Browsing by Subject "Heritability"

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An adjusted coefficient of determination (R2) for generalized linear mixed models in one go
(2023) Piepho, Hans‐Peter
The coefficient of determination (R2) is a common measure of goodness of fit for linear models. Various proposals have been made for extension of this measure to generalized linear and mixed models. When the model has random effects or correlated residual effects, the observed responses are correlated. This paper proposes a new coefficient of determination for this setting that accounts for any such correlation. A key advantage of the proposed method is that it only requires the fit of the model under consideration, with no need to also fit a null model. Also, the approach entails a bias correction in the estimator assessing the variance explained by fixed effects. Three examples are used to illustrate new measure. A simulation shows that the proposed estimator of the new coefficient of determination has only minimal bias.
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.
Quantitative-genetic evaluation of resistances to five fungal diseases in a large triticale diversity panel (×Triticosecale)
(2022) Miedaner, Thomas; Flath, Kerstin; Starck, Norbert; Weißmann, Sigrid; Maurer, Hans Peter
The man-made cereal triticale was fully resistant to the biotrophic diseases powdery mildew, leaf rust, yellow rust, and stem rust from its introduction in Europe in the mid-1970s until about 1990. In the following years, new races that were able to infect at least some triticale genotypes developed in all four pathogen populations, and resistance breeding came into focus. Here, we analyzed 656 winter triticale cultivars from 12 countries for resistance to these biotrophic diseases and Fusarium head blight (FHB) at up to 8 location-year combinations (environments). FHB ratings were corrected for plant height and heading stage by comparing three statistical methods. Significant (p < 0.001) genetic variances were found for all resistances with moderate to high entry-mean heritabilities. All traits showed a normal distribution, with the exception of stem rust, where the ratings were skewed towards resistance. There were no substantial correlations among the five disease resistances (r = −0.04 to 0.26). However, several genotypes were detected with multi-disease resistance with a disease rating below average for all five diseases simultaneously. In future, such genotypes must be selected primarily to cope with future challenges of less pesticide use and global climate change.