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(a) 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(a) was calculated with estimated h2 by either method, or the true value of the parameter. The MSEP of empirical BLUP(a) using Method R was greater than the MSEP of empirical BLUP(a) using REML. The latter statistic was closer to prediction error variance of BLUP(a) than the MSEP of empirical BLUP(a) using Method R, indicating that empirical BLUP(a) 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(a) calculated using estimates of h2 by Method R was larger than MSEP of EBLUP(a) calculated with REML estimates of h2.

BLUP for genetic evaluation of plants in non-inbred families of annual crops

“…Kruuk (2004) indicated that the BLUP/REML methodology is a powerful way to estimate the components of variance and to predict additive genetic values in natural populations. But Cantet et al (2000), in a simulation study, reported underestimation of heritability in the population under selection, because the relationship information was only partially available and the existence of selection makes heritability biased.…”

Effects of missing pedigree information on dairy cattle genetic evaluations (short communication)

“…This may be due to the higher selection intensity of males than females, and genetic independency between herds for DM. CANTET et al (2000) reported biased downward heritability estimates by loss of pedigree information. DONG et al (1988) studied the degree of completeness of relationships and reported lower heritabilities by REML if relationships are from sires only, compared to those from more complete pedigrees.…”

“…They concluded that if all data employ in making selection decisions, the selection process may be ignored and estimation may proceed as if selection has never been occurred. REML estimates are not biased by "ignorable selection" (IM et al, 1989;CANTET et al, 2000). There are two kinds of pedigree errors affecting the results of genetic evaluations, including wrong and missing pedigree information (HARDER et al, 2005).…”

“…Improvement of the computational power of computers has made it possible to perform more complicated animal models, and as well as single-trait animal models, multi-trait and random regression animal models are in use in various researches KREJČOVÁ et al, 2007a;KREJČOVÁ et al, 2007b). CANTET et al (2000) using a simulated data, studied the different situations of: (a) complete pedigree; (b) 50% of phenotypes with sire missing; (c) 50% of phenotypes with dam missing (d) and 50% of phenotypes with sire and dam missing (the paternities of 12.5%, the maternities of 12.5%, and the paternities and maternities of 12.5% of the records were lost at random). Choice (a) produced unbiased heritabilities very close to the true heritabilities.…”

Accounting for genetic differences among unknown parents in microevolutionary studies: how to include genetic groups in quantitative genetic animal models

“…Dong, Van Vleck & Wiggans ; Cantet et al . ). Such biases can arise when parent identities are missing randomly with respect to genetic value, because the resulting pedigree underestimates relatedness and inbreeding.…”