Linear models for diallel crosses: a review with R functions.

Area of Science:

• Quantitative Genetics
• Statistical Genetics
• Bioinformatics

Background:

• Diallel experiments are crucial for assessing genetic effects like general combining ability (GCA), specific combining ability (SCA), and heterosis.
• Existing diallel models are often presented as separate entities requiring specialized software.
• A unified approach is needed to integrate diallel analysis within standard statistical frameworks.

Purpose of the Study:

• To develop an R-software procedure for fitting fixed and random diallel models.
• To demonstrate that diallel models can be viewed as specific parameterizations of a general linear model.
• To provide tools for geneticists, breeders, and students to utilize common R functions for diallel analysis.

Main Methods:

• Reviewing established diallel models in the literature.
• Developing R tools to fit diallel models using the `lm()` function and related methods for ordinary least squares (OLS) estimation.
• Illustrating the application of these tools with examples for fixed and random/mixed-effect diallel models within a Bayesian framework.

Main Results:

• Diallel models can be effectively parameterized and fitted as general linear models (GLMs) in R.
• The developed procedure integrates diallel analysis with standard R statistical functions, simplifying the process.
• The R tools accommodate both fixed and random/mixed-effect diallel models, including Bayesian approaches.

Conclusions:

• A unified R-software procedure for diallel models has been successfully developed, enhancing accessibility.
• This approach treats diallel models as specific cases of GLMs, enabling the use of general-purpose R software.
• The tools facilitate the analysis of genetic effects and heterosis, benefiting researchers and breeders in plant and animal sciences.