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。      

自交率对Hardy-Weinberg平衡的效应

1908年,德国医生魏伯格（Weinberg）和英国数学 家哈德(Hard对分别发现随机交配群体遗传平衡规 律,它已成为群体遗传学、也是数量遗传学的基石。但 是Hardy-Weinberg 定律只是群体遗传学规律中的一 条特殊规律,它并不适应于许多类型自然群体的遗传 平衡。     

群体遗传平衡定律的应用

群体遗传平衡定律,即哈迪-魏伯格定律,是群体遗传学一个最基本最重要的定律,这是由英国数学家哈迪(Hardy)和德国医生魏伯格(Weinberg)在1908年先后独立地证明过的：在一个随机交配的大群体,如果没有其他因素(如突变、选择、迁移、漂变)的干扰,总是处于一种平衡状态,即从上一代到下一代基因型     

新疆维吾尔族四个STR位点遗传多态性分析

研究新疆维吾尔族人群D16S539、D13S317、D7S820和D5S818的STR基因位点的基因及基因型分布,获得4个基因座的群体遗传学数据。采用PCR扩增技术和基因扫描技术进行样本STR遗传结构分析,并与其他种族、人群的等位基因频率进行比较。结果表明4个基因位点在新疆维吾尔族人群中均具有遗传多态性。4个基因座的基因型分布均符合Hardy-Weinberg平衡定律（P＞0.05）,不同人群基因频率分布存在一定的差异,所得到的等位基因频率等数据可为遗传学研究、法医个体畜产品识别及亲子鉴定提供依据。     

多对独立杂合基因自交群体F1到Fn基因型熵的变化 规律

建立了具有多对独立杂合基因的自交群体的基因型熵的逐代演变数学模型, 给出每一世代中各个基因型所占的比例的三叉树算法。揭示出群体的基因型熵与独立杂合基因对数m存在线性关系, 与自交代数n存在非线性关系。固定代数n, 具有m对独立杂合基因的群体的基因型熵是仅有一对杂合基因的群体的基因型熵的m倍; 固定独立杂合基因对数m, 群体的基因型熵由F1至F3逐代递增, 在F3达到最大值, 从F3起逐代递减, 最终平衡在基因型熵最小的世代。讨论了这一模型对杂交育种工作的意义。     

一个具选择、突变、迁移的群体的遗传差分模型

假设一个群体是由“单位点—双基因”的个体所组成的,在该群体内存在选择、突变、迁移、生死等效应的作用。本文给出了在上述假设下并满足:(1)世代重叠,选择、突变、迁移、生死等效应的作用均在世代遗传之间完成;(2)群体适当大,个体间交配随机,符合孟德尔式遗传;(3)没有任何意外的灾祸等约定的群体遗传的数学模型。通过模型分析,我们能够进一步用数学语言来解释一些生命现象。模型分析指出:虽然某些群体不满足Hardy-Weinberg定律所叙述的条件,但可能具有和Hardy-Weinberg定律的结论相似的结果。该文中还就几个主要参数的变化讨论了群体遗传和进化的某些性质,如平衡等。最后,我们给出了该模型的一个数值例子。     

福清黑松醇溶蛋白的群体遗传分析

采用聚丙烯酰胺凝胶电泳技术,对福清黑松群体进行醇溶蛋白的多样性分析,共获得40种图谱,9个等位基因位点。对这些位点的统计分析表明,福清黑松的多肽位点百分率P=55.56%, 等位基因平均数A=3.00,平均等位基因有效数目Ae=2.28,预期杂合度He=0.533,平均实际杂合度Ho=0.402,固定指数F仅为0.246>0。该群体表现出遗传多样性水平较高,但该群体偏离了Hardy-Weinberg平衡定律,原因可能是取样偏差、群体中个体密度分布不均和个体生长状况不好,不能产生充分的随机交配,出现遗传漂移导致的。     

熵与生命和肿瘤的关系

热力学是研究能量转换规律的科学 ,本文针对热力学第二定律即熵与生命的关系提出一些见解和分析 ,来作以下讨论。1.熵与生命代谢的关系在克劳修斯的热力学第二定律中指出 :一个孤立系统不管其初始状态如何 ,最终将演化为最无序 ,最混乱的状态。而且满足热力学平衡的状态 ,简言之就是一个孤立系统的熵随时间增高 ,熵增加原理告诉我们自发过程是由比较有序向比较无序的方向进行的 ,自发过程总是伴随着熵的增加 ,或者说熵增加过程是自发过程。根据原理 ,熵的改变值 (△Ｓ)只由始态和终态确定 ,而与过程和途径无关。以人体为例 ,就生命的新陈代…     

中国普米族、傈僳族STR遗传多态性研究

采用荧光标记STR基因扫描技术对普米族和傈僳族进行了STR多态性调查,9个STR基因座在普米族群体中,检出85个等位基因,194种基因型,其频率分布在0．0050－0．5250和0．0098－0．3235,在傈僳族群体中,共检出63个等位基因,145种基因型,其频率分布在0．0050－0．4802和0．0099－0．3664,χ2检验表明,各基因座的基因型分布符合Hardy-Weinberg平衡定律（P＞0．05）,统计学结果显示,这些遗传标记在普米族和傈僳族群体中,杂合度均大于0．6,平均多态信息量高于0．7,个体识别力在0．8以上,非父排除率也都超过了0．5,说明实验所选STR标记对民族群体遗传学研究是极为有价值的。     

遗传漂变的计算机模拟

在生物群体繁衍过程中,经常出现基因丢失现象,原因之一是遗传漂变。与选择、突变等因素一样,遗传漂变也是影响群体基因频率的一个主要因素。只有在随机交配的大群体内,没有其他因素干扰,基因平衡定律才能完全实现。而无论自然界还是家养条件下,生     

Identification and characterization of microsatellites for striped bass from repeat-enriched libraries

Striped bass (Morone saxatilis) is economically important in the US due to its value as an aquaculture species and in supporting commercial and recreational fisheries, especially those off the Atlantic coast and in the Gulf of Mexico. Modern strategies for managing fishery populations and aquaculture broodstocks employ the use of molecular genetic markers to identify individuals, assign parentage, and characterize population genetic structure and levels of inbreeding and migration. As part of a collaborative effort to utilize molecular genetic technologies in striped bass breeding programs we generated microsatellite markers for use in population genetic studies, broodstock selection and management strategies, and the construction of a genetic map. We developed 345 new microsatellite markers for striped bass, a subset (n=71) of which was characterized by genotyping samples from two striped bass broodstock populations to evaluate marker polymorphism, percent heterozygosity, Hardy–Weinberg equilibrium (HWE), linkage disequilibrium (LD) and utility for population genetic studies.     

Hardy-Weinberg定律在专科教学中的课堂设计

Hardy-Weinberg定律是群体遗传学的第一理论基石,也是现代进化论、现代优生学和群体育种的理论基础,是遗传学教学中的重难点内容,但通过合理的教学设计可帮助学生全面理解、掌握并应用该定律,为后续学习奠定基础。     

How inbreeding and outbreeding influence the risk of extinction--a genetically explicit model

We have developed a stochastic model to explore the common effect which genetics and demography have on the extinction risk of endangered populations. The dynamics is formulated as a MARKOVian birth and death process (in continuous time), whereby selection acts through different mortalities of each genotype. With the help of this model we are able to show how inbreeding and outbreeding can influence the genetic variability and the survival of a population. Whether inbreeding or outbreeding takes place depends on the specific mating system. In our model we consider positive assortative as well as disassortative mating. In the case of additive fitness we show that inbreeding reduces the extinction risk and the genetic variability.     

Mathematical models in genetics

In this study, we present some of the basic ideas of population genetics. The founders of population genetics are R.A. Fisher, S. Wright, and J. B.S. Haldane. They, not only developed almost all the basic theory associated with genetics, but they also initiated multiple experiments in support of their theories. One of the first significant insights, which are a result of the Hardy–Weinberg law, is Mendelian inheritance preserves genetic variation on which the natural selection acts. We will limit to simple models formulated in terms of differential equations. Some of those differential equations are nonlinear and thus emphasize issues such as the stability of the fixed points and time scales on which those equations operate. First, we consider the classic case when selection acts on diploid locus at which wу can get arbitrary number of alleles. Then, we consider summaries that include recombination and selection at multiple loci. Also, we discuss the evolution of quantitative traits. In this case, the theory is formulated in respect of directly measurable quantities. Special cases of this theory have been successfully used for many decades in plants and animals breeding.     

IS INBREEDING DEPRESSION LOWER IN MALADAPTED POPULATIONS? A QUANTITATIVE GENETICS MODEL

Despite abundant empirical evidence that inbreeding depression varies with both the environment and the genotypic context, theoretical predictions about such effects are still rare. Using a quantitative genetics model, we predict amounts of inbreeding depression for fitness emerging from Gaussian stabilizing selection on some phenotypic trait, on which, for simplicity, genetic effects are strictly additive. Given the strength of stabilizing selection, inbreeding depression then varies simply with the genetic variance for the trait under selection and the distance between the mean breeding value and the optimal phenotype. This allows us to relate the expected inbreeding depression to the degree of maladaptation of the population to its environment. We confront analytical predictions with simulations, in well-adapted populations at equilibrium, as well as in maladapted populations undergoing either a transient environmental shift, or gene swamping in heterogeneous habitats. We predict minimal inbreeding depression in situations of extreme maladaptation. Our model provides a new basis for interpreting experiments that measure inbreeding depression for the same set of genotypes in different environments, by demonstrating that the history of adaptation, in addition to environmental harshness per se, may account for differences in inbreeding depression.     

非平衡群体基因变异测量的Shannon信息量方法

在Shannon信息量的基础上,对非平衡群体建立了群体基因型相对信息量S′（G）,纯合体相对信息量S′J（G）、杂合体相对信息量S′H（G）的概念,并赋予它们以遗传学意义,与基因一致度J和基因多样度D进行了理论比较,结果表明,二者在数量规律上有很好的一致性,但又是相对独立的指标体系,且各相对信息量还有新的内涵。S′（G）既能表征基因变异,又能反映基因型水平上的遗传变异,S′J（G）主要反映纯合体的遗传变异,S′H（G）主要反映杂合体的遗传变异,各相对信息量既可反映群体的遗传变异程度,又能比较不同位点间的遗传变异程度。     

100 Jahre Hardy-Weinberg-Gleichgewicht

One hundred years ago, Godfrey H. Hardy and Wilhelm Weinberg worked out, in independent publications, the formula that is regarded today as the elementary law for quantitative population genetics. In this article we describe the time period before the discovery of the Hardy–Weinberg law and try to illuminate the circumstances that surrounded its development. We will further name those scientists who also worked on this problem and who can be regarded as the predecessors of the Hardy–Weinberg principle.     

两个基因座位的遗传平衡原理

由于许多教科书中关于连锁平衡的介绍,多是引用结论或是推导不太严谨,使学生在学习群体遗传学时对理解连锁平衡的原理感到困难。本文从遗传平衡的基本条件出发,通过较严谨的数学推导,介绍了两个基因座的连锁平衡条件、平衡过程等原理,供教师和学生在群体遗传学教学中参考。Abstract: Because linkage equilibrium is introduced by directly quoting the conclusions or imprecise mathematical reasoning in most of textbooks, many students are puzzled with the problem of linkage equilibrium when they learn population genetics. Based on the radical conditions of genetic equilibrium, the principle of linkage equilibrium condition and process, for two gene loci is introduced by precise mathematical reasoning. The article may provide reference to teachers and students in the teaching and learning of population genetics.