UNEXPECTED ESTIMATES OF VARIANCE COMPONENTS WITH A TRUE MODEL CONTAINING GENETIC COMPETITION EFFECTS

Authors: Van Vleck, Lloyd; CASSADY, JOSEPH - NORTH CAROLINA STATE

Submitted to: Journal of Animal Science
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 9/29/2004
Publication Date: 1/1/2005
Citation: Van Vleck, L.D., Cassady, J.P. 2005. Unexpected estimates of variance components with a true model containing genetic competition effects. Journal of Animal Science 83:68-74.

Interpretive Summary: Animals raised in pens compete with each other. Competition of penmates may result in decreased (or in rare cases increased) performance of others in the pen. Models for records of animals in a pen can contain the usual fixed effects such as sex or age and also two kinds of genetic effects--the direct genetic effect of the animal with the record but also the sum of imbedded competition genetic effects of the penmates. In addition, the penmates share a common pen effect. Another complication is that the direct and competition genetic effects may be correlated (usually negatively). The statistical problem is that the direct and competition genetic effects are confounded with the pen effects. The animal model, through relationships among the animals, will allow separation of variation due to animal direct genetic, pen, and residual effects. With competition effects in the model, the question is whether relationships will also allow separation of variation due to competition genetic effects and also allow estimation of the direct-competition genetic covariance which is expressed in the covariance between the record of an animal and the records of all penmates which contain the competition genetic effect of the animal. This simulation study with 600 animals from two generations was replicated 400 times for each of 16 combinations of variances of direct genetic, competition genetic (with direct-competition genetic covariance), pen, and residual effects. Each simulated data set was analyzed with eight different statistical models to determine the effects on other variances of including or dropping certain effects from the analysis model. Results were: 1) Variance due to direct and competition genetic effects and pen effects can be partitioned. 2) When effects are dropped from the model, changes in estimates for components left in the model were generally small except that when competition effects were ignored, estimates of pen variance increased greatly because of covariance between records of pen mates due to competition effects in common. 3) Thus, a large variance due to pen effects from an analysis not including competition effects in the model may indicate competition effects should be included in the analysis. 4) Not including pen effects in the model may bias estimation of the direct-competition genetic covariance needed to calculate indexes of overall genetic value and expected responses due to selection. 5) A result with possible implications for other models is that treating pen effects as fixed greatly reduced standard errors of estimates of genetic covariance between the direct and imbedded competition effects and of estimates of genetic variance for competition effects.

Technical Abstract: Simulation of the model of Muir and Schinckel containing genetic competition effects was initiated to determine how well Restricted Maximum Likelihood (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, each mated to five unrelated females to produce 300 progeny with records from which 30 females (one per mating in previous generation) were mated to six unrelated males to produce 300 more progeny with records. 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 variances (with covariance), and pen and residual variances. 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 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 C(gc) were ignored. Overestimation depended on V(c) and number of competitors in common between records in a pen. Upward bias was somewhat greater when C(gc) was positive than when negative. For example, with C(gc) = 2, V(c) = 4 and V(p) = 0.1, 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 proportional to 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 reduced 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.