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General Formulas for Obtaining the MLEs and the Asymptotic Variance- Covariance Matrix in Mapping Quantitative Trait Loci When Using the EM Algorithm

1997; Oxford University Press; Volume: 53; Issue: 2 Linguagem: Inglês

10.2307/2533965

1541-0420

Chen-Hung Kao, Zhao‐Bang Zeng,

Genetic and phenotypic traits in livestock

We present in this paper general formulas for deriving the maximum likelihood estimates and the asymptotic variance-covariance matrix of the positions and effects of quantitative trait loci (QTLs) in a finite normal mixture model when the EM algorithm is used for mapping QTLs. The general formulas are based on two matrices D and Q, where D is the genetic design matrix, characterizing the genetic effects of the QTLs, and Q is the conditional probability matrix of QTL genotypes given flanking marker genotypes, containing the information on QTL positions. With the general formulas, it is relatively easy to extend QTL mapping analysis to using multiple marker intervals simultaneously for mapping multiple QTLs, for analyzing QTL epistasis, and for estimating the heritability of quantitative traits. Simulations were performed to evaluate the performance of the estimates of the asymptotic variances of QTL positions and effects.