Haplotype Construction of Sires with Progeny Genotypes Based on an Exact Likelihood

Abstract

A maximum likelihood method is presented that can be used to construct parental haplotypes based on their progeny genotypes. The exact error rate and choice of family size in haplotype construction were evaluated through mathematical expressions and numerical examples. Numerical results suggest that, if two markers are tightly linked (< or = 10 cM) and each has intermediate allele frequencies, a difference of one between progeny receiving parental and recombinant gametes is sufficient for constructing sire linkage phase; a difference of two or more progeny is required with two markers 30 cM apart. When each of two adjacent markers has two alleles with equal allelic frequencies, genotyping 10 and 50 progeny are needed to achieve a power of 0.85 for constructing a sire linkage phase of two tightly (10 cM) and moderately tightly linked (30 cM) markers, respectively. The family size is reduced by approximately half when both markers have three alleles with equal frequencies. Results suggest that, when an experiment requiring haplotype determination of a parent is being designed, researches should choose the appropriate threshold and family size in the context of marker allelic frequencies and recombination fractions.

The impact of genetic markers on selection.

“…In the evaluation phase, the linked markers are tested in target populations or families to determine whether the detected QTL are segregating in those populations. The phase of marker alleles and of QTL alleles in heterozygous parents can also be determined when there is sufficient information (Du et al, 1998). In the implementation phase, linked markers shown to be predictive in a population are used within families and direct markers are used across families to produce a database of genotypes.…”

Most parsimonious haplotype allele sharing determination

“…There is a rich and growing literature on haplotype inference, or haplotyping . Some works focus on unrelated individuals [ 23 - 30 ]; Research on related individuals include those based on either exact-likelihood computations [ 31 - 34 ], approximate-likelihood computations [ 31 , 32 , 35 ], or rule-based strategies [ 12 , 36 - 41 ]. Conceivably, all of these haplotyping algorithms, methods and programs have elements in common and have their own strengths and weaknesses.…”

Rapid haplotype reconstruction in pedigrees with dense marker maps

“…There are several methods which make use of all information present in offspring markers (Weeks et al 1995;Kruglyak et al 1996;Sobel and Lange 1996;Du et al 1998;O'Connell 2000;Tapadar et al 2000;Rohde and Fuerst 2001). These methods are, however, not useful for dense marker maps, as they have to analyse too many possible haplotypes in order to be finished within a reasonable time.…”

“…For example, in the case of 100 heterozygous markers on a chromosome there are 2 100)1 ¼ 6.34 · 10 29 possible haplotypes. The space of haplotype configurations is then simply too large for these methodswhether they evaluate all possible haplotypes (Du et al 1998), or use a search algorithm to find the most probable haplotype. Examples of search algorithms are Markov chains, simulated annealing (Sobel and Lange 1996), expectation maximization (Rohde and Fuerst 2001), genetic algorithms (Tapadar et al 2000) or combinations of these (Weeks et al 1995;Kruglyak et al 1996;O'Connell 2000).…”