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

—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 components (PCs) whenever N was smaller than the number of truss elements (P). Stability of eigenvalues and eigenvectors increased as the N:P ratio increased for all three species, but the N:P ratio at which stable results were achieved varied by species. Our results suggest that an N:P ratio of 3.5–8.0 was required for stability of PC2 and PC3, which is required for analysis of fish shape. Because some of our results varied among the species we examined, we recommend similar evaluations for other species. Results from past work that used PCA of truss elements and where N was less than P may require re-evaluation. Fish morphometrics are studied extensively in fishery science. A common application is to support descriptions of new species based on morphological dissimilarity to closely related species (e.g., Crabtree 1989; Creech 1992; Humphries and Cashner 1994; Stauffer and van Snik 1997; Teugels et al. 2001; Ingenito and Buckup 2005; Devaere et al. 2007; Welsh and Wood 2008). Some studies are taxonomic redescriptions that include analysis of morphometrics (e.g., Fink 1993; Bestgen and Propst 1996; Das and Nelson 1996; Vreven and Teugels 2005). Morphological analysis is also used to study phylogeny (Morrison et al. 2006), phenotypic plasticity (Hard et al. 1999; Gillespie and Fox 2003), fish condition (Smith et al. 2005), and differences among stocks or morphotypes (e.g., Kinsey et al. 1994; Bronte et al. 1999; Moore and Bronte 2001; Alfonso 2004; Hoff 2004; Zimmerman et al. 2006) and to determine parental species of purported hybrids (Taylor et al. 1986; Bostrom et al. 2002). In the Pacific Northwest, researchers used morphological analysis to describe changes associated with smoltification of anadromous salmonine fishes (Winans and Nishioka 1987) and to nonlethally predict when smoltification has occurred (Beeman et al. 1994). Morphological analysis has also been used to identify unique stocks of endangered cyprinids (Douglas et al. 1989) and to assess sexual dimorphism (Douglas 1993). Since publication of Bookstein et al. (1985), the collection and analysis of fish morphometrics has been dominated by truss measurements analyzed using multivariate statistics (hereafter, multivariate morphometrics). Traditional methods of collecting fish morphometrics (e.g., Hubbs and Lagler 1964) relied on numerous measurements along the longest axis of the body and thus failed to capture other aspects of shape (Bookstein et al. 1985). An advantage of the truss method promoted by Bookstein et al. (1985) is that the method is not dominated by redundant measurements along a single axis and thus provides a more complete characterization of shape. These data are commonly analyzed using multivariate statistics, such as principal components analysis (PCA), which is superior to * Corresponding author: [email protected] Received May 23, 2008; accepted November 28, 2008 Published online April 27, 2009 487 Transactions of the American Fisheries Society 138:487–496, 2009 Copyright by the American Fisheries Society 2009 DOI: 10.1577/T08-091.1 [Article]