Estimating Broad-Sense Heritability with Unbalanced Data from Agricultural Cultivar Trials

Broad-sense heritability is defined as the proportion of phenotypic variance that is attributable to an overall variance for the genotype. It is often calculated as a measure (i) to quantify and eventually compare the precision of agricultural cultivar trials, and/or (ii) to estimate the response to selection in plant breeding trials. In practice, most such trials are conducted at multiple environments (i.e., year–location combinations) resulting in a multienvironment trial (MET) with unbalanced data, as, for example, not all cultivars are tested at each environment. However, the standard method for estimating heritability implicitly assumes balanced data, independent genotype effects, and homogeneous variances. Therefore, we compared the estimates for broad-sense heritability computed via the standard method to those obtained via six alternative estimation methods (example codes: https://github.com/PaulSchmidtGit/Heritability). We did so by analyzing four cultivar METs, which all displayed a typically unbalanced data structure but differed in the genetic frameworks of their cultivars. Results indicate that the standard method may overestimate heritability for all datasets, whereas alternative methods show similar estimates per dataset and thus seem better able to handle this kind of unbalanced data. Finally, we show that to compare heritability estimates between different METs, genetic variance component estimates should be fixed to common values for both datasets.