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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 Vg, Vc, Cgc, Vp, and Ve, 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 Vg and Ve were fixed at 16.0. Values of Cgc were −2.0, −1.0, 0.1, 1.0, and 2.0. Values of Vc were 1.0 and 4.0, and values of Vp were 0.1, 1.0, and 10.0. With the full model, average estimates resembled true parameters, except that Vp was consistently overestimated when small (0.1 and 1.0), which in turn slightly changed other estimates. The most unexpected result was overestimation of Vp when Vc and Cgc were ignored. Overestimation depended on Vc and the number of competitors in common between records in a pen. Upward bias was somewhat greater when Cgc was positive than when it was negative. For example, with Cgc = 2, Vc = 4, and Vp = 0.1, the mean estimate of Vp was 20.4 when Cgc and Vc were dropped from the model and 15.3 when Cgc = −2.0. When Vp was ignored, estimates of both Cgc and Vc increased in proportion with Vp. Also Vg increased more with greater Vp. Another unexpected result occurred when pen was considered fixed. Empirical sampling standard errors of estimates of Cgc and Vc 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.