Bootstrap Confidence Regions for Canonical Variates: Application to Studies of Evolutionary Differentiation

Abstract

Theory recently developed to construct confidence regions based on the parametric bootstrap is applied to add inferential information to graphical displays of sample centroids in canonical variate analysis. Problems of morphometric differentiation among subspecies and species are addressed using numerical resampling procedures.

Population Structure of the SW Atlantic Estuarine Crab Neohelice granulata Throughout Its Range: a Genetic and Morphometric Study

“…Scatter plots of canonical scores in two-dimensional space were used for visual detection of groups. We also constructed confidence ellipses for the position of centroids of each sampling site (von Zuben et al 1998). Differences among sampling sites were assessed with Wilk's λ and associated F and P values (Anastasiadou and Leonardos 2008).…”

Morphological divergence rate tests for natural selection: uncertainty of parameter estimation and robustness of results

“…Therefore, the samples were grouped by the interaction term of lagoon and habitat (the collection sites described in the previous section), for an assessment of the direction of major variation among populations in shape space (while statistically controlling for within-group variation). The populations were represented by 95% confidence ellipses (with standard errors of centroids) generated by a parametric bootstrap resampling (Von Zuben et al, 1998), where 1000 replicates of the data matrices were constructed by random sampling, based on the original covariance matrix and the vector of means. Because of a marked sexual dimorphism, separate analyses were performed for males and females.…”

New Species of Brachycephalus (Anura: Brachycephalidae) from the Atlantic Rain Forest in São Paulo State, Southeastern Brazil

“…Dimension reduction of the 18 partial warps generated for the skull of the Brachycephalus taxa examined was achieved by canonical variates analysis, which maximizes variation among groups relative to variation within groups (Mardia et al, 2006). Confidence regions around sample centroids for canonical axes using parametric bootstrap (Ringrose, 1996) were computed by simulating 1,000 replicate data matrices (Von Zuben et al, 1998). Canonical axes were visualized in shape space by multivariate regression of partial-warp scores on canonical variates scores (Rohlf et al, 1996).…”

“…The shape variables (partial warps) computed using the thin-plate methodology (Bookstein, 1991(Bookstein, , 1996 and the inferential procedure developed for canonical variates analysis (Ringrose, 1996;Von Zuben et al, 1998) demonstrated that B. pitanga can be completely discriminated on the basis of cranial shape from the other species of Brachycephalus that occur in the state of Sã o Paulo. This finding is relevant because anuran morphology has been regarded as conservative both among and within species (Heyer, 1979;Austin et al, 2002;Lougheed et al, 2006).…”