【正文】 ng locus by locus, cumulative probabilities for Sij. – the second step involves moving back down the genome, sampling Sij from a univariate density that is a function of the associated cumulative probability, the previous sampled segregation indicator (Si j+1) and the rebination rate between loci j and j+1. 23:13 ? Introduction to Loki – Loki was originally designed for multipoint linkage analysis in general pedigrees using MCMC methods. – Then, it has since been modified for IBD probability calculation. – The user supplies Loki with the pedigree structure, marker genotypes, marker positions and QTL positions for which the IBD matrices are to be calculated. – Dependent chains of IBD probabilities are then obtained for each QTL position. – Convergence is determined by monitoring the IBD probabilities over the iteration number. – Once the probabilities stabilize, the sampler is deemed to have reached convergence. 23:13 Variance ponent estimation ? After having calculated IBD probabilities, there are two difficulties in estimating variance ponents by ML(REML). – Firstly, the IBD matrix is a pletely general symmetrical matrix and does not have an obvious inverse. – Secondly, the IBD matrix is likely to be singular. 23:13 ? why the IBD matrices are often singular? – The reason is that two related relatives can share 0 or 100% of their alleles IBD, which can cause a dependency in the matrix of IBD probabilities. – The genotypes of the parents are M1M2 and M3M4. If the progeny have genotypes M1M3 and M2M4(a), or M1M3 and M1M3(b), then the resulting IBD matrix is: a b 23:13 ? If the maximisation algorithm is based upon the plete matrix V (or V1), then there should not be a problem. ? If the maximisation is based upon an algorithm that requires Q1, then using genomic positions which are slightly distant from the markers will give a positivedefinite Q, 23:13 Implementation example ? Visscher et al. (1999) used the bination of an MCMC sampling approach and REML variance ponent estimation to map a QTL for bipolar disorder (manic depression) in a human pedigree. ? The pedigree size was 168, over 4 generations, and 143 individuals had a phenotypic score. ? The incidence of major recurrent depression (unipolar disorder) and bipolar disorder was 17/143 and 11/143. ? A small segment of chromosome 4 was considered because this region had previously shown linkage to bipolar disorder using a parametric linkage analysis, and 11 microsatellite markers were scored spanning 26 cM. 23:13 ? IBD probabilities were estimated using Loki, using 10,000 samples. ? REML was used to estimate 81 variance ponents, with an algorithm based upon the plete (co)variance matrix V, to avoid the problem of singular IBD matrices. 23:13 23:13 第四節(jié) LD (連鎖不平衡）定位 23:13 What is LD? ? Linkage disequilibrium is a measure of association between alleles at different loci. ? Suppose we have two biallelic loci, A and B, with allele frequencies pA1 and pA2, and pB1 and pB2, respectively. – LE: – LD: 23:13 Measures of LD for singleallelic marker 1. Falconer and Mackay, 1996。 162。 162。 23:13 23:13 第三節(jié) 方差組分 QTL定位 23:13 模型和檢驗統(tǒng)計量 ? An example of a linear mixed model for a single QTL analysis is: 23:13 ? Variance ponents can be estimated using maximum likelihood or restricted maximum likelihood (REML), The loglikelihood function is: ? The assumed mean and variance structure of the observations : – Q is the IBD matrix : 23:13 ? The distribution of the test statistics are, asymptotically, a mixture of zero (with probability 189。 ? GDD的優(yōu)勢在于獲得相同檢測能力的條件下比較少的個體需要被判定基因型； ? GDD比較容易收集數(shù)據(jù)，因為公牛的 AI體系。 23:13 單個半同胞家系 ? 單標記 –對于單個半同胞家系，唯一的要求就是共同祖先在一個標記位點是雜合子； –因此，能看到后代在一個位點的兩個等位基因的表型值平均差異； –該差異能使用 t檢驗進行顯著性檢驗； –單標記的單個半同胞家系類似于 BC設(shè)計。 Requires RILs with rebinations in region of interest . 23:13 RIST Experimental results F21 F22 C57L AKR AKXL16 P= D2MIT64 D2MIT200 P= B. Taylor A. Darvasi Obesity QTL 23:13 第二節(jié) 特定結(jié)構(gòu)的遠交群體QTL定位 23:13 近交和遠交群體的差別 ? 遠交群體也存在部分的近交； ? 遠交群體的主要特征是群體內(nèi)部沒有故意盡力讓親屬之間進行配種而創(chuàng)造近交（隨機交配）； ? 遠交群體與近交群體的主要差別