Gene Genealogy and Variance of Interpopulational Nucleotide Differences

A mathematical theory is developed for computing the probability that m genes sampled from one population (species) and n genes sampled from another are derived from l genes that existed at the time of population splitting. The expected time of divergence between the two most closely related genes sampled from two different populations and the time of divergence (coalescence) of all genes sampled are studied by using this theory. It is shown that the time of divergence between the two most closely related genes can be used as an approximate estimate of the time of population splitting (T) only when T identical to t/(2N) is small, where t and N are the number of generations and the effective population size, respectively. The variance of Nei and Li's estimate (d) of the number of net nucleotide differences between two populations is also studied. It is shown that the standard error (Sd) of d is larger than the mean when T is small (T much less than 1). In this case, Sd is reduced considerably by increasing sample size. When T is large (T greater than 1), however, a large proportion of the variance of d is caused by stochastic factors, and increase in the sample size does not help to reduce Sd. To reduce the stochastic variance of d, one must use data from many independent unlinked gene loci.     

Estimating divergence time with the use of microsatellite genetic distances: impacts of population growth and gene flow

Genetic distances play an important role in estimating divergence time of bifurcated populations. However, they can be greatly affected by demographic processes, such as migration and population dynamics, which complicate their interpretation. For example, the widely used distance for microsatellite loci, (deltamu)2, assumes constant population size, no gene flow, and mutation-drift equilibrium. It is shown here that (deltamu)2 strongly underestimates divergence time if populations are growing and/or connected by gene flow. In recent publications, the average estimate of divergence time between African and non-African populations obtained by using (deltamu)2 is about 34,000 years, although archaeological data show a much earlier presence of modern humans out of Africa. I introduce a different estimator of population separation time based on microsatellite statistics, T(D), that does not assume mutation-drift equilibrium, is independent of population dynamics in the absence of gene flow, and is robust to weak migration flow for growing populations. However, it requires a knowledge of the variance in the number of repeats at the beginning of population separation, V(0). One way to overcome this problem is to find minimal and maximal bounds for the variance and thus obtain the earliest and latest bounds for divergence time (this is not a confidence interval, and it simply reflects an uncertainty about the value of V(0) in an ancestral population). Another way to avoid the uncertainty is to choose from among present populations a reference whose variation is presumably close to what it might have been in an ancestral population. A different approach for using T(D) is to estimate the time difference between adjacent nodes on a phylogenetic population tree. Using data on variation at autosomal short tandem repeat loci with di-, tri-, and tetranucleotide repeats in worldwide populations, T(D) gives an estimate of 57,000 years for the separation of the out-of-Africa branch of modern humans from Africans based on the value of V(0) in the Southern American Indian populations; the earliest bound for this event has been estimated to be about 135,000 years. The data also suggest that the Asian and European populations diverged from each other about 20,000 years, after the occurrence of the out-of-Africa branch.     

Genealogy of neutral genes in two partially isolated populations

Gene genealogy in two partially isolated populations which diverged at a given time t in the past and have since been exchanging individuals at a constant rate m is studied based upon an analytic method for large t and a simulation method for any t. Particular attention is paid to the conditions under which neutral genes sampled from populations are mono-, para-, and polyphyletic in terms of coalescence (divergence) times of genes. It is shown tha the probability of monophyly is high if M = 2Nm less than 0.5 and T = t/(2N) greater than 1, where N is the size of ancestral and descendant haploid populations, in which case most gene genealogies are likely to be concordant with the population relatedness. This probbility decreases as the sample size of genes increases. On the other hand, the case where the probability of monophyly is low will be either that of M greater than 1 and any T or that of M less than 1 and T less than 1, but the clear distinction between these conditions appears very difficult to make. These results are also examined if the gene genealogy is reconstructed from nucleotide differences. It is then shown that the results based upon coalescence times remain valid if the number of nucleotide differences between any pair of genes is not much smaller than 10. To observe such large nucleotide differences in small populations and therefore infer a reliable gene genealogy, we must examine a fairly long stretch of DNA sequences.     

Quantitative genetic variation in an ecological setting

The machinery was developed to investigate the behavior of quantitative genetic variation in an ecological model of a finite number of islands of finite size, with migration rate m and extinction rate e, for a quantitative genetic model general for numbers of alleles and loci and additive, dominance, and additive by additive epistatic effects. It was necessary to reckon with seven quadratic genetic components, whose coefficients in the genotypic variance components within demes, sigma Gw2, between demes within populations, sigma s2, and between replicate populations, sigma r2, are given by descent measures. The descent measures at any time are calculated with the use of transition equations which are determined by the parameters of the ecological model. Numerical results were obtained for the coefficients of the quadratic genetic components in each of the three genotypic variance components in the early phase of differentiation. The general effect of extinction is to speed up the time course leading to fixation, to increase sigma r2, and to decrease sigma s2 (with a few exceptions) in comparison with no extinction. The general effect of migration is to slow down the time course leading to fixation, to increase sigma Gw2, at least in the later generations, and to decrease sigma s2 (with a few exceptions) in comparison with no migration. Except for these, the effects of migration and extinction on the variance components are complex, depending on the genetic model, and sometimes involve interaction of migration and extinction. Sufficient details are given for an investigator to evaluate numerically the results for variations in the quantitative genetic and ecological models.     

Population genetic structure of northern Dolly Varden char Salvelinus malma malma in Asia and North America

The level of genetic differentiation of northern Dolly Varden char Salvelinus malma malma from Asia and North America was evaluated using the data on mtDNA variation (regions ND1/ND2, ND5/ND6, and Cytb/D loop) obtained by means of PCR-RFLP analysis. For S. m. malma, the mean values of haplotype and nucleotide diversity were 0.5261 +/- 0.00388 and 0.001558, respectively. The mean estimate of the population nucleotide divergence constituted 0.055%. It was demonstrated that S. m. malma on the most part of the species range examined (drainages of the Beaufort Sea, Chukotka Sea, Bering Sea, and the Sea of Okhotsk) was characterized by the population genetic structure with the low level of genetic differentiation and divergence. At the same time, populations from the Pacific Ocean Gulf of Alaska demonstrated marked genetic differentiation, supported by the high pairwise phi(ST) values (from 0.4198 to 0.5211) and nucleotide divergence estimates (mean divergence, 0.129%), from Asian and North American populations. Nested analysis of molecular variance (AMOVA) showed that most of the mtDNA variation in S. m. malma fell in the intrapopulation component (72.5%). At the same time, the differences between the populations (21.1%) and between the regions (6.4%) made lower contribution to the total variation.     

Likelihood analysis of ongoing gene flow and historical association

Abstract.— We develop a Monte Carlo-based likelihood method for estimating migration rates and population divergence times from data at unlinked loci at which mutation rates are sufficiently low that, in the recent past, the effects of mutation can be ignored. The method is applicable to restriction fragment length polymorphisms (RFLPs) and single nucleotide polymorphisms (SNPs) sampled from a subdivided population. The method produces joint maximum-likelihood estimates of the migration rate and the time of population divergence, both scaled by population size, and provides a framework in which to test either for no ongoing gene flow or for population divergence in the distant past. We show the method performs well and provides reasonably accurate estimates of parameters even when the assumptions under which those estimates are obtained are not completely satisfied. Furthermore, we show that, provided that the number of polymorphic loci is sufficiently large, there is some power to distinguish between ongoing gene flow and historical association as causes of genetic similarity between pairs of populations.     

Intraspecific DNA sequence variation of the mitochondrial control region of white sturgeon (Acipenser transmontanus)

Intraspecific sequence variation in the D-loop region of mtDNA in white sturgeon (Acipenser transmontanus), a relict North American fish species, was examined in 27 individuals from populations of the Columbia and Fraser rivers. Thirty-three varied nucleotide positions were present in a 462-nucleotide D-loop sequence, amplified using the polymerase chain reaction. Bootstrapped neighbor-joining and maximum- parsimony trees of sequences from 19 haplotypes suggest that the two populations have recently diverged. This is consistent with the hypothesis that the Columbia River, a Pleistocene refugium habitat, was the source of founders for the Fraser River after the last glacial recession. On the basis of a divergence time of 10-12 thousand years ago, the estimated substitution rate of the white sturgeon D-loop region is 1.1-1.3 x 10(-7) nucleotides/site/year, which is comparable to rates for hypervariable sequences in the human D-loop region. Furthermore, the ratio of mean percent nucleotide differences in the D- loop (2.27%) to that in whole mtDNA (0.54%, as estimated from restriction-enzyme data) is 4.3, which is similar to the fourfold-to- fivefold-higher substitution rate estimated for the human D-loop. The high nucleotide substitution rate of the hypervariable region indicates that the vertebrate D-loop has potential as a genetic marker in molecular population studies.      

Population genetic structure of northern Dolly Varden char <Emphasis Type="Italic">Salvelinus malma malma</Emphasis> in Asia and North America

The level of genetic differentiation of northern Dolly Varden char Salvelinus malma malma from Asia and North America was evaluated using the data on mtDNA variation (regions ND1/ND2, ND5/ND6, and Cytb/D-loop) obtained by means of PCR-RFLP analysis. For S. m. malma, the mean values of haplo-type and nucleotide diversity were 0.5261 ± 0.00388 and 0.001558, respectively. The mean estimate of the population nucleotide divergence constituted 0.055%. It was demonstrated that S. m. malma on the most part of the species range examined (drainages of the Beaufort Sea, Chukotka Sea, Bering Sea, and the Sea of Okhotsk) was characterized by the population genetic structure with the low level of genetic differentiation and divergence. At the same time, populations from the Pacific Ocean Gulf of Alaska demonstrated marked genetic differentiation, supported by the high pairwise G4ST values (from 0.4198 to 0.5211) and nucleotide divergence estimates (mean divergence, 0.129%), from Asian and North American populations. Analysis of molecular variance (AMOVA) showed that most of the mtDNA variation in S. m. malma fell in the intrapopulation component (72.5%). At the same time, the differences between the populations (21.1%) and between the regions (6.4%) made lower contribution to the total variation.     

Environmental stochasticity and extinction risk in a population of a small songbird, the great tit

Using a long-term demographic data set, we estimated the separate effects of demographic and environmental stochasticity in the growth rate of the great tit population in Wytham Wood, United Kingdom. Assuming logistic density regulation, both the demographic (sigma2d = 0.569) and environmental (sigma2e = 0.0793) variance, with interactions included, were significantly greater than zero. The estimates of the demographic variance seemed to be relatively insensitive to the length of the study period, whereas reliable estimates of the environmental variance required long time series (at least 15 yr of data). The demographic variance decreased significantly with increasing population density. These estimates are used in a quantitative analysis of the demographic factors affecting the risk of extinction of this population. The very long expected time to extinction of this population (approximately 10(19) yr) was related to a relatively large population size (>/=120 pairs during the study period). However, for a given population size, the expected time to extinction was sensitive to both variation in population growth rate and environmental stochasticity. Furthermore, the form of the density regulation strongly affected the expected time to extinction. Time to extinction decreased when the maximum density regulation approached K. This suggests that estimates of viability of small populations should be given both with and without inclusion of density dependence.     

The distribution of the coalescence time and the number of pairwise nucleotide differences in a model of population divergence or speciation with an initial period of gene flow

This paper is concerned with a model of “isolation with an initial period of migration”, where a panmictic ancestral population split into n descendant populations which exchanged migrants symmetrically at a constant rate for a period of time and subsequently became completely isolated. In the limit as the population split occurred an infinitely long time ago, the model becomes an “isolation after migration” model, describing completely isolated descendant populations which arose from a subdivided ancestral population. The probability density function of the coalescence time of a pair of genes and the probability distribution of the number of pairwise nucleotide differences are derived for both models. Whilst these are theoretical results of interest in their own right, they also give an exact analytical expression for the likelihood, for data consisting of the numbers of nucleotide differences between pairs of DNA sequences where each pair is at a different, independent locus. The behaviour of the distribution of the number of pairwise nucleotide differences under these models is illustrated and compared to the corresponding distributions under the “isolation with migration” and “complete isolation” models. It is shown that the distribution of the number of nucleotide differences between a pair of DNA sequences from different descendant populations in the model of “isolation with an initial period of migration” can be quite different from that under the “isolation with migration model”, even if the average migration rate over time (and hence the total number of migrants) is the same in both scenarios. It is also illustrated how the results can be extended to other demographic scenarios that can be described by a combination of isolated panmictic populations and “symmetric island” models.     

The analysis of genetic diversity and differentiation of six Chinese cattle populations using microsatellite markers

A total of 321 individuals from six cattle populations of four species in a bovine subfamily in China were studied using 12 pairs of microsatellite markers. The genetic diversities within and between populations were calculated. The phylogenetic trees were constructed by （δμ）^2 and DA distances, and the divergence times between populations were estimated by （δμ）^2. Altogether, 144 microsatellite alleles were detected including 24 private alleles and nine shared alleles. Chinese Holstein had the largest number of private alleles （10）, whereas Bohai black and Buffalo had the smallest number of private alleles （2）. Chinese Holstein showed the highest genetic variability. Its observed number of alleles （Na）, mean effective number of alleles （MNA）, and mean heterozygosity （He） were 7.7500, 4.9722, and 0.7719, respectively, whereas, the Buffalo and Yak showed low genetic variability. In the phylogenetic trees, Luxi and Holstein grouped first, followed by Bohai and Minnan. Yak branched next and buffalo emerged as the most divergent population from other cattle populations. Luxi and Bohai were estimated to have diverged 0.039-0.105 million years ago （MYA）, however, buffalo and Holstein diverged 0.501-1.337 MYA. The divergence time of Yak versus Minnan, Holstein and buffalo was 0.136-0.363, 0.273-0.729, and 0.326-0.600 MYA, respectively.     

Divergence population genetics of chimpanzees

The divergence of two subspecies of common chimpanzees (Pan troglodytes troglodytes and P. t. verus) and the bonobo (P. paniscus) was studied using a recently developed method for analyzing population divergence. Under the isolation with migration model, the posterior probability distributions of divergence time, migration rates, and effective population sizes were estimated for large multilocus DNA sequence data sets drawn from the literature. The bonobo and the common chimpanzee are estimated to have diverged approximately 0.86 to 0.89 MYA, and the divergence of the two common chimpanzee subspecies is estimated to have occurred 0.42 MYA. P. t. troglodytes appears to have had a larger effective population size (22,400 to 27,900) compared with P. paniscus, P. t. verus, and the ancestral populations of these species. No evidence of gene flow was found in the comparisons involving P. paniscus; however a clear signal of unidirectional gene flow was found from P. t. verus to P. t. troglodytes (2Nm = 0.51).     

Population mixing and the adaptive divergence of quantitative traits in discrete populations: a theoretical framework for empirical tests

Empirical tests for the importance of population mixing in constraining adaptive divergence have not been well grounded in theory for quantitative traits in spatially discrete populations. We develop quantitative-genetic models to examine the equilibrium difference between two populations that are experiencing different selective regimes and exchanging individuals. These models demonstrate that adaptive divergence is negatively correlated with the rate of population mixing (m, most strongly so when m is low), positively correlated with the difference in phenotypic optima between populations, and positively correlated with the amount of additive genetic variance (G, most strongly so when G is low). The approach to equilibrium is quite rapid (fewer than 50 generations for two populations to evolve 90% of the distance to equilibrium) when either heritability or mixing are not too low (h2 > 0.2 or m > 0.05). The theory can be used to aid empirical tests that: (1) compare observed divergence to that predicted using estimates of population mixing, additive genetic variance/covariance, and selection; (2) test for a negative correlation between population mixing and adaptive divergence across multiple independent population pairs; and (3) experimentally manipulate the rate of mixing. Application of the first two of these approaches to data from two well-studied natural systems suggests that population mixing has constrained adaptive divergence for color patterns in Lake Erie water snakes (Nerodia sipedon), but not for trophic traits in sympatric pairs of benthic and limnetic stickleback (Gasterosteus aculeatus). The theoretical framework we outline should provide an improved basis for future empirical tests of the role of population mixing in adaptive divergence.     

A comparison of biallelic markers and microsatellites for the estimation of population and conservation genetic parameters in Atlantic salmon (Salmo salar)

Biallelic markers such as single nucleotide polymorphisms (SNPs) and insertion/deletion polymorphisms have become increasingly popular markers for various population genetics applications. However, the effort required to develop biallelic markers in nonmodel organisms is still substantial. In this study, we compared the estimation of various population genetic parameters (genetic divergence and structuring, isolation-by-distance, genetic diversity) using a limited number of biallelic markers (in total 7 loci) to those estimated with 14 microsatellite loci in 21 Atlantic salmon (Salmo salar) populations from northern Europe. Pairwise FST values were significantly correlated between biallelic loci and microsatellite datasets, as was overall heterozygosity when both anadromous and nonanadromous populations were analyzed together. However, when the anadromous and nonanadromous samples were analyzed separately, only genetic divergence correlations remained significant. Biallelic markers alone were not sufficient for reliable neighbor-joining clustering of populations but gave highly similar isolation-by-distance signals when compared with microsatellites. Finally, although several population prioritization measures for conservation exhibited significant correlation between different marker types, the specific populations highlighted as being most valuable for conservation purposes varied depending on the marker type and conservation criteria applied. This study demonstrates that a relatively small set of biallelic markers can be sufficient for obtaining concordant results in most of the analyses compared with microsatellites, although estimates of genetic distance are generally more concordant than estimates of genetic diversity. This suggests that a relatively small number of biallelic markers can provide useful information for various population genetic applications. However, we emphasize that the use of much higher number of loci is preferable, especially when the genetic differences between populations are subtle or individual multilocus genotype-based analyses are to be performed.     

Variance of Neutral Genetic Variances within and between Populations for a Quantitative Character

The variances of genetic variances within and between finite populations were systematically studied using a general multiple allele model with mutation in terms of identity by descent measures. We partitioned the genetic variances into components corresponding to genetic variances and covariances within and between loci. We also analyzed the sampling variance. Both transient and equilibrium results were derived exactly and the results can be used in diverse applications. For the genetic variance within populations, sigma 2 omega, the coefficient of variation can be very well approximated as [formula: see text] for a normal distribution of allelic effects, ignoring recurrent mutation in the absence of linkage, where m is the number of loci, N is the effective population size, theta 1(0) is the initial identity by descent measure of two genes within populations and t is the generation number. The first term is due to genic variance, the second due to linkage disequilibrium, and third due to sampling. In the short term, the variation is predominantly due to linkage disequilibrium and sampling; but in the long term it can be largely due to genic variance. At equilibrium with mutation [formula: see text] where u is the mutation rate. The genetic variance between populations is a parameter. Variance arises only among sample estimates due to finite sampling of populations and individuals. The coefficient of variation for sample gentic variance between populations, sigma 2b, can be generally approximated as [formula: see text] when the number of loci is large where S is the number of sampling populations.     

Intraspecific molecular phylogeny, genetic variation and phylogeography of Reticulitermes speratus (Isoptera: Rhinotermitidae)

Population structure was investigated in Reticulitermes speratus populations in the Korean Peninsula and the Japanese Archipelago. All trees derived from analyses of the combined sequence dataset of two mitochondrial genes, COII and COIII, showed that R. speratus populations cluster into two major clades comprising the Korean/southern Japanese populations and the north-ern Japanese populations. Analysis of population ge-netic structure showed strong genetic partitioning between populations of the two clades. To understand historical migration routes and current distributions, the phylogeographic history of R. speratus was inferred from intra-/interspecific phylogeny and diver-gence times estimated between the clades of the phylogenetic tree. The estimated migration route and divergence time of ancestral R. speratus are congruent with recent paleogeographic hypotheses involving land-bridge connections between the Asian continent and the Japanese Archipelago. We suggest that ancestral R. speratus separated into northern and southern Japanese populations after its migration into the Japanese main islands from East China during the early Pleistocene via the East China Sea basin, which may have been exposed during that period. The Korean populations seem to have diverged recently from southern Japanese populations; this may explain the current distribution of R. speratus in the Japanese Arachipelago, and account for why it is restricted to northern areas of the Tokara Strait.     

缢蛏种群遗传多样性的周年变异分析

利用线粒体COI标记分析了福建省宁德市漳湾镇横屿村滩涂5个月份缢蛏群体(S3,S5,S7,S9,S11)的遗传结构,以期评估不同月份时期种群的遗传多样性差异。基于线粒体COI基因的结果表明,5个缢蛏群体的平均核苷酸差异数位于2.7836-3.6894之间,核苷酸多样性指数位于0.0050-0.0066之间,遗传多样性水平大致表现为S3和S5群体较高于S7和S9群体,明显高于S11群体。AMOVA分析结果显示,群体间遗传变异量占总变异的7.18%,而群体内变异达到了92.82%,说明遗传差异主要来自于群体内部。由此可见,从3月份到11月份,缢蛏群体的遗传多样性水平呈现出下降趋势,尤其是在11月份,差异最为明显。     

Migration rates, frequency-dependent selection and the self-incompatibility locus in Leavenworthia (brassicaceae)

Loci subject to negative frequency-dependent selection are expected to exhibit higher effective migration rates compared to reference loci. Although the number of gene copies transferred between populations by migration is the same for all genes, those subject to negative frequency-dependent selection are more likely to be retained in the immigrant population because rare alleles are selectively favored. So far, evidence for this prediction has been indirect, based on summary statistics rather than on migration rate estimates. Here, we introduce an approximate Bayesian procedure to jointly estimate migration rates at two predefined sets of loci between two populations. We applied the procedure to compare migration rate estimates at the self-incompatibility locus (S-locus) with that at 10 reference loci in two plant species, Leavenworthia alabamica and L. crassa (Brassicaceae). The maximum likelihood estimate for the proportion of migrants (m) was four times higher at the S-locus than at reference loci, but the difference was not statistically significant. Lack of significance might be due to insufficient data, but perhaps also to the recent divergence of the two species (311 ka), because we also show using simulations that the effective migration rate at the S-locus is expected to increase with increasing divergence time. These findings aid in understanding the evolutionary dynamics of negative frequency-dependent selection and they suggest that divergence time should be accounted for when employing migration rates to help detect negative frequency-dependent selection.     

A simple method of removing the effect of a bottleneck and unequal population sizes on pairwise genetic distances

In this paper, we derive the expectation of two popular genetic distances under a model of pure population fission allowing for unequal population sizes. Under the model, we show that conventional genetic distances are not proportional to the divergence time and generally overestimate it due to unequal genetic drift and to a bottleneck effect at the divergence time. This bias cannot be totally removed even if the present population sizes are known. Instead, we present a method to estimate the divergence times between populations which is based on the average number of nucleotide differences within and between populations. The method simultaneously estimates the divergence time, the ancestral population size and the relative sizes of the derived populations. A simulation study revealed that this method is essentially unbiased and that it leads to better estimates than traditional approaches for a very wide range of parameter values. Simulations also indicated that moderate population growth after divergence has little effect on the estimates of all three estimated parameters. An application of our method to a comparison of humans and chimpanzee mitochondrial DNA diversity revealed that common chimpanzees have a significantly larger female population size than humans.     

马尾松和黄山松两个核基因位点的群体遗传多样性和种间分化

利用两个核基因座位C3H和GI, 对重叠分布于中国东南部的两个松属(Pinus)物种马尾松(P. massoniana)和黄山松(P. hwangshanensis)的22个群体88个个体进行了遗传多样性和种间分化模式研究。在这两个核基因座位上, 两种植物都表现出较低的核苷酸多样性水平(马尾松π_sil = 0.001 71; 黄山松π_sil = 0.003 40), 但是马尾松要显著低于黄山松; 在种内分化水平上, 马尾松的种内遗传分化也明显低于黄山松(马尾松F_ST = 0.059; 黄山松F_ST = 0.339)。这可能是由于黄山松的海拔分布高于马尾松, 而高海拔分布使黄山松的分布区域更加片段化, 促使其形成较高的种内遗传多样性和遗传分化。分子变异分析(AMOVA)发现, 两物种基于两个核基因座位的种间差异为48.86%, 而GI基因座位上的种间差异明显高于C3H座位(GI: 77.24%, C3H: 20.48%), 同时, 基因谱系显示两物种的共享单倍型仅在C3H座位上存在。结合这两个基因的功能, 推测GI基因可能在物种形成过程中受到了一定的选择压力, 因为GI基因参与调控植物的开花时间, 而C3H与木质素表达水平的调控有关。不同的选择压力使得GI的进化速度相对较快, 从而加速了黄山松和马尾松的物种分化。