Approximate Reliability of Best Linear Unbiased Prediction in Models with and Without Relationships

Open Access
Publisher Website
Google Scholar
Abstract
In sire summaries, attention is paid to reliability of estimates of breeding values, often expressed as the squared correlation between estimated and true breeding values. In best linear unbiased prediction procedures, which account for relationships between sires, reliability is approximated by (ne + ka-1 - k)/(ne + ka-1), where ne is the effective number of daughters, i.e., the diagonal of the sire coefficient matrix after absorption of fixed effects; k is the ratio of residual and sire variance; and A-1 is the diagonal element of the inverse of the numerator relationship matrix (A-1). In simulatated data this approximation compared with the true reliability, computed from direct inversion of the sire coefficient matrix including A-1 k after absorption of fixed effects, was biased upward for sire evaluations based on many effective daughters and few direct sire comparisons of few effective daughters and relationship to its sire. In field data, the effective number of daughters and the number of direct sire comparisons were correlated 0.97, and the formula gave good approximation (deviation < 3%) when bulls were unrelated. When bulls were related, bias was considerable. Another approximation derived from selection index theory reduced the bias < 4%. This approximation took the effective number of offspring of the bulls'' sire into account and reduced to ne/(ne = K) if a bulls'' sire had no daughter records. It can be applied easily and required only small computational effort.