RELIABILITY OF SIRE EVALUATIONS FOR CALVING EASE BY A THRESHOLD-MODEL ANALYSIS

Two approximate formulas for calculating reliability of evaluations for calving ease by a threshold model are presented. Approximations are based on the upper and lower bounds of true reliability from progeny data and then adjusted by the weighted average reliability of evaluations of sires and maternal grandsires of bulls with progeny information. Each approximation was applied in two data sets small enough so that the predicted reliability could be compared with the expected reliability from a complete inverse of the threshold model equations. Data set 1 had 280 bulls with progeny and a range in expected reliability of 4 to 96%. The range in expected reliability for the 374 bulls in data set 2 was from 66 to 94%. Predicted reliability by the approximate formulas was compared for progeny data alone and with the addition of pedigree information through the inverse of the relationship matrix. Mean square error of predicted reliability was reduced by including pedigree information, 69.4 and 16.3% in data sets 1 and 2, respectively. Approximate formulas tended to overpredict expected reliability by as much as 14% (data set 1) or 7% (data set 2), but reliability was less severely overpredicted when both the sire and maternal grandsire had progeny data (6 and 5% in data sets 1 and 2, respectively).