Unexpected estimates of variance components with a true model containing genetic competition effects.

Simulation of a model containing genetic competition effects was initiated to determine how well REML could untangle variances due to direct and competition genetic effects and pen effects. A two-generation data set was generated with six unrelated males that were each mated to five unrelated females to produce 300 progeny, from which 30 females (one per mating in previous generation) were mated to six unrelated males to produce 300 more progeny. Progeny were randomly assigned, six per pen, to 50 pens per generation. Parameters were V(g), V(c), C(gc), V(p), and V(e), representing direct and competition genetic variance with covariance, and pen and residual variance. Eight statistical models were used to analyze each of 400 replicates of 16 sets of parameters. Both V(g) and V(e) were fixed at 16.0. Values of C(gc) were -2.0, -1.0, 0.1, 1.0, and 2.0. Values of V(c) were 1.0 and 4.0, and values of V(p) were 0.1, 1.0, and 10.0. With the full model, average estimates resembled true parameters, except that V(p) was consistently overestimated when small (0.1 and 1.0), which in turn slightly changed other estimates. The most unexpected result was overestimation of V(p) when V(c) and Cgc were ignored. Overestimation depended on V(c) and the number of competitors in common between records in a pen. Upward bias was somewhat greater when Cg(c) was positive than when it was negative. For example, with C(gc) = 2, V(c) = 4, and V(p) = 0.1, the mean estimate of V(p) was 20.4 when C(gc) and V(c) were dropped from the model and 15.3 when C(gc) = -2.0. When V(p) was ignored, estimates of both C(gc) and V(c) increased in proportion with V(p). Also V(g) increased more with greater V(p). Another unexpected result occurred when pen was considered fixed. Empirical sampling standard errors of estimates of C(gc) and V(c) were decreased generally by factors of 2 to 30. Based on these results, we conclude a high estimate of pen variance may indicate genetic competition effects are important, and ignoring either the pen or competition effects will bias estimates of other components.