Application of mixed model methodology to the evaluation of performance tested boars

Abstract

<p>Alternative designs applicable to the estimation of breeding values of performance tested boars using mixed model methodology were simulated and evaluated. Designs were based on composite estimates of parameters from the literature and results from a survey of central swine testing station managers in the United States. Of interest were the evaluations for the traits average daily gain and backfat probe. Family size, number of families per test, degree of relationship among animals within and across tests, and strength of genetic ties across tests were varied to determine how changes in one affected the others, as well as how they interacted with each other. The criterion upon which comparisons were based was accuracy, the correlation of true and estimated breeding values (r(,uu) = SQRT.(1 - V(u-u)/(sigma)(,G)('2) )). The prediction error variance V(u-u) is obtained from the inverse of the coefficient matrix of the mixed model equations. The single-trait animal model was assumed to be y(,ij) = s(,i) + b(,ij) + e(,ij), where y(,ij) was the observation (average daily gain or backfat) on the j('th) boar in the i('th) station-season, s(,i) was the fixed effect due to the i('th) station-season, b(,ij) was the random effect due to the j('th) boar in the i('th) station-season and e(,ij) was the random residual error associated with the observation on the j('th) boar in the i('th) station-season. Small subclass numbers in conjunction with evaluation of closely related families caused average accuracy to decrease instead of increase because directly tied animals were less accurately evaluated. Designing the relationship matrix by requiring entry of specific relatives would help to correct the problem. Tying station-seasons together through the relationship matrix formed a large set of interdependent equations and improved the average accuracy of predicted breeding values, since the slight decrease in accuracy for directly tied animals was more than offset by the increase for their test mates. Full-sibs across stations provided the strongest genetic tie, while the traditional half-sib (sire) tie was 1/4 as strong as the full-sib tie. Half-cousin ties were the weakest investigated (1/64 as large as full-sib ties), but could allow more genetic progress by increasing the selection differential. Applications of findings to the swine industry were discussed.</p>