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Open Access Methodology article

Maximum likelihood estimates of two-locus recombination fractions under some natural inequality restrictions

Ying Zhou1, Ning-Zhong Shi1, Wing-Kam Fung2 and Jianhua Guo1*

Author Affiliations

1 Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, P. R. China

2 Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong, P. R. China

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BMC Genetics 2008, 9:1  doi:10.1186/1471-2156-9-1

Published: 4 January 2008



The goal of linkage analysis is to determine the chromosomal location of the gene(s) for a trait of interest such as a common disease. Three-locus linkage analysis is an important case of multi-locus problems. Solutions can be found analytically for the case of triple backcross mating. However, in the present study of linkage analysis and gene mapping some natural inequality restrictions on parameters have not been considered sufficiently, when the maximum likelihood estimates (MLEs) of the two-locus recombination fractions are calculated.


In this paper, we present a study of estimating the two-locus recombination fractions for the phase-unknown triple backcross with two offspring in each family in the framework of some natural and necessary parameter restrictions. A restricted expectation-maximization (EM) algorithm, called REM is developed. We also consider some extensions in which the proposed REM can be taken as a unified method.


Our simulation work suggests that the REM performs well in the estimation of recombination fractions and outperforms current method. We apply the proposed method to a published data set of mouse backcross families.