**Submitted to:** Beef Improvement Federation Proceedings

**Publication Type:** Proceedings

**Publication Acceptance Date:** 4/30/2009

**Publication Date:** 5/4/2009

**Citation:** Thallman, R.M., Hanford, K.J., Quaas, R.L., Kachman, S.D., Tempelman, R.J., Fernando, R., Kuehn, L.A., Pollak, E.J. 2009. Estimation of the Proportion of Genetic Variation Accounted for by DNA Tests. Proc., Beef Improvement Federation 41st Research Symposium and Annual Meeting, Sacramento, CA. April 29-May 3, 2009. pp. 184-209.

**Interpretive Summary:**

**Technical Abstract:** An increasingly relevant question in evaluating commercial DNA tests is "What proportion of the additive genetic variation in the target trait is accounted for by the test?" Therefore, several estimators of this quantity were evaluated by simulation of a population of 1000 animals with 100 sires, each with 10 progeny. Three heritabilities (0.1, 0.3, and 0.5) of the target trait and four proportions of genetic variation (0.04, 0.16, 0.36, and 0.64) accounted for by the molecular breeding value (MBV) for the DNA test were simulated. The first estimator evaluated is the reduction in estimated sire variance (RV) when the MBV is added as a fixed covariate to a single-trait model for the target trait divided by the sire variance from the model without the MBV. The second estimator is based on the regression of phenotype on MBV (RPM) from a single trait sire model in which the MBV is a fixed covariate (this is the model that has been standard in independent validations since DNA tests began being reported as MBV). The third estimator is the restricted maximum likelihood (REML) estimate of additive genetic correlation squared (MT) in a two-trait animal model for the target trait and the MBV (as the second trait). In this case, the only fixed effect in the model for MBV is a mean. The standard error of MT was computed by multiplying the standard error of the genetic correlation by twice the genetic correlation. The mean of MT tended to be closer to the simulated values than RV and RPM, although all three estimators performed reasonably for most parameter sets. The standard deviations of estimates among replicates of MT were generally smaller than RV and RPM and, at low heritability, were much smaller. All three estimators can produce erratic results in replicates in which the estimate of the additive variance approaches zero. Data sets in which the estimated heritability is much lower than expected should be considered inadequate for estimating the proportion of additive variation. The RV estimator can produce negative estimates and the RV and RPM estimators can produce estimates > 1 of the proportion of additive variance explained. The MT estimator has the advantage of producing estimates within the parameter space. The computed standard errors of MT were similar to the standard deviation of the estimates. This property is another advantage of MT over RV and RPM, for which empirical methods for computing standard errors are not obvious. It is recommended that the MT estimator be used for estimating the proportion of additive variation explained by a DNA test. Similar estimators of the proportion of phenotypic variance explained by DNA tests for application in marker-assisted management (MAM) will also be explored. Practical considerations in the application of these statistics are discussed.