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Effects of Selection on Variances and Covariances of Simulated First and Second Lactations

Department of Animal Science, Cornell University, Ithaca, NY 14853

ABSTRACT

When variances and covariances are estimated for a number of traits of individuals, frequently each animal does not have records on all traits as a result of selection for one or more traits. Usual estimators of components of variances and covariances are biased by selection. Components of variance for sires and errors for production in first and second lactations and for sire and error covariances between those lactations were estimated from unselected and selected simulated data by Maximum Likelihood and Henderson's Method 1. Estimates by Maximum Likelihood were computed by an iterative algorithm based on Henderson's mixed model equations. Estimates by Method 1 from unselected data were unbiased. Estimates by Method 1 of variances of second records and covariances between records from data with 50% selection were biased. There were only slight differences between the parameters and estimates by Maximum Likelihood from either unselected or selected data. These results suggest the usefulness of Maximum Likelihood to estimate variances and covariances when selection within fixed subclasses exists.

¹ Department of Dairy Science, University of Maryland, College Park 20742.