Estimating heritability in plant breeding programs

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Heritability is defined as the ratio of genetic and phenotypic variance. It is a key quantity for the evaluation of plant breeding programs. For example, it may be used to compute the response to selection. Thus, heritability is routinely assessed in the analysis of plant breeding trials. Standard equations used in plant breeding, such as for the response to selection, assume a simple data structure. Specifically, it is assumed that the data follow a simple mixed model with normally distributed random effects and that the data is balanced. These simple assumptions are almost always violated in real plant breeding programs. Typically, such data are unbalanced. For example, not all genotypes may have been tested in all environments. Moreover, trials in individual environments almost always use some form of incomplete blocking. Also, spatial analysis methods are becoming increasingly popular. In these situations, the phenotype is usually an adjusted mean, which does not meet the assumptions needed for the common definitions of heritability, because these means are correlated and their variance may not be constant. Moreover, the phenotype is often estimated by best linear unbiased prediction, for example in order to exploit pedigree or genome-wide marker information, which further complicates the assessment of heritability.Two further problems are that many traits are assessed as counts or ordinal scores, which do not meet the normality assumption, and that repeated measurements may be taken on the same observational unit (plot, plant etc), in which case serial correlation needs to be taken into account. In these situations, it is not obvious how heritability should best be assessed.The objective of this project is therefore to propose new methods for estimating heritability that are specifically designed for unbalanced plant breeding data and to compare these methods to existing proposals both empirically using real plant breeding data sets as well as Monte Carlo simulation. Moreover, existing approaches that are exclusively restricted to normally distributed data will be extended (i) to non-normal data, in particular to count data that can be modelled by generalized linear mixed models (GLMM), as well as (ii) to repeated measures data.