The Effect of Sample Size on the Stability of Principal Components Analysis of Truss-Based Fish Morphometrics

Abstract Multivariate analysis of fish morphometric truss elements for stock identification, description of new species, assessment of condition, and other applications is frequently conducted on data sets that have sample sizes smaller than those recommended in the literature. Minimum sample size recommendations are rarely accompanied by empirical support, and we know of no previous assessment of minimum sample sizes for multivariate analysis of fish truss elements. We examined the stability of outcomes of principal components analysis (PCA) of truss elements, a commonly applied method of morphometric analysis for fishes, by conducting PCA on 1,000 resamples for each of 24 different sample sizes (N; each sample drawn without replacement) from collections of yellow perch Perca flavescens (397 fish), white perch Morone americana (208 fish), and siscowet lake trout Salvelinus namaycush (560 fish). Eigenvalues were inflated and loadings on eigenvectors were highly unstable for the first three principal compo...