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The Inverse of the Gametic Relationship Matrix

Centre for Genetic Improvement of Livestock, Department of Animal and Poultry Science, University of Guelph, Guelph, Ontario N1G 2W1, Canada

ABSTRACT

Gametic models are an extension of animal models in that the paternal and maternal sources of gametes are important to the analysis. One example is the case where autosomally inherited effects from either the maternal or paternal gamete, but not both, are expressed. This type of model requires a variance-covariance matrix of the gametic effects and the inverse of this matrix is necessary for analysis by BLUP. This paper described the construction of the gametic relationship matrix and derives the rules for the simple computation of the inverse of this matrix provided that the animals are arranged chronologically. Finally, the gametic model is applied to a small example in which maternally imprinted inheritance is involved.

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