In this paper, we propose a new Bayesian approach for QTL mapping of family data. The main purpose is to model a phenotype as a function of QTLs' effects. The model considers the detailed familiar dependence and it does not rely on random effects. It combines the probability for Mendelian inheritance of parents' genotype and the correlation between flanking markers and QTLs. This is an advance when compared with models which use only Mendelian segregation or only the correlation between markers and QTLs to estimate transmission probabilities. We use the Bayesian approach to estimate the number of QTLs, their location and the additive and dominance effects. We compare the performance of the proposed method with variance component and LASSO models using simulated and GAW17 data sets. Under tested conditions, the proposed method outperforms other methods in aspects such as estimating the number of QTLs, the accuracy of the QTLs' position and the estimate of their effects. The results of the application of the proposed method to data sets exceeded all of our expectations.
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