Linkage analysis is now being widely used to map markers on each chromosome in the human genome, to map genetic diseases, and to identify genetic forms of common diseases. Two-locus linkage analysis and multi-locus analysis have been investigated comprehensively, and many computer programs have been developed to perform linkage analysis. Yet there exists a shortcoming in traditional methods, i.e., the parameter space of two-locus recombination fractions has not been emphasized sufficiently in the usual analyses. In this paper, we propose a new strategy for estimating the two-locus recombination fractions based on data of backcross family in the framework of some natural and necessary parameter restrictions. The new strategy is based on a restricted projection algorithm, which can provide fast reasonable estimates of recombination fraction, and can therefore serve as a superior alternative algorithm. Results obtained from both real and simulated data indicate that the new algorithm performs well in the estimation of recombination fractions and outperforms current methods.

Testing linkage heterogeneity between two loci is an important issue in genetics. Currently, there are four methods (K-test, A-test, B-test and D-test) for testing linkage heterogeneity in linkage analysis, which are based on the likelihood-ratio test. Among them, the commonly used methods are the K-test and A-test. In this paper, we present a novel test method which is different from the above four tests, called G-test. The new test statistic is based on estimating function, possessing a theoretic asymptotic distribution, and therefore demonstrates its own advantages. The proposed test is applied to analyse a real pedigree dataset. Our simulation results also indicate that the G-test performs well in terms of power of testing linkage heterogeneity and outperforms the current methods to some degree.

Accurate genetic data are important prerequisite of performing genetic linkage test or association test. Currently, most analytical methods assume that the observed genotypes are correct. However, due to the constraint at the technical level, most of the genetic data that people used so far contain errors. In this paper, we considered the problem of QTL mapping based on biological data with genotyping errors. By analysing all possible genotypes of each individual in framework of multiple-interval mapping, we proposed an algorithm of inferring all model parameters through the expectation-maximization (EM) algorithm and discussed the hypothesis testing of the existence of QTL. We carried out extensive simulation studies to assess the proposed method. Simulation results showed that the new method outperforms the method that does not take the genotyping errors into account, and therefore it can decrease the impact of genotyping errors on QTL mapping. The proposed method was also applied to analyse a real barley dataset.