Using `lme()` to fit the Environmental Variance mixed model to genotype experiments

Published at December 4, 2025 ·  11 min read

Yield stability is a key aspect in the selection of crop genotypes. Its definition is not entirely straightforward (see, for example, Annichiarico, 2002), but, in simple terms, it refers to the ability of a crop to maintain its yield potential across different environments, helping farmers safeguard their income. Several statistical indicators of stability have been proposed (see, e.g., Mohammadi, 2008). In this post, however, I will focus on the so-called environmental variance, which represents the portion of phenotypic variance attributable to environmental (non-genetic) factors and is measured as the overall variance across environments for each genotype.

Using `lme()` to fit the Stability Variance mixed model to genotype experiments

Published at December 2, 2025 ·  11 min read

Yield stability is a fundamental aspect of the selection of crop genotypes. Its definition is rather complex (see, for example, Annichiarico, 2002), but, in simple terms, it represents the ability of a crop to maintain its potential yield level across environments, which helps farmers preserve their income. Several statistical indicators of stability exist (see, e.g., Mohammadi, 2008) and, in this post, I would like to concentrate on the so-called stability variance, that is, for a specific genotype, the amount of yield variability across different environments, after correcting for the additive effects of each environment, which are common to all genotypes under investigation (Shukla, 1972).

Dealing with correlation in designed field experiments: part II

Published at February 10, 2025 ·  11 min read

With field experiments, studying the correlation between the observed traits may not be an easy task. For example, we can consider a genotype experiment, laid out in randomised complete blocks, with 27 wheat genotypes and three replicates, where several traits were recorded, including yield (Yield) and weight of thousand kernels (TKW). We might be interested in studying the correlation between those two traits, but we would need to face two fundamental problems: