Simulation results with stepwise mutation model and their interpretations

Summary Monte Carlo simulations are performed to compare the predictions based on the two presently used theoretical models for studying genetic variations in natural populations, the infinite allele model and the stepwise mutation model. Distribution of heterozygosity is noticed to be similar under these models until the product of population size and mutation rate is large. It is seen that electromorphs with high population frequency usually contain older alleles (at the codon level) than an electromorph of low population frequency. The interpretations of these results in explaining the allelic variations at electrophoretic level is also discussed.Research supported by U.S. Public Health Service General Research Support Grant 5 SO 5 RR 07148 from the University of Texas Health Science Center, Graduate School of Biomedical Sciences, Houston, Texas     

The impact of microsatellite electromorph size homoplasy on multilocus population structure estimates in a tropical tree (Corythophora alta) and an anadromous fish (Morone saxatilis)

Microsatellite allelic states are determined by electrophoretic sizing of polymerase chain reaction fragments to define electromorphs. Numerous studies have documented that identical microsatellite electromorphs are potentially heterogeneous at the DNA sequence level, a phenomenon called electromorph size homoplasy. Few studies have examined the impact of electromorph size homoplasy on estimates of population genetic parameters. We investigated the frequency of microsatellite electromorph size homoplasy for 12 loci in the tropical tree Corythophora alta and 11 loci in the anadromous fish Morone saxatilis by sequencing 14-23 homozygotes per locus sampled from multiple populations for a total of 453 sequences. Sequencing revealed no homoplasy for M. saxatilis loci. Seven C. alta loci exhibited homoplasy, including single and compound repeat motifs both with and without interruptions. Between 12.5 and 42.9% of electromorphs sampled per locus showed size homoplasy. Two methods of correction for homoplasy in C. alta generally produced little or no change in single-locus estimates of RST, except for two loci in which some additional differentiation among populations was revealed. Twelve-locus estimates of RST (including the seven loci corrected for homoplasy) were slightly greater than estimates from uncorrected data, although the 95% confidence intervals overlapped. The frequency of methodological errors such as clerical mistakes or sample mislabelling per genotype scored was estimated at 5.4 and 7.3% for C. alta and M. saxatilis, respectively. Simulations showed that the increase in RST produced by homoplasy correction was only slightly larger than variation in RST estimates expected to be caused by methodological errors.     

Allelic Variants at the Xanthine Dehydrogenase Locus Affecting Enzyme Activity in DROSOPHILA PSEUDOOBSCURA

Quantitative studies of enzyme activity on gels show about four-fold differences in enzyme activity of different xanthine dehydrogenase (XDH ) alleles. At least three different activity classes could be distinguished among the 23 strains isogenic for the XDH locus. No association of high activity with the high frequency electromorph was observed; instead, the low frequency electromorphs had 0.5 to 2 times the activity of the high frequency electromorph. The frequency of low activity, high activity and intermediate activity XDH alleles among these 23 lines is 0.13, 0.09, and 0.78, respectively.     

Methodologies for estimating the sample size required for genetic conservation of outbreeding crops

Summary The main purpose of germplasm banks is to preserve the genetic variability existing in crop species. The effectiveness of the regeneration of collections stored in gene banks is affected by factors such as sample size, random genetic drift, and seed viability. The objective of this paper is to review probability models and population genetics theory to determine the choice of sample size used for seed regeneration. A number of conclusions can be drawn from the results. First, the size of the sample depends largely on the frequency of the least common allele or genotype. Genotypes or alleles occurring at frequencies of more than 10% can be preserved with a sample size of 40 individuals. A sample size of 100 individuals will preserve genotypes (alleles) that occur at frequencies of 5%. If the frequency of rare genotypes (alleles) drops below 5%, larger sample sizes are required. A second conclusion is that for two, three, and four alleles per locus the sample size required to include a copy of each allele depends more on the frequency of the rare allele or alleles than on the number. Samples of 300 to 400 are required to preserve alleles that are present at a frequency of 1%. Third, if seed is bulked, the expected number of parents involved in any sample drawn from the bulk will be less than the number of parents included in the bulk. Fourth, to maintain a rate of breeding (F) of 1 %, the effective population size (N _e) should be at least 150 for three alleles, and 300 for four alleles. Fifth, equalizing the reproductive output of each family to two progeny doubles the effective size of the population. Based on the results presented here, a practical option is considered for regenerating maize seed in a program constrained by limited funds.Part of this paper was presented at the Global Maize Germplasm Workshop, CIMMYT, El Batan, Mexico, March 6–12, 1988     

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   

Non-equilibrium theory of the allele frequency spectrum

A forward diffusion equation describing the evolution of the allele frequency spectrum is presented. The influx of mutations is accounted for by imposing a suitable boundary condition. For a Wright-Fisher diffusion with or without selection and varying population size, the boundary condition is lim(x downward arrow0)xf(x,t)=thetarho(t), where f(.,t) is the frequency spectrum of derived alleles at independent loci at time t and rho(t) is the relative population size at time t. When population size and selection intensity are independent of time, the forward equation is equivalent to the backwards diffusion usually used to derive the frequency spectrum, but this approach allows computation of the time dependence of the spectrum both before an equilibrium is attained and when population size and selection intensity vary with time. From the diffusion equation, a set of ordinary differential equations for the moments of f(.,t) is derived and the expected spectrum of a finite sample is expressed in terms of those moments. The use of the forward equation is illustrated by considering neutral and selected alleles in a highly simplified model of human history. For example, it is shown that approximately 30% of the expected total heterozygosity of neutral loci is attributable to mutations that arose since the onset of population growth in roughly the last 150,000 years.     

A Reanalysis of Protein Polymorphism in Drosophila Melanogaster, D. Simulans, D. Sechellia and D. Mauritiana: Effects of Population Size and Selection

Comparison of synonymous and nonsynonymous variation/substitution within and between species at individual genes has become a widely used general approach to detect the effect of selection versus drift. The sibling species group comprised of two cosmopolitan (Drosophila melanogaster and Drosophila simulans) and two island (Drosophila mauritiana and Drosophila sechellia) species has become a model system for such studies. In the present study we reanalyzed the pattern of protein variation in these species, and the results were compared against the patterns of nucleotide variation obtained from the literature, mostly available for melanogaster and simulans. We have mainly focused on the contrasting patterns of variation between the cosmopolitan pair. The results can be summarized as follows: (1) As expected the island species D. mauritiana and D. sechellia showed much less variation than the cosmopolitan species D. melanogaster and D. simulans. (2) The chromosome 2 showed significantly less variation than chromosome 3 and X in all four species which may indicate effects of past selective sweeps. (3) In contrast to its overall low variation, D. mauritiana showed highest variation for X-linked loci which may indicate introgression from its sibling, D. simulans. (4) An average population of D. simulans was as heterozygous as that of D. melanogaster (14.4% v.s. 13.9%) but the difference was large and significant when considering only polymorphic loci (37.2% v.s. 26.1%). (5) The species-wise pooled populations of these two species showed similar results (all loci = 18.3% v.s. 20.0%, polymorphic loci = 47.2% v.s. 37.6%). (6) An average population of D. simulans had more low-frequency alleles than D. melanogaster, and the D. simulans alleles were found widely distributed in all populations whereas the D. melanogaster alleles were limited to local populations. As a results of this, pooled populations of D. melanogaster showed more polymorphic loci than those of D. simulans (48.0% v.s. 32.0%) but the difference was reduced when the comparison was made on the basis of an average population (29.1% v.s. 21.4%). (7) While the allele frequency distributions within populations were nonsignificant in both D. melanogaster and D. simulans, melanogaster had fewer than simulans, but more than expected from the neutral theory, low frequency alleles. (8) Diallelic loci with the second allele with a frequency less than 20% had similar frequencies in all four species but those with the second allele with a frequency higher than 20% were limited to only melanogaster the latter group of loci have clinal (latitudinal) patterns of variation indicative of balancing selection. (9) The comparison of D. simulans/D. melanogaster protein variation gave a ratio of 1.04 for all loci and 1.42 for polymorphic loci, against a ratio of approximately 2-fold difference for silent nucleotide sites. This suggests that the species ratios of protein and silent nucleotide polymorphism are too close to call for selective difference between silent and allozyme variation in D. simulans. In conclusion, the contrasting levels of allozyme polymorphism, distribution of rare alleles, number of diallelic loci and the patterns of geographic differentiation between the two species suggest the role of natural selection in D. melanogaster, and of possibly ancient population structure and recent worldwide migration in D. simulans. Population size differences alone are insufficient as an explanation for the patterns of variation between these two species.     

Population Bottlenecks and Nonequilibrium Models in Population Genetics. II. Number of Alleles in a Small Population That Was Formed by a Recent Bottleneck

A model is presented in which a large population in mutation/drift equilibrium undergoes a severe restriction in size and subsequently remains at the small size. The rate of loss of genetic variability has been studied. Allelic loss occurs more rapidly than loss of genic heterozygosity. Rare alleles are lost especially rapidly. The result is a transient deficiency in the total number of alleles observed in samples taken from the reduced population when compared with the number expected in a sample from a steady-state population having the same observed heterozygosity. Alternatively, the population can be considered to possess excess gene diversity if the number of alleles is used as the statistical estimator of mutation rate. The deficit in allele number arises principally from a lack of those alleles that are expected to appear only once or twice in the sample. The magnitude of the allelic deficiency is less, however, than the excess that an earlier study predicted to follow a rapid population expansion. This suggests that populations that have undergone a single bottleneck event, followed by rapid population growth, should have an apparent excess number of alleles, given the observed level of genic heterozygosity and provided that the bottleneck has not occurred very recently. Conversely, such populations will be deficient for observed heterozygosity if allele number is used as the sufficient statistic for the estimation of 4Nev. Populations that have undergone very recent restrictions in size should show the opposite tendencies.     

种群微卫星DNA分析中样本量对各种遗传多样性度量指标的影响

我们以中国飞蝗种群的微卫星遗传分析数据为例 ,评估了取样对种群遗传多样性指标的影响 ,结果显示 :样本大小与所观测到的每位点等位基因数、平均等位基因数及基因丰富度指数均呈显著正相关 ,而与期望杂合度无显著相关 ;微卫星位点多态性的高低直接影响所观测到的种群基因丰富度及其检测所需的样本量 ;对大多数种群遗传和分子生态学研究而言 ,30 - 5 0个个体是微卫星DNA分析所需要的最小样本量。基因丰富度经过稀疏法或多次随机抽样法校正后 ,可适用于瓶颈效应等种群历史数量变动的检测。另外 ,在研究中 ,还应避免采集时间的不同及样本的性比构成所可能造成的对种群遗传结构的影响     

Sampling for Microsatellite-Based Population Genetic Studies: 25 to 30 Individuals per Population Is Enough to Accurately Estimate Allele Frequencies

One of the most common questions asked before starting a new population genetic study using microsatellite allele frequencies is “how many individuals do I need to sample from each population?” This question has previously been answered by addressing how many individuals are needed to detect all of the alleles present in a population (i.e. rarefaction based analyses). However, we argue that obtaining accurate allele frequencies and accurate estimates of diversity are much more important than detecting all of the alleles, given that very rare alleles (i.e. new mutations) are not very informative for assessing genetic diversity within a population or genetic structure among populations. Here we present a comparison of allele frequencies, expected heterozygosities and genetic distances between real and simulated populations by randomly subsampling 5–100 individuals from four empirical microsatellite genotype datasets (Formica lugubris, Sciurus vulgaris, Thalassarche melanophris, and Himantopus novaezelandia) to create 100 replicate datasets at each sample size. Despite differences in taxon (two birds, one mammal, one insect), population size, number of loci and polymorphism across loci, the degree of differences between simulated and empirical dataset allele frequencies, expected heterozygosities and pairwise F_ST values were almost identical among the four datasets at each sample size. Variability in allele frequency and expected heterozygosity among replicates decreased with increasing sample size, but these decreases were minimal above sample sizes of 25 to 30. Therefore, there appears to be little benefit in sampling more than 25 to 30 individuals per population for population genetic studies based on microsatellite allele frequencies.     

C8A and C8B polymorphisms in Norwegians and Norwegian lapps

C8 inheritance patterns in 364 mother-child pairs formed the basis for evaluation of the existence of silent alleles (null alleles) in the genes determining the two known polymorphic C8 systems. While evidence for such alleles was not found in C8A (alpha-gamma complex), two observations of null allele segregation in C8B (beta chain) indicate a C8BQ*0 allele frequency of about 0.07. Two population samples comprising 150 Lappish and 1,264 non-Lappish Norwegians were examined for phenotype distributions in C8A and C8B. The phenotype distributions were mainly in accordance with the expected Hardy-Weinberg distribution. The results for C8A indicated simple, codominant inheritance of two frequent and several rare alleles. Allele frequencies were similar in the two populations. The C8A B gene frequency in Norwegians was significantly lower than that in FRG and higher than that in Negroes. C8B allele frequencies were also calculated from gene counts in the population material, but with due corrections for the C8BQ*0 frequency observed in the mother-child material.     

Genetic drift and estimation of effective population size

The statistical properties of the standardized variance of gene frequency changes (a quantity equivalent to Wright's inbreeding coefficient) in a random mating population are studied, and new formulae for estimating the effective population size are developed. The accuracy of the formulae depends on the ratio of sample size to effective size, the number of generations involved (t), and the number of loci or alleles used. It is shown that the standardized variance approximately follows the chi(2) distribution unless t is very large, and the confidence interval of the estimate of effective size can be obtained by using this property. Application of the formulae to data from an isolated population of Dacus oleae has shown that the effective size of this population is about one tenth of the minimum census size, though there was a possibility that the procedure of sampling genes was improper.     

Heterosis or Neutrality?

Various statistics have been proposed on an ad hoc basis to test whether alleles at a locus are selectively neutral. By considering population models in which selection operates, this paper shows that the population homozygosity is a powerful test statistic for testing departures from neutrality, in the direction of heterozygote advantage or disadvantage. The sample homozygosity plays a similar role when only sample data are available. Some numerical examples are included, showing the application of the test.—An analysis is made of the effect of heterosis on such quantities as the expected number of alleles in the population or sample, the effective number of alleles, the expected homozygosity, and on the population and sample allele frequency distributions generally.     

A Model to Estimate the Increase of Genetic Variability Due to Electrophoretically Cryptic Alleles

To consider the problem of the increase of genetic variability due to electrophoretically cryptic alleles, the equally degenerate electromorph model is proposed. Mutation, random sampling drift and selection can be incorporated in this model. Simple formulas are obtained to show how genetic variability increases when cryptic alleles are distinguished. This model is extended to a two-population system to see the effect of cryptic allele variation on genetic differentiation.     

Contrasting Patterns of Nucleotide Sequence Variation at the Glucose Dehydrogenase (Gld) Locus in Different Populations of Drosophila Melanogaster

We have analyzed nucleotide sequence variation at the Glucose dehydrogenase (Gld) locus from four populations of Drosophila melanogaster from four continents. All four population samples show a significant reduction in silent variation compared to the neutral expectation. The levels of silent variation across all four populations are consistent with the predictions of the background selection model; however, Zimbabwe has a remarkably low level of variation. In the face of dramatically reduced silent polymorphism, an amino acid variant, leading to the common allozyme polymorphism at Gld, remains in low to intermediate frequency in all non-African samples. In the Chinese population sample, the ratio of replacement to silent variation is significantly elevated compared to the neutral expectation. The difference in patterns of variation across these population samples suggests that selection on Gld (or the Gld region) has been different in the Chinese population than in the other three.     

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.     

Variation of Microsatellite Size Homoplasy Across Electromorphs, Loci, and Populations in Three Invertebrate Species

Size homoplasy was analyzed at microsatellite loci by sequencing electromorphs, that is, variants of the same size (base pairs). This study was conducted using five interrupted and/or compound loci in three invertebrate species, the honey bee Apis mellifera, the bumble bee Bombus terrestris, and the freshwater snail Bulinus truncatus. The 15 electromorphs sequenced turned out to hide 31 alleles (i.e., variants identical in sequence). Variation in the amount of size homoplasy was detected among electromorphs and loci. From one to seven alleles were detected per electromorph, and one locus did not show any size homoplasy in both bee species. The amount of size homoplasy was related to the sequencing effort, since the number of alleles was correlated with the number of copies of electromorphs sequenced, but also with the molecular structure of the core sequence at each locus. Size homoplasy within populations was detected only three times, meaning that size homoplasy was detected mostly among populations. We analyzed population structure, estimating F _st and a genetic distance, based on either electromorphs or alleles. Whereas little difference was found in A. mellifera, uncovering size homoplasy led to a more marked population structure in B. terrestris and B. truncatus. We also showed in A. mellifera that the detection of size homoplasy may alter phylogenetic reconstructions. Received: 21 July 1997 / Accepted: 29 January 1998     

Temporal Allele Frequency Change and Estimation of Effective Size in Populations with Overlapping Generations

In this paper we study the process of allele frequency change in finite populations with overlapping generations with the purpose of evaluating the possibility of estimating the effective size from observations of temporal frequency shifts of selectively neutral alleles. Focusing on allele frequency changes between successive cohorts (individuals born in particular years), we show that such changes are not determined by the effective population size alone, as they are when generations are discrete. Rather, in populations with overlapping generations, the amount of temporal allele frequency change is dependent on the age-specific survival and birth rates. Taking this phenomenon into account, we present an estimator for effective size that can be applied to populations with overlapping generations.     

RARE ALLELES AS INDICATORS OF GENE FLOW

A. method for estimating the average level of gene flow in a subdivided population, as measured by the average number of migrants exchanged between local populations, Nm, is presented. The results from a computer simulation model show that the logarithm of Nm is approximately linearly related to the logarithm of the average frequency of private alleles, p?(1), in a sample of alleles from the population. It is shown that this result is relatively insensitive to changes in parameters of the model other than Nm and the number of individuals sampled per population. The dependence of the value of p?(1) on the numbers of individuals sampled provides a rough way to correct for differences in sample size. This method was applied to data from 16 species, showing that estimated values of Nm range from much greater than 1 to less than 0.1. These results confirm the qualitative analysis of Slatkin (1981). This method was also applied to subsamples from a population to show how to measure the extent of isolation of local populations.     

Human neutral alpha-glucosidase C: genetic polymorphism including a "null" allele.

We describe a genetic polymorphism of human neutral alpha-glucosidase C, detected in lymphoid cells by a combination of starch gel electrophoresis and isoelectric focusing. The seven phenotypes observed appear to result from the expression of four different alleles. The distribution of the observed phenotypes fits the expected distribution predicted from calculated gene frequencies in Hardy-Weinberg equilibrium. Family studies are consistent with autosomal inheritance of the gene. The product of one of the alleles is unusual in that it is "silent," with an estimated gene frequency of .174 in an outbred white population. Approximately one-third of the population is heterozygous "null." Homozygosity for the allele has not been associated with any obvious disease state. This is the third example of a "null" allele which has a substantial gene frequency in an outbred population but does not appear to result in disease in the homozygous state.