Sample size and genetic divergence: a principal component analysis for soybean traits

Biometric techniques, including the principal component analysis, are commonly applied in soybean genetic divergence studies. However, the sample size used in such studies is often determined empirically, neglecting its potential impact on inference interpretation. Therefore, this study aimed (i) to analyze the response of principal components to the number of plants sampled per experimental unit (plot); (ii) to determine the multivariate representative sample size, and (iii) to construct a methodology to predict sample size for principal components as a function of the precision level defined a priori. Six experiments were performed in two locations in Rio Grande do Sul, Brazil, with three experiments being carried out in each location. All experiments were conducted using a complete randomized block design with three repetitions, and 20 soybean genotypes were utilized, resulting in 360 plots (60 plots per experiment). From each plot, twenty plants were sampled, totaling 7200 plants. A resampling bootstrap procedure was applied to the principal component technique for 10 biometric traits. Posteriorly, the sample size was defined based on predefined precision levels, and power logistic models were parametrized to predict the sample size per experimental unit. The precision of the eigenvalues obtained from the principal component analysis gradually improves with larger sample sizes. Eigenvalues that capture a higher variance tend to require smaller sample sizes for accurate estimation. The fitted models demonstrated satisfactory predictive ability in determining the optimal number of plants per experimental unit, serving as a complementary tool for defining sample size at the desired precision level. Eighteen plants per experimental unit are enough to estimate the eigenvalues of the first two soybean principal components reliably. The developed predictive methodology and sample dimensioning per experimental unit can support future research aimed at identifying divergent genotypes, making them useful tools for soybean plant breeding programs.