How many test locations and replications are needed in crop variety trials for a target region?

Abstract

How many test locations and replications are needed in crop variety trials is a question every plant breeder has to ask. Simple formulas were developed to estimate the optimum number of replicates and test locations. The optimum number of replicates in a trial was estimated by the formula ${\text{N}}_{{\text{r}}} {\text{ = 3}}\left( {\sigma _{\epsilon }^{{\text{2}}} /\sigma _{{\text{g}}}^{{\text{2}}} } \right)$, where $\sigma_{\text{g}}^{2}$ and $\sigma_{\epsilon }^{2}$ are the variance components for genotypic main effect and experimental error in the trial, respectively. The optimum number of test locations for a target region was estimated by ${\text{N}}_{\text{e}} = 1 + 3\left( {{\raise0.7ex\hbox{${\sigma_{\text{ge}}^{2} }$} \!\mathord{\left/ {\vphantom {{\sigma_{\text{ge}}^{2} } {\sigma_{\text{g}}^{2} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\sigma_{\text{g}}^{2} }$}}} \right)$, where $\sigma_{\text{g}}^{2}$ and $\sigma_{\text{ge}}^{2}$ are the variance components for genotypic main effect and genotype-by-location interaction, respectively. These formulas were applied to data from the oat registration trials conducted in eastern Canada in 2006–2012. The optimum number of replicates within a trial at the Ottawa site was estimated to be fewer than three for all traits considered. The estimated optimum number of test locations for the whole eastern Canada was fewer than four for all traits except for grain yield and lodging scores. For grain yield, the estimated optimum number of test locations was 20, twice as many as the actual test locations used. Mega-environment analysis using a “GGL+GGE biplot” revealed two distinct subregions in eastern Canada. Analysis within mega-environment revealed that the number of test locations actually used was close to optimal for one mega-environment but severely inadequate for the other.