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Unexpected estimates of variance components with a true model containing genetic competition effects¹

L. D. Van Vleck^*,2 and J. P. Cassady

^* ARS, USDA, Roman L. Hruska U.S. Meat Animal Research Center, Lincoln 68583-0908; and and North Carolina State University, Raleigh 27695-7627

² Correspondence: A218 Animal Sciences (phone: 402-472-6010; fax: 402-472-6362; e-mail: lvanvleck{at}unlnotes.unl.edu).

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.

Key Words: Genetic Parameters • Pen Effects • Restricted Maximum Likelihood • Simulation

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