哈代-温伯格定律的妙用

1908年和1909年英国数学家哈代和德国医生温伯格分别独立证明，如果一个种群符合下列条件：①种群是极大的；②种群个体间交配是随机的；③没有突变产生；④种群之间不存在个体的迁移或基因交流；⑤没有自然选择。那么。这个种群的基因频率（包括基因型频率）就可以一代代保持平衡，这就是哈代-温伯格定律。也称遗传平衡定律。下面探讨该定律在相关问题中的应用。     

遗传平衡定律的推广及应用

生物进化的实质是种群基因频率的改变.介绍了遗传平衡定律的适用范围、表达式、推广及应用,概述了突变、基因重组、自然选择、迁移、遗传漂变等因素对遗传平衡及基因频率的影响.     

"基因自由组合定律"的教学设计

在学生已有知识和能力的基础上,用层层质疑和环环相扣的情境问题,启发学生从2对相对性状遗传现象入手,逐步探究位于非同源染色体上的非等位基因之间的关系,直至基因自由组合定律的本质。     

“基因自由组合定律”的教学设计

“提高生物科学素养”是高中生物学课程的核心理念之一。在生物学教学过程中,学生获得生物科学和技术的基本知识,学会科学探究的方法,培养分析和解决问题的能力．形成科学态度和科学价值观等,是高中生物学课程的重要任务。在高中生物学的学习内容中．孟德尔定律是培养学生科学素养的有力素材,尤其是基因的自由组合定律的教学活动,对培养学生的探究意识和创新精神,以及接受科学方法的训练有着重要作用。为了达到预期教学目标,笔者对基因的自由组合定律的教学设计如下。     

群体遗传学教学与研究辅助软件的设计与应用

为群体遗传学教学与研究的需要, 采用Visual Basic6.0开发设计了群体遗传学教学与研究辅助软件。软件设计综合考虑了影响群体结构各方面因素, 通过各种条件参数的设置、理论推算、计算机模拟和显示状态的选择, 以图、表的方式精确、形象直观地输出群体基因频率和基因型频率在世代间的变化、分布规律和统计特征。该软件无论从功能上, 还是从操作、界面上都是目前较为完善的教学与研究辅助软件。     

《基因的自由组定律》教学的感悟

<正>自由组合定律是经典遗传学中的核心知识,是教学的重点和难点。如何有效地突破重点和难点,笔者认为,关键是要理解性状的自由组合其实质是基因的自由组合。一、如何理解性状之间的组合基因的自由组合定律是在基因的分离定律的基础上总结出来的。     

"基因的分离定律"的教学分析与设计

基因的分离定律是关于一对相对性状分离的遗传原理,揭示了杂合子内等位基因的独立性、分离性和随机结合性等一系列连续的遗传行为。等位基因分离导致性状分离这一命题,是孟德尔通过豌豆的一对相对性状的杂交实验,运用“假说-演绎”科学方法,历经“提出问题-构建假说-验证假说-获取结论”建立起来的。该命题是由显性基因、隐性基因、等位基因、显性性状、隐性性状、相对性状和性状分离等一系列概念组成的严密的逻辑体系,它不仅是构成基冈的自由组合定律和伴性遗传定律的基石,而且本身具有重要的方法论价值。本文是对教学实践经验的思考和提炼,主要探讨“假说-演绎”这一科学方法的内涵、施教策略以及如何进行命题性知识的教学。     

"基因的分离定律"新课的教学设计

将新课程标准中注重生物科学史学习的教学建议贯穿于“基因的分离定律”的教学中,利用生物科学史创设情境,以有效的问题串提问来提高学生的学习兴趣和学习能力．使学生体验科学家发现问题、解决问题、深化认识的过程和探索精神,促进学生构建良好的认知结构。     

“基因频率与基因型频率”的教学点滴

必修2第7章第2节中“种群基因频率的改变与生物进化”是本节内容的重点,但其中的“基因频率与基因型频率”则是学生学习的难点,为了突破此难点,在教学过程中我把这部分知识进行整理、归纳,总结如下：一、基本概念的理解 基因频率是指特定基因在种群中出现的频率。     

基于发现学习的“自由组合定律”教学设计

以基于探究和建构主义的“发现学习”理论为指导。设计了面向高中学生的“自由组合定律”一节的教学,引导学生使用“假说一演绎”这种现代科学研究中常用的科学方法,结合数学统计推导,分析孟德尔2对相对性状杂交实验,尝试对不同性状自由组合现象作出解释和假说,同时,启发学生根据已有知识设计测交实验,并预测和推导实验结果,再与孟德尔的实际测交实验结果比较,进一步检验假说是否成立,最终构建对自由组合定律的科学理解。     

A straightforward multiallelic significance test for the Hardy-Weinberg equilibrium law

Much forensic inference based upon DNA evidence is made assuming Hardy-Weinberg Equilibrium (HWE) for the genetic loci being used. Several statistical tests to detect and measure deviation from HWE have been devised, and their limitations become more obvious when testing for deviation within multiallelic DNA loci. The most popular methods-Chi-square and Likelihood-ratio tests-are based on asymptotic results and cannot guarantee a good performance in the presence of low frequency genotypes. Since the parameter space dimension increases at a quadratic rate on the number of alleles, some authors suggest applying sequential methods, where the multiallelic case is reformulated as a sequence of "biallelic" tests. However, in this approach it is not obvious how to assess the general evidence of the original hypothesis; nor is it clear how to establish the significance level for its acceptance/rejection. In this work, we introduce a straightforward method for the multiallelic HWE test, which overcomes the aforementioned issues of sequential methods. The core theory for the proposed method is given by the Full Bayesian Significance Test (FBST), an intuitive Bayesian approach which does not assign positive probabilities to zero measure sets when testing sharp hypotheses. We compare FBST performance to Chi-square, Likelihood-ratio and Markov chain tests, in three numerical experiments. The results suggest that FBST is a robust and high performance method for the HWE test, even in the presence of several alleles and small sample sizes.     

Large Hardy-Weinberg equilibrium deviations in the Daphnia longispina of Lake El Tobar

The population structure of Daphnia longispina in Lake El Tobar, Spain was studied by measuring variation at the aldehyde oxidase (AO), phosphoglucose isomerase (PGI) and phosphoglucose mutase (PGM) loci in each of 1337 individuals from four collections. In 9 of the 12 comparisons between observed allele frequencies and those expected by Hardy-Weinberg equilibrium there was an excess of heterozygotes. We found 27 of the potential number of 54 composite electromorphs (clones) based on the three allozymes. Clone diversities were rather high in all collections. Three clones reached frequencies of over 25% and different clones were dominant in each of the four collections. Strong temporal variation was found in the genetic structure of this Daphnia population. This variation was driven by changes in the relative frequencies of the component clones in the lake rather than by a recruitment of novel clones into the population.We conclude with a consideration of the role of models relating allele and genotype frequencies in populations of cyclical parthenogens. Because the breeding system of these populations infrequently involves recombination between clones, models such as the Hardy-Weinberg have limited value in providing meaningful measures of population structure.     

A new method of testing for Hardy-Weinberg equilibrium and ordering populations

The assumption of Hardy-Weinberg equilibrium (HWE) among alleles in a nonevolving population is of fundamental importance in genetic studies. Deviation from HWE in a population usually indicates inbreeding, stratification and sometimes problems in genotyping. In populations of affected individuals, these deviations can also provide evidence for association. In this paper, we introduce a measure based on the Kullback-Leibler discrimination information function that quantifies the deviation from HWE in a population. We use this measure to order populations. We also propose a test for HWE based on an estimate of this measure. The test is a statistically consistent test of the null hypothesis for all alternatives and is very easy to implement. Our proposed test statistic is compared with an earlier, widely used, test. Finally, the use of the proposed new test is shown in an illustrative example.     

A P-Value for an Exact Two-Sided Test of Hardy-Weinberg Equilibrium

A two-tailed P-value is proposed for testing two-sided departures from Hardy-Weinberg equilibrium at a diallelic locus. The calculation of P uses the exact conditional distribution of the test statistic P, the observed number of heterozygotes in the sample. The proposed P-value is always two-tailed, unlike other P-values proposed in the literature.     

Representation of nonepistatic selection models and analysis of multilocus Hardy-Weinberg equilibrium configurations

Summary The paper develops conditions for the existence and the stability of central equilibria emanating from selection recombination interaction with generalized nonepistatic selection forms operating in multilocus multiallele systems. The selection structure admits a natural representation as simple sums of Kronecker products based on a common set of marginal selection components. A flexible parametrization of the recombination process is introduced leading to a canonical derivation of the transformation equations connecting gamete frequency states over successive generations. Conditions for the existence and stability of multilocus Hardy-Weinberg (H.W.) type equilibria are elaborated for the classical nonepistatic models (multiplicative and additive viability effects across loci) as well as for generalized nonepistatic selection expressions. It is established that the range of recombination distributions maintaining a stable H.W. polymorphic equilibrium is confined to loose linkage in the pure multiplicative case, but is not restricted in the additive model. In the bisexual case we ascertain for the generalized nonepistatic model the stability conditions of a common H.W. polymorphism.This paper was supported in part by NIH Grant GM 10452-14 and NSF Grant MCS 75-23608.     

关于最大信息熵原理与群体遗传平衡一致性的探讨

汪小龙等建立了用最大信息熵原理推导一个基因座上群体遗传平衡的统一数学模型,并给出了模型的最大值解,此解正是Hardy-Weinberg平衡定律所给出的基因型频率。这说明当群体基因型信息熵最大时,群体基因型频率不再变化,达到平衡状态,从而证明了最大信息熵原理与Hardy-Weinberg平衡定律具有一致性,同时指出这一结论可以推广至有迁移、突变、选择、遗传漂变、近亲交配的群体以及多个基因座情形。概括地说就是：最大信息熵原理与群体遗传平衡具有一致性。但是,他们仅仅证明了最大信息熵原理与一个基因座上Hardy-Weinberg平衡定律具有一致性,本文在这个范围内将其推广至多个基因座,且每一个基因座均为复等位基因情形。至于最大信息熵原理是否与其它的群体遗传平衡具有一致性,他们的结论仅仅是猜想,并未严格推导。事实上,要想将这种一致性推广到迁移、突变、随机漂变和近亲交配等群体,则不见得正确。      

中国畲族、锡伯族、壮族和藏族Penta E位点的遗传多态性

应用复合PCR扩增技术和荧光毛细管DNA自动电泳分型的方法,使用国产试剂盒,检测Penta E位点在中国畲族、锡伯族、壮族和藏族中的基因频率分布情况。获得了4个民族各约100名无关个体的Penta E位点的等位片段及基因型频率,共发现20个等位片段,其频率分布在0.0048～0.2396之间。各民族的平均杂合度为0.8838,平均个体识别力0.9748,平均非父排除率0.7635,平均多态信息总量0.8950。研究表明Penta E位点属高杂合度、高识别能力的遗传标记,是法庭科学亲子鉴定和个体识别的理想位点。      

On S.N. Bernstein's derivation of Mendel's Law and 'rediscovery' of the Hardy-Weinberg distribution

Around 1923 the soon-to-be famous Soviet mathematician and probabilist Sergei N. Bernstein started to construct an axiomatic foundation of a theory of heredity. He began from the premise of stationarity (constancy of type proportions) from the first generation of offspring. This led him to derive the Mendelian coefficients of heredity. It appears that he had no direct influence on the subsequent development of population genetics. A basic assumption of Bernstein was that parents coupled randomly to produce offspring. This paper shows that a simple model of non-random mating, which nevertheless embodies a feature of the Hardy-Weinberg Law, can produce Mendelian coefficients of heredity while maintaining the population distribution. How W. Johannsen's monograph influenced Bernstein is discussed.     

Global convergence properties in multilocus viability selection models: the additive model and the Hardy-Weinberg law

A natural coordinate system is introduced for the analysis of the global stability of the Hardy-Weinberg (HW) polymorphism under the general multilocus additive viability model. A global convergence criterion is developed and used to prove that the HW polymorphism is globally stable when each of the loci is diallelic, provided the loci are overdominant and the multilocus recombination is positive. As a corollary the multilocus Hardy-Weinberg law for neutral selection is derived.Research supported in part by NIH grants GM 39907-01, GM 10452-26 and NSF Grant DMS 86-06244Research supported in part by a US-Israel Binational Science Foundation grant 85-00021 and NIH grant GM 28016