Estimation of epistasis among finite polygenic loci for complex traits with a mixed model using Gibbs sampling

Epistasis among loci is important factor behind the expression of many complex traits, but many analyses have ruled out its possibility. A method to estimate epistasis was introduced with a mixed model using Gibbs sampling (MMGS). The posterior mean estimate for every possible genotype combined from multiple loci was calculated as the mean of the conditional expected values of the parameters in post warming-up rounds from Gibbs sampling. A simulation study was performed to compare MMGS with restricted partition method (RPM). Mean square prediction error (MSPE) using MMGS was smaller than that using RPM (P < 0.05), which might be due to information loss introduced by grouping of genotypes in RPM. This was also supported by the result that MSPE increased as the number of merged groups decreased. The simulation study implied that MMGS was more plausible in estimating epistatic effects than the RPM.