks and reduced gene flow between populations. We also found that some alleles present in the wider population had been lost in the study troop, and suggest that conservation management strategies be implemented to increase gene flow between troops in order to increase genetic variation.     

Evolutionary jumping and breakthrough in tree masting evolution

Many long-lived plants such as trees show masting or intermittent and synchronized reproduction. In a coupled chaos system describing the dynamics of individual-plant resource budgets, masting occurs when the resource depletion coefficient k (ratio of the reproductive expenditure to the excess resource reserve) is large. Here, we mathematically studied the condition for masting evolution. In an infinitely large population, we obtained a deterministic dynamical system, to which we applied the pairwise invasibility plot and convergence stability of evolutionary singularity analyses. We prove that plants reproducing at the same rate every year are not evolutionarily stable. The resource depletion coefficient k increases, and the system oscillates with a period of 2 years (high and low reproduction) if k<1. Alternatively, k may evolve further and jump to a value >1, resulting in the sudden start of intermittent reproduction. We confirm that a high survivorship of young plants (seedlings) in the light-limited understory favors masting evolution, as previously suggested by computer simulations and field observations. The stochasticity caused by the finiteness of population size also promotes masting evolution.     

Mapping regions within cosmopolitan inversion In(3R)Payne associated with natural variation in body size in Drosophila melanogaster

Associations between genotypes for inversions and quantitative traits have been reported in several organisms, but little has been done to localize regions within inversions controlling variation in these traits. Here, we use an association mapping technique to identify genomic regions controlling variation in wing size within the cosmopolitan inversion In(3R)Payne in Drosophila melanogaster. Previous studies have shown that this inversion strongly influences variation in wing size, a trait highly correlated with body size. We found three alleles from two separate regions within In(3R)Payne with significant additive effects on wing size after the additional effect of the inversion itself had been taken into account. There were also several alleles with significant genotype-by-inversion interaction effects on wing size. None of the alleles tested had a significant additive effect on development time, suggesting different genes control these traits and that clinal patterns in them have therefore arisen independently. The presence of multiple regions within In(3R)Payne controlling size is consistent with the idea that inversions persist in populations because they contain multiple sets of locally adapted alleles, but more work needs to be done to test if they are indeed coadapted.     

Evidence of population bottleneck in Astragalus michauxii (Fabaceae), a narrow endemic of the southeastern United States

Genetic factors such as decreased genetic diversity and increased homozygosity can have detrimental effects on rare species, and may ultimately limit potential adaptation and exacerbate population declines. The Gulf and Atlantic Coastal Plain physiographic region has the second highest level of endemism in the continental USA, but habitat fragmentation and land use changes have resulted in catastrophic population declines for many species. Astragalus michauxii (Fabaceae) is an herbaceous plant endemic to the region that is considered vulnerable to extinction, with populations generally consisting of fewer than 20 individuals. We developed eight polymorphic microsatellites and genotyped 355 individuals from 24 populations. We characterized the population genetic diversity and structure, tested for evidence of past bottlenecks, and identified evidence of contemporary gene flow between populations. The mean ratios of the number of alleles to the allelic range (M ratio) across loci for A. michauxii populations were well below the threshold of 0.68 identified as indicative of a past genetic bottleneck. Genetic diversity estimates were similar across regions and populations, and comparable to other long-lived perennial species. Within-population genetic variation accounted for 92 % of the total genetic variation found in the species. Finally, there is evidence for contemporary gene flow among the populations in North Carolina. Although genetic factors can threaten rare species, maintaining habitats through prescribed burning, in concert with other interventions such as population augmentation or (re)introduction, are likely most critical to the long term survival of A. michauxii.     

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     

Deviations from Hardy-Weinberg Proportions: Sampling Variances and Use in Estimation of Inbreeding Coefficients

An analysis is made of the distribution of deviations from Hardy-Weinberg proportions with k alleles and of estimates of inbreeding coefficients (f) obtained from these deviations.—If f is small, the best estimate of f in large samples is shown to be 2Σ _i(T_ii/N_i)/(k - 1), where T_ii is an unbiased measure of the excess of the ith homozygote and N_i the number of the ith allele in the sample [frequency = N_i/(2N)]. No extra information is obtained from the T_ij, where these are departures of numbers of heterozygotes from expectation. Alternatively, the best estimator can be computed from the T_ij, ignoring the T_ii. Also (1) the variance of the estimate of f equals 1/(N(k - 1)) when all individuals in the sample are unrelated, and the test for f = 0 with 1 d.f. is given by the ratio of the estimate to its standard error; (2) the variance is reduced if some alleles are rare; and (3) if the sample consists of full-sib families of size n, the variance is increased by a proportion (n - 1)/4 but is not increased by a half-sib relationship.—If f is not small, the structure of the population is of critical importance. (1) If the inbreeding is due to a proportion of inbred matings in an otherwise random-breeding population, f as determined from homozygote excess is the same for all genes and expressions are given for its sampling variance. (2) If the homozygote excess is due to population admixture, f is not the same for all genes. The above estimator is probably close to the best for all f values.     

Population dynamics of sex-determining alleles in honey bees and self-incompatibility alleles in plants

Mathematical theories of the population dynamics of sex-determining alleles in honey bees are developed. It is shown that in an infinitely large population the equilibrium frequency of a sex allele is 1/n, where n is the number of alleles in the population, and the asymptotic rate of approach to this equilibrium is 2/(3n) per generation. Formulae for the distribution of allele frequencies and the effective and actual numbers of alleles that can be maintained in a finite population are derived by taking into account the population size and mutation rate. It is shown that the allele frequencies in a finite population may deviate considerably from 1/n. Using these results, available data on the number of sex alleles in honey bee populations are discussed. It is also shown that the number of self-incompatibility alleles in plants can be studied in a much simpler way by the method used in this paper. A brief discussion about general overdominant selection is presented.