Browsing by Person "Schmidt, Paul"

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    Estimating heritability in plant breeding programs
    (2019) Schmidt, Paul; Piepho, Hans-Peter
    Heritability is an important notion in, e.g., human genetics, animal breeding and plant breeding, since the focus of these fields lies on the relationship between phenotypes and genotypes. A phenotype is the composite of an organism’s observable traits, which is determined by its underlying genotype, by environmental factors and by genotype-environment interactions. For a set of genotypes, the notion of heritability expresses the proportion of the phenotypic variance that is attributable to the genotypic variance. Furthermore, as it is an intraclass correlation, heritability can also be interpreted as, e.g., the squared correlation between phenotypic and genotypic values. It is important to note that heritability was originally proposed in the context of animal breeding where it is the individual animal that represents the basic unit of observation. This stands in contrast to plant breeding, where multiple observations for the same genotype are obtained in replicated trials. Furthermore, trials are usually conducted as multi-environment trials (MET), where an environment denotes a year × location combination and represents a random sample from a target population of environments. Hence, the observations for each genotype first need to be aggregated in order to obtain a single phenotypic value, which is usually done by obtaining some sort of mean value across trials and replicates. As a consequence, heritability in the context of plant breeding is referred to as heritability on an entry-mean basis and its standard estimation method is a linear combination of variances and trial dimensions. Ultimately, I find that there are two main uses for heritability in plant breeding: The first is to predict the response to selection and the second is as a descriptive measure for the usefulness and precision of cultivar trials. Heritability on an entry-mean basis is suited for both purposes as long as three main assumptions hold: (i) the trial design is completely balanced/orthogonal, (ii) genotypic effects are independent and (iii) variances and covariances are constant. In the last decades, however, many advancements in the methodology of experimental design for and statistical analysis of plant breeding trials took place. As a consequence it is seldom the case that all three of above mentioned assumptions are met. Instead, the application of linear mixed models enables the breeder to straightforwardly analyze unbalanced data with complex variance structures. Chapter 2 exemplarily demonstrates some of the flexibility and benefit of the mixed model framework for typically unbalanced MET by using a bivariate mixed model analyses to jointly analyze two MET for cultivar evaluation, which differ in multiple crucial aspects such as plot size, trial design and general purpose. Such an approach can lead to higher accuracy and precision of the analysis and thus more efficient and successful breeding programs. It is not clear, however, how to define and estimate a generalized heritability on an entry-mean basis for such settings. Therefore, multiple alternative methods for the estimation of heritability on an entry-mean basis have been proposed. In Chapter 3, six alternative methods are applied to four typically unbalanced MET for cultivar evaluation and compared to the standard method. The outcome suggests that the standard method over-estimates heritability, while all of the alternative methods show similar, lower estimates and thus seem able to handle this kind of unbalanced data. Finally, it is argued in Chapter 4 that heritability in plant breeding is not actually based on or aiming at entry-means, but on the differences between them. Moreover, an estimation method for this new proposal of heritability on an entry-difference basis (H_Delta^2/h_Delta^2) is derived and discussed, as well as exemplified and compared to other methods via analyzing four different datasets for cultivar evaluation which differ in their complexity. I argue that regarding the use of heritability as a descriptive measure, H_Delta^2/h_Delta^2, can on the one hand give a more detailed and meaningful insight than all other heritability methods and on the other hand reduces to other methods under certain circumstances. When it comes to the use of heritability as a means to predict the response to selection, the outcome of this work discourages this as a whole. Instead, response to selection should be simulated directly and thus without using any ad hoc heritability measure.