<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Abstract The diallel mating designs have been extensively employed to gain genetic information by crop and tree breeders, but analysis of diallel data faces some challenges because the same parent acts both male and female roles. Theoretically, little attention was paid to the statistical inference and hypothesis testing for a fixed diallel linear model. In this paper we provide a uniform solution to any fixed diallel linear model with matrix expression based on the theory of restricted linear models. We derive formulae for estimating diallel parameters and their standard errors, and obtain uniform statistics for hypothesis testing of parameters, factors and differences between general combining abilities (GCA) or specific combining abilities (SCA). To put the result into practice, we have developed a Windows<sup>®</sup> software program “GSCA” for analyzing a flexible diallel linear model that could contain the GCA, SCA, reciprocal, block and environment effects as well as interaction effects such as GCA by environment. GSCA can perform analyses not only for Griffing’s four types of diallel crosses but also for more complicated diallel crosses whether the data structure is balanced or unbalanced. A real example is given to illustrate the convenience, flexibility and power of our software for diallel analysis.</p></abstract>

The diallel mating designs have been extensively employed to gain genetic information by crop and tree breeders, but analysis of diallel data faces some challenges because the same parent acts both male and female roles. Theoretically, little attention was paid to the statistical inference and hypothesis testing for a fixed diallel linear model. In this paper we provide a uniform solution to any fixed diallel linear model with matrix expression based on the theory of restricted linear models. We derive formulae for estimating diallel parameters and their standard errors, and obtain uniform statistics for hypothesis testing of parameters, factors and differences between general combining abilities (GCA) or specific combining abilities (SCA). To put the result into practice, we have developed a Windows® software program “GSCA” for analyzing a flexible diallel linear model that could contain the GCA, SCA, reciprocal, block and environment effects as well as interaction effects such as GCA by environment. GSCA can perform analyses not only for Griffing’s four types of diallel crosses but also for more complicated diallel crosses whether the data structure is balanced or unbalanced. A real example is given to illustrate the convenience, flexibility and power of our software for diallel analysis.

GSCA: New Software and Algorithms to Analyse Diallel Mating Designs Based on Restricted Linear Model

Silvae Genetica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The diallel mating designs have been extensively employed to gain genetic information by crop and tree breeders, but analysis of diallel data faces some...

GSCA: New Software and Algorithms to Analyse Diallel Mating Designs Based on Restricted Linear Model

Published Online: Aug 01, 2017

Page range: 126 - 132

Received: Dec 03, 2001

DOI: https://doi.org/10.1515/sg-2012-0016

Keywords
Diallel mating design, restricted linear models, general combining ability, specific combining ability, least squares

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

GSCA: New Software and Algorithms to Analyse Diallel Mating Designs Based on Restricted Linear Model

Published Online: Aug 01, 2017

Page range: 126 - 132

Received: Dec 03, 2001

DOI: https://doi.org/10.1515/sg-2012-0016

KeywordsDiallel mating design, restricted linear models, general combining ability, specific combining ability, least squares

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Diallel mating design, restricted linear models, general combining ability, specific combining ability, least squares