Genotypic covariance matrices and their inverses for models allowing dominance and inbreeding

Summary - Dominance models are parameterized under conditions of inbreeding. The properties of an infinitesimal dominance model are reconsidered. It is shown that mixedmodel methodology is justifiable as normality assumptions can be met. Tabular methods for calculating genotypic covariances among inbred relatives are described. These methods employ 5 parameters required to accommodate additivity, dominance and inbreeding. Rules for calculating inverse genotypic covariance matrices are presented. These inverse matrices can be used directly to set up the mixed-model equations. The mixed-model methodology allowing for dominance and inbreeding provides a powerful framework to better explain and utilize the observed variation in quantitative traits.

[1]  A. Robertson.  Selection in animals: synthesis. , 1955, Cold Spring Harbor symposia on quantitative biology.

[2]  D. L. Harris,et al.  GENOTYPIC COVARIANCES BETWEEN INBRED RELATIVES. , 1964, Genetics.

[3]  O. Kempthorne.  The correlation between relatives on the supposition of mendelian inheritance , 1968 .

[4]  W. G. Hill.  The rate of selection advance for non-additive loci. , 1969, Genetical research.

[5]  M. Kimura,et al.  An introduction to population genetics theory , 1971 .

[6]  C. Cockerham.  Higher order probability functions of identity of allelles by descent. , 1971, Genetics.

[7]  M. Bulmer,et al.  The Effect of Selection on Genetic Variability , 1971, The American Naturalist.

[8]  C. R. Henderson.  SIRE EVALUATION AND GENETIC TRENDS , 1973 .

[9]  R. Nadot,et al.  Apparentement et identite. Algorithme du Calcul des Coefficients D'Identite , 1973 .

[10]  C. R. Henderson.  Rapid Method for Computing the Inverse of a Relationship Matrix , 1975 .

[11]  H. Kacser,et al.  The molecular basis of dominance. , 1981, Genetics.

[12]  W. G. Hill,et al.  Population and quantitative genetics of many linked loci in finite populations , 1983, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[13]  F. Allaire,et al.  Efficient selection rules to increase non-linear merit: application in mate selection , 1985, Génétique, sélection, évolution.

[14]  G. Jansen,et al.  Selecting mating pairs with linear programming techniques. , 1985, Journal of dairy science.

[15]  B. W. Kennedy,et al.  Mixed model methodology under genetic models with a small number of additive and non-additive loci. , 1986 .

[16]  Daniel Gianola,et al.  Bayesian Methods in Animal Breeding Theory , 1986 .

[17]  K. Hammond,et al.  Portfolio theory, utility theory and mate selection , 1987, Génétique, sélection, évolution.

[18]  Brian P. Kinghorn.  On computing strategies for mate allocation , 1987 .

[19]  Bruce Tier,et al.  A Derivative-Free Approach for Estimating Variance Components in Animal Models by Restricted Maximum Likelihood1 , 1987 .

[20]  B. Tier.  Computing inbreeding coefficients quickly , 1990, Genetics Selection Evolution.

[21]  SP Smith,et al.  Use of sparse matrix absorption in animal breeding , 1989, Genetics Selection Evolution.

[22]  L. Penrose,et al.  THE CORRELATION BETWEEN RELATIVES ON THE SUPPOSITION OF MENDELIAN INHERITANCE , 2022 .