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Estimation of Genetic Variances from Unselected and Selected Populations¹

University of Guelph³, Guelph, Ontario, Canada N1G 2W1

Abstract

In random mating populations of finite size, with an additive genetic model, the additive genetic variance declines due to inbreeding. Estimation of the base population additive genetic variance using all of the data is possible using a modified method 3 estimator or a generalized form of minimum variance quadratic unbiased estimation (MIVQUE). Unbiased estimation requires the use of an animal model and the complete relationship matrix among breeding values. Simulation results show that the MIVQUE estimator has considerably smaller sampling variance than the modified method 3 estimator. With directional selection, assuming an additive model with very large numbers of loci, the genetic variance declines both due to inbreeding and due to the generation of gametic disequilibrium. The latter induces a bias in analysis of variance estimators such as method 3. The MIVQUE estimator using an animal model and a complete relationship matrix is not biased by selection. Simulation results indicate that the use of MIVQUE on selected data can lead to unbiased estimates of the base population additive genetic variance. A method is proposed to estimate the additive genetic variance in later generations using the MIVQUE algorithm.

¹ Financial support was provided by the Natural Sciences and Engineering Research Council of Canada, the Holstein-Friesian Association of Canada and the Ontario Ministry of Agriculture and Food.

² Current Address: Fisheries and Oceans, Pacific Biol. Sta., Nanaimo, B.C., Canada V9R 5K6.

³ Dept. of Anim. and Poul. Sci.

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