【正文】 162。 162。). 2?23:13 ? The advantage of this likelihoodbased approach. ? The full maximum likelihood approach simultaneously estimates the IBD probabilities and the variance ponents, in a bined segregation analysis and linkage analysis framework. –―distribution method‖ –―expectation method‖ 23:13 ? So why is QTL mapping in general pedigrees not used more frequently, in particular in large, deep pedigrees? – IBD estimation in large pedigrees. – the unavailability of (userfriendly) software for the variance ponent estimation part of the analysis. – a finite budget. – the unavailability of DNA samples from most ancestors 23:13 IBD 估計(jì) 23:13 Perfect marker ? As in the case of sibpairs, IBD sharing using a fully informative marker is straightforward, because we can simply count the number of alleles that two relatives share by descent. ? At a location linked to a perfect marker, IBD probabilities can be calculated from the observed IBD probability at the marker, the average relationship between individuals, and the rebination rate between the marker and putative QTL position. 23:13 The general case: missing data and noninformative markers ? The marker information in plex pedigrees is often inplete. ? Unknown linkage phases, noninformative markers and/or missing marker genotypes plicate the calculation of Q. ? The calculation methods of Q are: – recursive algorithms, – correlation based algorithms – simulation based algorithms. 23:13 Implementation in Loki ? The multiplesite segregation sampler in Loki is a cleverly designed Gibbs sampler with ?batch updating‘. – – is the probability of the segregation indicators across n loci at the ith segregation conditional on all other segregation indicators and observed marker data. 23:13 ? A two step strategy to sample – The first step involves moving through the genome, calculating 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 ped