Comparison of restricted maximum likelihood and method ℜ for estimating heritability and predicting breeding value under selection

Abstract

Method ℜ and Restricted Maximum Likelihood (REML) were compared for estimating heritability (h2) and subsequent prediction of breeding values (a) with data subject to selection. A single-trait animal model was used to generate the data and to predict breeding values. The data originated from 10 sires and 100 dams and simulation progressed for 10 overlapping generations. In simulating the data, genetic evaluation used the underlying parameter values and sires and dams were chosen by truncation selection for greatest predicted breeding values. Four alternative pedigree structures were evaluated: complete pedigree information, 50% of phenotypes with sire identities missing, 50% of phenotypes with dam identities missing, and 50% of phenotypes with sire and dams identities missing. Under selection and with complete pedigree data, Method ℜ was a slightly less consistent estimator of h2 than REML. Estimates of h2 by both methods were biased downward when there was selection and loss of pedigree information and were unbiased when no selection was practiced. The empirical mean square error (EMSE) of Method ℜ was several times larger than the EMSE of REML. In a subsequent analysis, different combinations of generations selected and generations sampled were simulated in an effort to disentangle the effects of both factors on Method ℜ estimates of h2. It was observed that Method ℜ overestimated h2 when both the sampling that is intrinsic in the method and the selection occurred in generations 6 to 10. In a final experiment, BLUP(α) were predicted with h2 estimated by either Method ℜ or REML. Subsequently, five more generations of selection were practiced, and the mean square error of prediction (MSEP) of BLUP(α) was calculated with estimated h2 by either method, or the true value of the parameter. The MSEP of empirical BLUP(α) using Method ℜ was greater than the MSEP of empirical BLUP(α) using REML. The latter statistic was closer to prediction error variance of BLUP(α) than the MSEP of empirical BLUP(α) using Method ℜ, indicating that empirical BLUP(α) calculated using REML produced accurate predictions of breeding values under selection. In conclusion, the variability of h2 estimates calculated with Method ℜ was greater than the variability of h2 estimates calculated with REML, with or without selection. Also, the MSEP of EBLUP(α) calculated using estimates of h2 by Method ℜ was larger than MSEP of EBLUP(α) calculated with REML estimates of h2.