一个基于熵的精细定位数量性状位点的指数

针对数量性状位点的精细定位,本文采用群体的极端样本,利用稠密的标记位点,通过比较标记的熵和条件熵,给出了一个基于熵的指数。该指数是标记基因和性状位点间连锁不平衡系数的函数,它不依赖于标记基因的频率。该指数对应我们之前提出的数量性状位点精细定位的哈迪-温伯格不平衡(HWD)指数,但在精细定位数量性状位点时,本文提出的指数的效能要高于哈迪-温伯格不平衡(HWD)指数。通过计算机模拟,文章调查了不同遗传参数下该指数的性质。模拟结果表明该指数用作精细定位是有效的。     

一个基于熵的对疾病基因精细定位的指数

针对人类疾病基因的精细定位,本文利用稠密的标记位点,通过比较标记的熵和条件熵,给出了一个基于熵的指数。该指数可以度量标记基因和性状位点间连锁不平衡(LD)程度。该指数的特性是它不依赖于标记基因的频率。同时它对应疾病易感位点(DSL)精细定位的哈迪-温伯格不平衡(HWD)指数。通过计算机模拟,文章调查了不同遗传参数下该指数的性质。模拟结果表明该指数用作疾病易感位点精细定位是有效的。     

使用极端样本构建一个基于熵的对数量性状位点关联研究的统计量

基于熵理论,Zhao等提出了一个对复杂疾病易感基因进行关联研究的统计量．本文拓展了这一理论到数量性状,利用熵理论。获得了一个对数量性状位点进行关联研究的采用群体极端样本及稠密标记的统计量．     

通过熵理论使用核心家系进行精细定位(英文)

针对精细定位人类复杂性状基因位点,我们拓展了基于熵的连锁不平衡指数到使用病例-父母和无关的对照-父母设计的家系研究.这个指数比较杂合子父母传递给受累子代和非受累子代基因的熵和条件熵.在单一群体和混合群体两种情形下,我们通过模拟调查了该指数的性质.结果表明在不同遗传模型下利用该指数定位的概率随着样本容量的增大而增大.当样本容量超过200,显性模型和加性模型的概率在90%以上.当样本容量超过300,隐性模型和乘积模型的概率在80%以上.当存在群体混杂时,该指数仍然适用于精细定位.     

基因型错误对数量性状精细定位的哈迪-温伯格不平衡指数的效应

使用紧密相邻的标记位点且与标记基因频率无关的哈迪-温伯格不平衡(HWD)指数被用来对数量性状位点(QTL)进行精细定位.本文讨论了当存在基因型错误时HWD指数的性质.文章指出,当存在基因型错误时,对于在群体的标记基因频率已知的情形使用的两个HWD指数尽管受基因型错误的影响但仍然有效;而仅仅极端样本的标记基因频率已知的情形下使用的两个HWD指数同时与基因型错误和标记基因频率有关.计算机模拟表明,仅仅极端样本的标记基因频率已知的情形下使用的两个HWD指数在精细定位时会产生偏差,不适宜作精细定位.     

使用哈迪-温伯格不平衡检验来检测多个标记-疾病关联(英文)

多位点单体型的可用性为疾病易感位点(DSL)的遗传分析提供了有价值的工具.DSL定位可以通过检测患病个体中一个标记位点的哈迪-温伯格不平衡(HWD)来实现.本文拓展了HWD检验到多个标记位点对DSL进行单体型关联分析.我们调查了HWD检验的统计功效并与常用的x~2统计量进行比较.结果表明HWD检验具有高的功效且比常用的x~2统计量的功效高.     

中国对虾抗WSSV及其它经济性状的QTL定位初步研究

以中国对虾抗WSSV选育群体第四代雌虾和野生中国对虾雄虾为亲本,采用人工精荚移植方式产生F1代家系,家系内个体姊妹交获得R家系材料,42尾R家系个体采用口饲法进行WSSV（White Spot Syndrome Virus）攻毒实验,获得个体抗WSSV及其它相关数据。构建了中国对虾的AFLP（Amphfied Fragment Length Polymorphism）分子标记遗传连锁图谱。利用MAPMAKER／QTL1．1软件进行了中国对虾体长、全长、体重及抗WSSV性状的QTL（Quantitative TraitsLoci）定位分析,首次实现了中国对虾重要经济性状的QTL定位。在LOD值大于2．0的条件下,共检测到和体长相关的QTL位点1个,与全长相关的QTL位点2个,与体重相关的QTL位点2个,与抗WSSV性状相关的位点2个,分别位于3个连锁群上,位点变异解释率从26．6％-66．9％不等。在其中的1个连锁群上检测到了体重、全长和抗WSSV性状相关的三个QTL位点,1个连锁群上检测到了体重和抗WSSV性状相关的两个QTL位点,1个连锁群上检测到了全长和体长相关的两个QTL位点。表明在中国对虾在此生长阶段,抗WSSV性状和个体大小存在一定程度的正相关关系[动物学报54（6）：1075-1081,2008]。     

人类混血群体连锁不平衡的遗传学模型与基因定位

人类混血群体可以说是混合群体的一种特例．在无选择、无突变、无限随机交配群体的假定前提下,研究了亲本群体的基因频率对混血群体及其衍生后代群体连锁不平衡结构的影响,导出了各群体连锁不平衡值的表达式,建立了一个估计基因间重组率的简便方法;同时, 采用估算分子标记与QTL之间连锁不平衡系数的统计分析方法,分析了人类混血群体及其衍生后代群体QTL检测与估计的关系,建立了该关系的系列理论公式．研究结果表明,本方法不仅适用于人类疾病(包括复杂遗传疾病)基因定位,而且适合于人类正常基因的定位,同时也适用于人类普通多基因性状的QTL分析．     

一种有效的复杂疾病基因定位的检测法

连锁不平衡（LD）应用于某些复杂疾病基因的定位,近年来发展了许多LD定位方法,除TDT外,大多数LD定位方法须先假定无人群混和,人群混合可增大在疾病基因定位时犯Ⅰ类错误的机率,产生无效结果。此方法利用LD来检测标记位点和疾病敏感位点（DSL）的连锁（有连锁不平衡）相关（有连锁）。分析时采用不相关样本,已知其父母基因型和至少父母之一为杂合子,再将随机样本依基因型不同分类,然后对来自不同类的数据应用有力的统计方法进行单独和联合分析。此LD定位法不仅适用于患病和正常个体,而且有效消除据父母基因分类的样本定位时人群混合的影响,分析结果和模拟结果也表明此方法解决了在检测标记位点和疾病敏感位点之间的连锁和相关时人群混和的问题,但与TDT比,此法在检测的位点为DSL时丙能有效和充分地利用矫正数据,检测位点不是DSL时,此法和TDT法可相互补充更有效地检测连锁的DSL。     

RIL群体区间分子标记-QTL定位的相关方法

分析了RIL群体中以分子区间标记进行QTL定位的相关方法．通过对分子标记赋值可获得与数量性状表型值的简单相关系数．然后,在此基础上进行连锁检验．此外．在特定情况下利用R值,可以估计数量性状座位(QTL)和分子标记位点(ML)间的重组值．     

An entropy-based measure for QTL mapping using extreme samples of population

Quantitative trait locus (QTL) mapping can be accomplished through the method of selective genotyping, which is based on the differences of frequencies between an upper sample and a lower sample in population. However, amplifying the differences in marker allele frequencies in extreme samples may increase the probability for QTL mapping. Shannon entropy, which is a nonlinear function of allele frequencies, can be used to amplify the differences in marker allele frequencies. In this paper, we present a novel measure for linkage disequilibrium (LD) between a marker and single QTL, that is based on the comparison of the entropy and conditional entropy in a marker in extreme samples of population. This measure of LD between the marker and the trait locus can be used when the marker allele frequencies are known in the extreme samples of a population. We investigate the mapping performance in both analytic and simulation scenarios of a single QTL linked to a single marker. Our results show that the measure has very reasonable performance. In addition, a simulation study is performed on the basis of the haplotype frequencies of 10 SNPs of angiotensin-I converting enzyme (ACE) genes.     

Analysis and Optimization of Bulk DNA Sampling with Binary Scoring for Germplasm Characterization

The strategy of bulk DNA sampling has been a valuable method for studying large numbers of individuals through genetic markers. The application of this strategy for discrimination among germplasm sources was analyzed through information theory, considering the case of polymorphic alleles scored binarily for their presence or absence in DNA pools. We defined the informativeness of a set of marker loci in bulks as the mutual information between genotype and population identity, composed by two terms: diversity and noise. The first term is the entropy of bulk genotypes, whereas the noise term is measured through the conditional entropy of bulk genotypes given germplasm sources. Thus, optimizing marker information implies increasing diversity and reducing noise. Simple formulas were devised to estimate marker information per allele from a set of estimated allele frequencies across populations. As an example, they allowed optimization of bulk size for SSR genotyping in maize, from allele frequencies estimated in a sample of 56 maize populations. It was found that a sample of 30 plants from a random mating population is adequate for maize germplasm SSR characterization. We analyzed the use of divided bulks to overcome the allele dilution problem in DNA pools, and concluded that samples of 30 plants divided into three bulks of 10 plants are efficient to characterize maize germplasm sources through SSR with a good control of the dilution problem. We estimated the informativeness of 30 SSR loci from the estimated allele frequencies in maize populations, and found a wide variation of marker informativeness, which positively correlated with the number of alleles per locus.     

Statistical Mechanics and the Evolution of Polygenic Quantitative Traits

The evolution of quantitative characters depends on the frequencies of the alleles involved, yet these frequencies cannot usually be measured. Previous groups have proposed an approximation to the dynamics of quantitative traits, based on an analogy with statistical mechanics. We present a modified version of that approach, which makes the analogy more precise and applies quite generally to describe the evolution of allele frequencies. We calculate explicitly how the macroscopic quantities (i.e., quantities that depend on the quantitative trait) depend on evolutionary forces, in a way that is independent of the microscopic details. We first show that the stationary distribution of allele frequencies under drift, selection, and mutation maximizes a certain measure of entropy, subject to constraints on the expectation of observable quantities. We then approximate the dynamical changes in these expectations, assuming that the distribution of allele frequencies always maximizes entropy, conditional on the expected values. When applied to directional selection on an additive trait, this gives a very good approximation to the evolution of the trait mean and the genetic variance, when the number of mutations per generation is sufficiently high (4Nμ > 1). We show how the method can be modified for small mutation rates (4Nμ → 0). We outline how this method describes epistatic interactions as, for example, with stabilizing selection.     

The use of multiple restriction fragment length polymorphisms in prenatal risk estimation. II. Conditional risk distributions

Although analytical procedures for multiple marker risk estimation are now well established, we still lack a unified optimal procedure for deciding which family members to examine and which markers to use. Towards this goal, the application of conditional risk distributions is developed, along with a suggested statistic for judging the utility of a marker. The conditional risk distribution depends on what knowledge has already been obtained about the pedigree, and indicates the expected outcome of risk estimates after another marker is examined. Population genetic aspects including haplotype frequencies, linkage disequilibrium, family size and pedigree structure and the statistical confidence in the linkage map all influence the optimal strategy for multiple marker risk estimation.     

Measuring Ambiguity in HLA Typing Methods

In hematopoietic stem cell transplantation, donor selection is based primarily on matching donor and patient HLA genes. These genes are highly polymorphic and their typing can result in exact allele assignment at each gene (the resolution at which patients and donors are matched), but it can also result in a set of ambiguous assignments, depending on the typing methodology used. To facilitate rapid identification of matched donors, registries employ statistical algorithms to infer HLA alleles from ambiguous genotypes. Linkage disequilibrium information encapsulated in haplotype frequencies is used to facilitate prediction of the most likely haplotype assignment. An HLA typing with less ambiguity produces fewer high-probability haplotypes and a more reliable prediction. We estimated ambiguity for several HLA typing methods across four continental populations using an information theory-based measure, Shannon's entropy. We used allele and haplotype frequencies to calculate entropy for different sets of 1,000 subjects with simulated HLA typing. Using allele frequencies we calculated an average entropy in Caucasians of 1.65 for serology, 1.06 for allele family level, 0.49 for a 2002-era SSO kit, and 0.076 for single-pass SBT. When using haplotype frequencies in entropy calculations, we found average entropies of 0.72 for serology, 0.73 for allele family level, 0.05 for SSO, and 0.002 for single-pass SBT. Application of haplotype frequencies further reduces HLA typing ambiguity. We also estimated expected confirmatory typing mismatch rates for simulated subjects. In a hypothetical registry with all donors typed using the same method, the entropy values based on haplotype frequencies correspond to confirmatory typing mismatch rates of 1.31% for SSO versus only 0.08% for SBT. Intermediate-resolution single-pass SBT contains the least ambiguity of the methods we evaluated and therefore the most certainty in allele prediction. The presented measure objectively evaluates HLA typing methods and can help define acceptable HLA typing for donor recruitment.     

A new distance measure for comparing sequence profiles based on path lengths along an entropy surface

We describe a new distance measure for comparing DNA sequence profiles. For this measure, columns in a multiple alignment are treated as character frequency vectors (sum of the frequencies equal to one). The distance between two vectors is based on minimum path length along an entropy surface. Path length is estimated using a random graph generated on the entropy surface and Dijkstra's algorithm for all shortest paths to a source. We use the new distance measure to analyze similarities within familes of tandem repeats in the C. elegans genome and show that this new measure gives more accurate refinement of family relationships than a method based on comparing consensus sequences.     

Markov process of maintained impulse activity in central single neurons

To clarify the stochast properties of the maintained impulse activity of the central nervous system, we proposed a measure of statistical dependency on the basis of Shannon's entropy. This measure could provide the Markov properties of the neural impulse sequences, representing the necessary and sufficient condition for the statistical dependence. The order of Markov process of the sequence is determined by the conditional entropy which is derived from the joint entropy. Here the joint entropy in the case of Gaussian process is directly related with the covariance matrix which is substituted for the matrix of the serial correlation coefficients. Therefore the condition to determine the order of Markov process is obtained by the equation of the matrices of the serial correlation coefficients. The order of Markov process of the neural impulse sequences recorded from the mesencephalic reticular formation (MRF), red nucleus (RN), and lateral geniculate nucleus (LGN) neurons has been estimated. The maintained impulse activity of the MRF and RN neurons had from the 2-nd to 4-th order Markov property, while that of the LGN had no Markov property, in the consecutive impulse sequences.     

An entropy-based measure of founder informativeness

Optimizing quantitative trait locus (QTL) mapping experiments requires a generalized measure of marker informativeness because variable information is obtained from different marker systems, marker distribution and pedigree types. Such a measure can be derived from the concept of Shannon entropy, a central concept in information theory. Here we introduce entropy-based founder informativeness (EFI), a new measure of information content generalized across pedigrees, maps, marker systems and mating configurations. We derived equations for inbred- and outbred-derived mapping populations. Mathematical properties of EFI include enhanced sensitivity to mapping population type and extension to any number of founders. To illustrate the use of EFI, we compared experimental designs for QTL mapping for three examples: (i) different marker systems for an F2 pedigree, (ii) different marker densities and sampling sizes for a BC1 pedigree and (iii) a comparison of haplotypic versus zygotic analyses of an outbred pedigree. As an a priori generalized measure of information content, EFI does not require phenotypic data for optimizing experimental designs for QTL mapping.