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Estimation of Genetic Variances and Covariances Using Symmetric Differences Squared¹

The Ohio Agricultural Research and Development Center, Wooster 44691 and and The Ohio State University, Columbus 43210

Abstract

A new method is given for estimating genetic and environmental variance and covariance components which simultaneously utilizes all genetic relationships in a sample. If phenotype is expressed in terms of an appropriate genetic model, then the expectation of the squared differences between individuals can be derived to yield genetic and environmental variances and covariances as functions of the genetic relationships. Based on diese expectations, normal equations involving the differences squared and relationships between each pair of individuals can be formed and solved by ordinary least squares to give unbiased estimates of genetic and environmental variance and co-variance components. The algebra for the 'symmetric differences squared' (SDS) method is given for single and multiple traits with models that include direct, maternal and dominance effects. Also, the results of a computer simulation study and from an analysis of data on a control line of mice are given.

¹ Published with the approval of the director as Paper No. 169–79, Journal Series, The Ohio Agri. Res. & Devel. Center.

² Present address: Experimental statistics Unit, College of Agr. Sci., Clemson Univ., Clemson, SC 29631.

³ Anim. Sci. Dept., Columbus, OH 43210.