Linkage map construction with dominant and missing markers by Newton-Raphson method
Date Issued
2004
Date
2004
Author(s)
Liu, Miao-Yi
DOI
zh-TW
Abstract
The purpose of this study is to construct the linkage map with dominant and missing markers. A correct and accurate gene linkage map is vital for mapping and analysing quantitative trait loci (QTL). If the gene linkage map is unknown for a sequence of markers in the genome, we have to firstly divide the markers in the sequence into linkage groups, and then determine the most likely order of markers and the distances between neighboring markers within a linkage group. This is done by maximum likelihood (ML) method.
When markers within a linkage group are fully observed, using the multilocus likelihood function to simultaneously estimate the recombination frequencies for all markers is equivalent to using two point analysis to independently estimate recombination frequency for each pair of markers. However, when some markers are partially observed or missing, the only way to calculate the recombination frequencies of markers is to simultaneously estimate the recombination frequencies according to the information of all markers within a linkage group by multilocos likelihood function. Usually, the multilocus likelihood function is too complicated to have a closed form solution and we can only use numerical analysis methods such as Newton-Raphson or EM algorithms to derive an approximate solution by iteration. The EM algorithm does not use the second order derivatives of likelihood function, so the convergence rate is slower and is unable to calculate the asymptotic covariance matrix of ML estimates.
This study simulated the backcross data and F2 intercross data, using the Newton-Raphson method to simultaneously calculate the ML estimates of the recombination frequencies of all markers within a linkage group. The Newton-Raphson method can get not only ML estimates but also the asymptotic covariance matrix of ML estimates, the latter enables us to evaluate the plausibility of our statistical inference based on ML estimates, and then applying Haldane’s mapping function to transform the estimated recombination frequencies into genetic distances. We found the calculated distances are similar to what we originally assigned. The asymptotic covariance matrix showed that the standard errors are pretty small. In addition, the results of ML estimates by the Newton-Raphson method are identical to those of the EM algorithm.
Subjects
遺傳標識
連鎖圖譜
漸近變異矩陣
牛頓法
最大概似估計值
genetic markers
linkage map
Newton-Raphson metho
Type
thesis
File(s)![Thumbnail Image]()
Loading...
Name
ntu-93-R91621202-1.pdf
Size
23.31 KB
Format
Adobe PDF
Checksum
(MD5):148bdab9002583f88fd2e5668cc0c32e