Single-locus gametophytic incompatibility: the symmetric equilibrium is globally asymptotically stable

The deterministic dynamics of the classical single-locus multiple-allele model of gametophytic incompatibility is analyzed with the intention to prove the conjecture that the symmetric state (uniform distribution of genotypes) is the only polymorphic equilibrium and that this equilibrium is globally asymptotically stable in the interior of the frequency simplex. It is shown that the minimum allelic frequency increases strictly over the generations as long as a uniform allelic distribution is not realized. Hence, the minimum allelic frequency is a Ljapunov function for the invariant set of genotypic frequencies characterized by a uniform allelic distribution. Within this set, the uniform genotypic distribution is approached in an exponential fashion, which proves the assertion. An evolutionary optimization rule associated with the global convergence to the symmetric state is implied by the fact that at this state the overall amount of pollen elimination resulting from incompatible crosses is minimized.     

Polymorphic markers Val762Ala and Leu54Phe of the ADPRT1 gene associated with chronic glomerulonephritis in Russian patients from the city of Moscow

A comparative analysis of allelic and genotype distribution of polymorphic markers Val762Ala and Leu54Phe of ADPRT1 gene encoding poly(ADP-ribose)polymerase I has been performed in chronic glomerulonephritis patients compared to normal controls. This has shown a significant difference in the ADPRTI gene polymorphic marker Val762Ala allelic and genotype frequency distribution between chronic glomerulonephritis patients and healthy controls (according to Fisher's exact test). At the same time the allelic and genotype frequency for a polymorphic marker Leu54Phe distribution did not show significant difference between these groups. Therefore, we have concluded that the ADPRTI gene polymorphic marker Val762Ala is associated with the development of chronic glomerulonephritis in Russian patients of the Moscow region.     

香菇基因型及对蔗渣降解水平的研究

在江南一些地方采集九株野生香菇,分析担孢子基因型并测定A、B不亲和因子等位基因的数目及差异,保藏以A_xB_x(或A-yB_y)标记的单核菌丝体。实验结果表明,每一菌株的四个基因型呈随机分配。香菇A·B因子具有地区性,重复频率很低,等位基因差异明显。九个菌株的单核菌丝体的基因型从A_1B_1到A_(18)B_(18)不同。进一步对14个菌株(包括上述野生菌株)在蔗渣培养基上生长70天后对主要基质降解程度的测定表明,除个别菌株比较适合用蔗渣进行栽培外,其它菌株对蔗渣中纤维素、半纤维素和木质素的分解利用能力都较差。     

Moments,cumulants, and polygenic dynamics

A new approach for describing the evolution of polygenic traits subject to selection and mutation is presented. Differential equations for the change of cumulants of the allelic frequency distribution at a particular locus and for the cumulants of the distributions of genotypic and phenotypic values are derived. The derivation is based on the assumptions of random mating, no sex differences, absence of random drift, additive gene action, linkage equilibrium, and Hardy-Weinberg proportions. Cumulants are a set of parameters that, like moments, describe the shape of a probability density. Compared with moments, however, they have properties that make them a much more convenient tool for investigating polygenic traits. Applications to directional and stabilizing selection are given.     

A strategy to discover genes that carry multi-allelic or mono-allelic risk for common diseases: a cohort allelic sums test (CAST)

A method is described to discover if a gene carries one or more allelic mutations that confer risk for any specified common disease. The method does not depend upon genetic linkage of risk-conferring mutations to high frequency genetic markers such as single nucleotide polymorphisms. Instead, the sums of allelic mutation frequencies in case and control cohorts are determined and a statistical test is applied to discover if the difference in these sums is greater than would be expected by chance. A statistical model is presented that defines the ability of such tests to detect significant gene-disease relationships as a function of case and control cohort sizes and key confounding variables: zygosity and genicity, environmental risk factors, errors in diagnosis, limits to mutant detection, linkage of neutral and risk-conferring mutations, ethnic diversity in the general population and the expectation that among all exonic mutants in the human genome greater than 90% will be neutral with regard to any effect on disease risk. Means to test the null hypothesis for, and determine the statistical power of, each test are provided. For this "cohort allelic sums test" or "CAST", the statistical model and test are provided as an Excel program, CASTAT(c) at . Based on genetics, technology and statistics, a strategy of enumerating the mutant alleles carried in the exons and splice sites of the estimated approximately 25,000 human genes in case cohort samples of 10,000 persons for each of 100 common diseases is proposed and evaluated: A wide range of possible conditions of multi-allelic or mono-allelic and monogenic, multigenic or polygenic (including epistatic) risk are found to be detectable using the statistical criteria of 1 or 10 "false positive" gene associations approximately 25,000 gene-disease pair-wise trials and a statistical power of >0.8. Using estimates of the distribution of both neutral and gene-inactivating nondeleterious mutations in humans and the sensitivity of the test to multigenic or multicausal risk, it is estimated that about 80% of nullizygous, heterozygous and functionally dominant gene-common disease associations may be discovered. Limitations include relative insensitivity of CAST to about 60% of possible associations given homozygous (wild type) risk and, more rarely, other stochastic limits when the frequency of mutations in the case cohort approaches that of the control cohort and biases such as absence of genetic risk masked by risk derived from a shared cultural environment.     

Unequal allelic frequencies at the self‐incompatibility locus within local populations of Prunus avium L.: an effect of population structure?

In this paper, we investigated the genetic structure and distribution of allelic frequencies at the gametophytic self-incompatibility locus in three populations of Prunus avium L. In line with theoretical predictions under balancing selection, genetic structure at the self-incompatibility locus was almost three times lower than at seven unlinked microsatellites. Furthermore, we found that S-allele frequencies in wild cherry populations departed significantly from the expected isoplethic distribution towards which balancing selection is expected to drive allelic frequencies (i.e. identical frequency equal to the inverse of the number of alleles in the population). To assess whether this departure could be caused either by drift alone or by population structure, we used numerical simulations to compare our observations with allelic frequency distributions expected : (1) within a single deme from a subdivided population with various levels of differentiation; and (2) within a finite panmictic population with identical allelic diversity. We also investigated the effects of sample size and degree of population structure on tests of departure from isoplethic equilibrium. Overall, our results showed that the observed allele frequency distributions were consistent with a model of subdivided population with demes linked by moderate migration rate.     

中国人dystrophin基因RFLPs的初步研究

We have studied the RFLPs distribution and frequency of dystrophin gene in Chinese by using 14 subclones of complete 14 kb cDNA for the dystrophin gene as hybridization probes. Allelic fragments are detected in hybridization patterns of Pvu II/1a, Taq I/2b-3, Taq I/5b-7, Xba I/10. Among them, the allelic fragments (26 kb and 3.8 kb) in Pvu II/2b-3 patterns and the allelic fragments (10 kb and 8.4 kb) in Taq I/5b-7 patterns are the new RFLPs which have never been reported. From the comparison of our data with those of Caucasian and Japanese respectively and their statistical analysis, we can obtain the results as follows: There is remarkable difference (p less than 0.01) of the allelic fragment frequency in Taq I/2 b-3 (A1 = 3.4 kb, fre. 0.04; A2 = 3.2 kb, fre. 0.96) and Xba I/10 (A1 = 7.4 kb, fre. 0.41; A2 = 6.7 kb, fre. 0.59) between Chinese and Caucasian. The frequency of the allelic fragments A2 in Taq I/8 (A1 = 6.5 kb, A2 = 5.6 kb) and EcoR V/9 (A1 = 11.8 kb, A2 = 10.7 kb) are high in Caucasian, but have not been detected in Chinese. These differences are also highly significant. But the B1B2 allelic frequencies in Taq I/5 b-7 (B1 = 3.2 kb, B2 = 1.6 kb) are the same. There is no significant difference in the frequency of the allelic fragments A1A2 and B1B2 in Pvu II/1 a between Chinese and Japanese. Preliminary results suggest that there probably are high frequencies for spontaneous neutral mutations in the evolution process of the huge dystrophin gene (about 2,300 kb). In the meantime, the neutral mutation frequencies of various sectional sequences have remarkable differences, and that of some sectional sequences of the gene between Chinese and Caucasian may also have remarkable differences.     

Comparing the frequencies of restriction fragment length polymorphisms for dystrophin gene in Chinese with those from Japanese and Caucasian populations

The restriction fragment length polymorphisms distribution and frequency of dystrophin gene in Chinese were studied by using 14 subclones of the entire 14kb cDNA for the dystrophin as hybridization probes. Allelic fragments were detected in hybridization patterns of PvuⅡ/la, Taq Ⅰ/2b-3, Taq Ⅰ/5b-7, and Xba Ⅰ/10. Among them, the allelic fragments (26kb and 3.8kb) in PvuⅡ/2b-3 pattern and the allelic fragments (10.0kb and 8.4kb) in Taq Ⅰ/5b-7 patterns had never been reported previously. Compared with the data from Caucasians and Japanese, it indicated that there was a significant difference (P<0.01) of the allelic fragment frequency in Taq Ⅰ/2b-3 and Xba Ⅰ/10 patterns between Chinese and Caucasians. The frequencies of allelic fragments A2 (5.6kb) in Taq Ⅰ/8 and A2 (10.Tkb) in EcoR Ⅴ/9 were high in Caucasians, yet had not been detected in Chinese, the differences were also highly significant. But in Chinese and Caucasians, the B1B2 allelic frequencies in Taq Ⅰ/5b-7 are the same. As to the frequency of the allelic fragments A1A2 and B1B2 in Pvu Ⅱ/la, there was no significant difference between Chinese and Japanese.     

Allele multiplicity in simple Mendelian disorders.

A model of selection involving two selectively equivalent classes of alleles at a locus is considered. One class consists of normal alleles A1, A2, A3,. . .; the other class consists of detrimental alleles a1, a2, a3, . . . . Mutation within and between allelic classes can occur without restriction, but selection operates in such a way as to maintain an approximately constant overall frequency of A-type and a-type alleles is derived, and it is shown that the distribution of allele frequencies in a sample of detrimental alleles depends on the forward (A to a) mutation rate but not on the selection coefficient, degree of dominance, or mutation rate among a-type alleles. Recurrent mutation therefore generates allelic multiplicity among detrimental alleles, and this is discussed in the context of clinical heterogeneity in simple Mendelian disorders.     

Evolutionary Dynamics of Sporophytic Self-Incompatibility Alleles in Plants

The stationary frequency distribution and allelic dynamics in finite populations are analyzed through stochastic simulations in three models of single-locus, multi-allelic sporophytic self-incompatibility. The models differ in the dominance relationships among alleles. In one model, alleles act codominantly in both pollen and style (SSIcod), in the second, alleles form a dominance hierarchy in pollen and style (SSIdom). In the third model, alleles interact codominantly in the style and form a dominance hierarchy in the pollen (SSIdomcod). The SSIcod model behaves similarly to the model of gametophytic self-incompatibility, but the selection intensity is stronger. With dominance, dominant alleles invade the population more easily than recessive alleles and have a lower frequency at equilibrium. In the SSIdom model, recessive alleles have both a higher allele frequency and higher expected life span. In the SSIdomcod model, however, loss due to drift occurs more easily for pollen-recessive than for pollen-dominant alleles, and therefore, dominant alleles have a higher expected life span than the more recessive alleles. The process of allelic turnover in the SSIdomcod and SSIdom models is closely approximated by a random walk on a dominance ladder. Implications of the results for experimental studies of sporophytic self-incompatibility in natural populations are discussed.     

Allelic Richness following Population Founding Events – A Stochastic Modeling Framework Incorporating Gene Flow and Genetic Drift

Allelic richness (number of alleles) is a measure of genetic diversity indicative of a population''s long-term potential for adaptability and persistence. It is used less commonly than heterozygosity as a genetic diversity measure, partially because it is more mathematically difficult to take into account the stochastic process of genetic drift for allelic richness. This paper presents a stochastic model for the allelic richness of a newly founded population experiencing genetic drift and gene flow. The model follows the dynamics of alleles lost during the founder event and simulates the effect of gene flow on maintenance and recovery of allelic richness. The probability of an allele''s presence in the population was identified as the relevant statistical property for a meaningful interpretation of allelic richness. A method is discussed that combines the probability of allele presence with a population''s allele frequency spectrum to provide predictions for allele recovery. The model''s analysis provides insights into the dynamics of allelic richness following a founder event, taking into account gene flow and the allele frequency spectrum. Furthermore, the model indicates that the “One Migrant per Generation” rule, a commonly used conservation guideline related to heterozygosity, may be inadequate for addressing preservation of diversity at the allelic level. This highlights the importance of distinguishing between heterozygosity and allelic richness as measures of genetic diversity, since focusing merely on the preservation of heterozygosity might not be enough to adequately preserve allelic richness, which is crucial for species persistence and evolution.     

The genetic differentiation at quantitative trait loci under local adaptation

Most adaptive traits are controlled by large number of genes that may all together be the targets of selection. Adaptation may thus involve multiple but not necessarily substantial allele frequency changes. This has important consequences for the detection of selected loci and implies that a quantitative genetics framework may be more appropriate than the classical 'selective sweep' paradigm. Preferred methods to detect loci involved in local adaptation are based on the detection of 'outlier' values of the allelic differentiation F(ST) . A quantitative genetics framework is adopted here to review theoretical expectations for how allelic differentiation at quantitative trait loci (F(STQ) ) relates to (i), neutral genetic differentiation (F(ST) ) and (ii), phenotypic differentiation (Q(ST) ). We identify cases where results of outlier-based methods are likely to be poor and where differentiation at selected loci conveys little information regarding local adaptation. A first case is when neutral differentiation is high, so that local adaptation does not necessitate increased differentiation. A second case is when local adaptation is reached via an increased covariance of allelic effects rather than via allele frequency changes, which is more likely under high gene flow when the number of loci is high and selection is recent. The comparison of theoretical predictions with observed data from the literature suggests that polygenic local adaptation involving only faint allele frequency changes are very likely in some species such as forest trees and for climate-related traits. Recent methodological improvements that may alleviate the weakness of F(ST) -based detection methods are presented.     

Some natural viability systems for a multiallelic locus: a theoretical study

The maintenance of genetic polymorphism under various natural structured viability regimes vs. general unrestricted fitness assignments are compared. The selection models considered include a generalized dominance fitness system, a generalized viability model based on allelic activity values, viability matrices based on multilocus activity levels, viability matrices defined by partitioned "resource" or "substrate" variables, and circulant-type viability matrices. A number of examples that support these formulations are discussed. Detailed results on the nature of the genotype frequency equilibrium configurations for the specified viability models are presented. An increased likelihood for a globally stable equilibrium is predicted for the more structured viability models.     

随机漂移亚群体等位基因频率分布的假定及在DNA指纹数据中的应用

研究影响计算两ＤＮＡ指纹偶然匹配率的亚群体结构,首次提出随机漂移各亚群体单个位点等位基因频率服朋参数为（ｐ１（１－θ）／θ,ｐ２（１－θ）／θ,…ｐｍ（１－θ）／θ）的Ｄｉｒｉｃｈｌｅｔ分布的假定（ｐ１,ｐ２,…,ｐｍ为随机漂移初始频率,θ为近交系数）,证明依分布产生亚群体,其结构、性质与群体遗传理论、样本理论一致;将该分布应用于ＤＮＡ指纹数据,得到了其它方法的类似结论。     

Most recent common ancestor probability distributions in gene genealogies under selection

A computational study is made of the conditional probability distribution for the allelic type of the most recent common ancestor in genealogies of samples of n genes drawn from a population under selection, given the initial sample configuration. Comparisons with the corresponding unconditional cases are presented. Such unconditional distributions differ from samples drawn from the unique stationary distribution of population allelic frequencies, known as Wright's formula, and are quantified. Biallelic haploid and diploid models are considered. A simplified structure for the ancestral selection graph of S. M. Krone and C. Neuhauser (1997, Theor. Popul. Biol. 51, 210-237) is enhanced further, reducing the effective branching rate in the graph. This improves efficiency of such a nonneutral analogue of the coalescent for use with computational likelihood-inference techniques.     

Maximum Likelihood Analysis of Population Differences in Allelic Frequencies

Statistical techniques are presented for the analysis of geographic variation in allelic frequencies. Likelihood ratio test criteria are derived from a multinominal sampling distribution, and are used to answer three questions. (1) Are there geographic differences in allelic frequencies? (2) Are population differences in allelic frequencies associated with environmental differences? (3) Is there any residual "lack of fit" variation among populations, after accounting for that variation associated with environmental differences? The two- and three-allele cases are explicitly treated, and the extension to more alleles is indicated.     

Comparison of methods used for recovering the line origin of alleles in a cross between outbred lines

Here, we introduce the idea of probabilities of line origins for alleles in general pedigrees as found in crosses between outbred lines. We also present software for calculating these probabilities. The proposed algorithm is based on the linear regression method of Haley, Knott and Elsen (1994) combined with the Markov chain Monte Carlo (MCMC) method for estimating quantitative trait locus coefficients used as regressors. We compared the relative precision of our method and the original method as proposed by Haley et al. (1994). The scenarios studied varied in the allelic distribution of marker alleles in parental lines and in the frequency of missing marker genotypes. We found that the MCMC method achieves a higher accuracy in all scenarios considered. The benefits of using MCMC approximation are substantial if the frequency of missing marker data is high or the number of marker alleles is low and the allelic frequency distribution is similar in both parental lines.     

Polymorphic and monomorphic serum esterase heterogeneity in catostomid fish populations

A one-locus, two-allele serum esterase polymorphism is described in populations of Catostomus (Pantosteus) clarki in the connected and disconnected tributaries of the lower Colorado River system. A clinal distribution of allelic frequency is linearly correlated with latitude. This distribution of allelic frequencies, and other characteristics of the polymorphism in C. (P.) clarki populations, are indicative of the selective maintenance of the heterogeneity. Sympatric species of the subgenus Catostomus exhibit a monomorphic esterase phenotype indistinguishable from the heterozygote phenotype in polymorphic populations of C. (P.) clarki. Genetic mechanisms involved in the evolution of one polymorphic locus and/or two homozygous loci from an ancestral gene are discussed.     

Allele frequencies after a bottleneck

The effect that a recent change in population size (a “bottleneck”) has on the genetic composition of a random sample of genes is studied. The population is assumed to evolve as in the Wright-Fisher model with infinitely many neutral alleles. Simple analytic formulas are found for such quantities as the probability distribution and moments of the total number of alleles, the allelic “frequency spectrum,” and the homozygosity, in the sample. Numerical examples are given which compare these results with those obtained previously by a variety of other methods.     

Simulation Studies on Electrophoretically Detectable Genetic Variability in a Finite Population

Using a new model of isoalleles, extensive Monte Carlo experiments were performed to examine the pattern of allelic distribution in a finite population. In this model it was assumed that the set of allelic states is represented by discrete points on a one-dimensional lattice and that change of state by mutation occurs in such a way that an allele moves either one step in the positive direction or one step in the negative direction on the lattice. Such a model was considered to be appropriate for estimating theoretically the number of electrophoretically detectable alleles within a population. The evenness of allelic distribution was measured by the ratio of the effective to the actual number of alleles (n(e)/n(a)). The results of the Monte Carlo experiments have shown that this ratio is generally larger under the new model of isoalleles than under the conventional Kimura-Crow model of neutral isoalleles. In other words, the distribution of allelic frequencies within a population is expected to be more uniform in the new model. By comparing the Monte Carlo results with actual observations, it was concluded that the observed deviation from what is predicted under the new model with selective neutrality is not in the direction of conforming to the overdominance hypothesis but is, in fact, in the opposite direction.