Comparison of linear-linear vs. linear- threshold models for prediction of breeding values using simulated data

In order to compare two linear-linear (LLM) and linear-threshold (LTM) models in prediction of breeding values، two populations consisting of 6700 animals were simulated using of the Visual Basic programming language. In both populations the heritability’s for the first and second trait were assumed to be 0. 30 and 0. 10 respectively، but the genetic correlation between two traits was 0. 50 in population A and -0. 50 in population B. Selection of parents did on two trait selection index and mating of selected parents conducted randomly for 15 years. The second trait transformed into a categorical trait assigning 50 % of observed data in the first category، 34 % in the second، and 16 % in the third using the probit function. In the LLM breeding values were predicted under animal model and derivative free restricted maximum likelihood methodology and in the LTM predicted breeding values were obtained using a Bayesian method، implemented via Gibbs sampling procedure. Pearson correlation between two models for predicted breeding values in two populations (A and B) in continues trait (0. 93 and 0. 88) and in the threshold trait (0. 82 and 0. 62) was relatively high. Ranked correlation between predicted breeding values of two models was similar to Pearson correlation. Accuracy of selection in tow populations in the LLM was higher than LTM. The results indicated that the LLM was superior to LTM in prediction of breeding values and the LLM more accurately considers genetic correlation between traits than LTM.