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Mixed modelling for phenotypic data from plant breeding
(2011) Möhring, Jens; Piepho, Hans-Peter
Phenotypic selection and genetic studies require an efficient and valid analysis of phenotypic plant breeding data. Therefore, the analysis must take the mating design, the field design and the genetic structure of tested genotypes into account. In Chapter 2 unbalanced multi-environment trials (METs) in maize using a factorial design are analysed. The dataset from 30 years is subdivided in periods of up to three years. Variance component estimates for general and specific combining ability are calculated for each period. While mean grain yield increased with ongoing inter-pool selection, no changes for the mean of dry matter yield or for variance component estimate ratios were found. The continuous preponderance of general combining ability variance allows a hybrid selection based on general combining effects. The analysis of large datasets is often performed in stage-wise fashion by analysing each trial or location separately and estimating adjusted genotype means per trial or location. These means are then submitted to a mixed model to calculate genotype main effects across trials or locations. Chapter 3 studies the influence of stage-wise analysis on genotype main effect estimates for models which take account of the typical genetic structure of genotype effects within plant breeding data. For comparison, the genetic effects were assumed both fixed and random. The performance of several weighting methods for the stage-wise analysis are analysed by correlating the two-stage estimates with results of one-stage analysis and by calculating the mean square error (MSE) between both types of estimate. In case of random genetic effects, the genetic structure is modelled in one of three ways, either by using the numerator relationship matrix, a marker-based kinship matrix or by using crossed and nested genetic effects. It was found that stage-wise analysis results in comparable genotype main effect estimates for all weighting methods and for the assumption of random or fixed genetic effect if the model for analysis is valid. In case of choosing invalid models, e.g., if the missing data pattern is informative, both analyses are invalid and the results can differ. Informative missing data pattern can result from ignoring information either used for selecting the analysed genotypes or for selecting the test environments of genotypes, if not all genotypes are tested in all environments. While correlated information from relatives is rarely directly used for analysis of plant breeding data, it is often used implicitly by the breeder for selection decisions, e.g. by looking at the performance of a genotype and the average performance of the underlying cross. Chapter 4 proposed a model with a joint variance-covariance structure for related genotypes in analysis of diallels. This model is compared to other diallel models based on assumptions regarding the inheritance of several independent genes, i.e. on genetic models with more restrictive assumptions on the relationship between relatives. The proposed diallel model using a joint variance-covariance structure for parents and parental effects in crosses is shown to be a general model subsuming other more specialized diallel models, as these latter models can be obtained from the general model by adding restrictions on the variance-covariance structure. If no a priori information about the genetic model is available the proposed general model can outperform the more restrictive models. Using restrictive models can result in biased variance component estimates, if restrictions are not fulfilled by the data analysed. Chapter 5 evaluates, whether a subdivision of 21 triticale genotypes into heterotic pools is preferable. Subdividing genotypes into heterotic pools implies a factorial mating design between heterotic pools and a diallel mating design within each heterotic pool. For two (or more) heterotic pools the model is extended by assuming a joint variance-covariance structure for parental effects and general combing ability effects within the diallel and within the factorials. It is shown that a model with two heterotic pools has the best model fit. The variance component estimates for the general combing ability decrease within the heterotic pools and increase between heterotic pools. The results in Chapter 2 to 5 show, that an efficient and valid analysis of phenotypic plant breeding data is an essential part of the plant breeding process. The analysis can be performed in one or two stages. The used mixed models recognizing the field and mating design and the genetic structure can be used for answering questions about the genetic variance in cultivar populations under selection and of the number of heterotic pools. The proposed general diallel model using a joint variance-covariance structure between related effects can further be modified for factorials and other mating designs with related genotypes.