Optimal diallel cross designs for the interval estimation of heredity

Abstract

SummaryThe results on optimal diallel cross designs are based on standard linear model assumptions where the general combining ability effects are taken as fixed. In many practical situations, this assumption may not be tenable since often one studies only a sample of inbred lines from a possibly large hypothetical population. A random effects model is proposed in this paper that allows us to obtain an interval estimate of a ratio of the variance components. We address the issue of optimal designs by considering the D l -optimality criteria. Designs that are D l -optimal for the estimation of heredity are obtained in the sense that the designs minimize the maximum expected length of the h confidence intervals. The approach leads to certain connections with the optimization problem under the fixed effects model.

Diallel cross in swine production: A review

“…This method will be useful in identifying the most productive genetic combinations that will be viable in the natural habitat of the breeds, as it will have more impact on pig production. This is necessary as Assis et al, (2004);Dickerson, (1993); Ghosh and Das, (2004) agree that diallel cross is an effective method to evaluate the genetic and heterotic potential of the breeds or lines involved in genetic improvement programs.…”

“…Most of the theory of optimal diallel cross designs is based on standard linear model assumptions where the general combining ability effects are taken as fixed and the primary interest lies in comparing the lines with respect to their general combining ability effects. Under such a model, among others, (Gupta and Kageyama 1994, Dey and Midha 1996, Mukerjee 1997, Das et al 1998, Ghosh and Das 2004) have characterized and obtained optimal completely randomised designs and incomplete block designs for diallel crosses. Jakubec et al, (1987) most importantly developed and evaluated three models for the analysis of complete (full) diallel crosses in animal breeding, derived from (Gardner and Eberhart 1966), (Harvey 1960) and (Griffing 1956) models, which is advantageous when the parental population is small and most efficient as it gives detailed information about crossbreeding parameters.…”

Nonorthogonal Optimal Partial Diallel Cross Designs for Consistent Estimation of Heritability

“…and has maximum trace, thus proving that the series of designs d e (m, n) are asymptotically universally optimal under fixed effects. Therefore, these designs should also have high efficiencies in the context of A, D, E-optimality under fixed effects model and L-optimality under random effects model (Ghosh and Das (2003b)). …”

Genetic Analyses of Growth, Carcass and Meat Quality Traits in Maternal Lines of Rabbits and Their Diallel Cross/ Análisis Genético de Caracteres de Crecimiento, Matadero y Calidad de Carne en Lineas Maternales de Conejo y en su Cruzamiento Dialélico

“…s ij = specific heterosis between lines i and j. Dickerson (1993), Ghosh and Das (2004) and Lessa de Assis and Carneiro (2004) agree that the diallel cross is an effective method to evaluate the genetic and heterotic potential of the breeds or lines involved in genetic programs.…”