A matter of genetic divergence: sizing up the sample for soybean canonical variables

Abstract

Empirical sampling can result in inaccurate estimates of the variance captured in canonical variables, therefore affecting their scores and the identification of genetic divergence. This study aimed to analyze the response of canonical variables as a function of the number of plants sampled per experimental unit, and to define a representative multivariate sample size based on the percentage variance absorbed by the canonical variables. Six soybean experiments were performed in two locations in Rio Grande do Sul, Brazil, using a complete randomized block experimental design with three repetitions and 20 genotypes (360 plots), and ten traits were assessed in 20 plants per plot. Bootstrap resampling was applied for the canonical variable analysis. Posteriorly, sample size per experimental unit was dimensioned using nonlinear models and defining the maximum curvature point via perpendicular distances. The estimate of the percentage variance retained in the canonical variables was sensitive to the sample size per experimental unit. The 95% confidence interval width of the absorbed variance decreased as sample size increased, and the precision for estimating the variance was improved, stabilizing once 36 plants per experimental unit were sampled. Insufficient sampling harms the identification of divergent genotypes, thus increasing sample size gradually improves the quality of the canonical variables’ variance estimates. Thirty-six plants per experimental unit are enough to estimate the variance explained in the first four canonical variables for soybean reliably. The sample size recommendations presented may be useful for researchers in the genetic divergence field, increasing the efficiency of soybean breeding programs.