PRINCIPAL CURVES: A NEW TECHNIQUE FOR INDIRECT AND DIRECT GRADIENT ANALYSIS

Abstract

Principal curves are smooth one-dimensional curves in a high dimensional space that are ideally suited for indirect gradient analysis of multispecies abundance data. A principal curves ordination will simultaneously estimate the species response curves and locate sites on a single ecological gradient. By means of theoretical argument and simulations, they are shown to be superior to both correspondence analysis and multidimensional scaling, outperforming them in 77% and 72% of simulations, respectively. The species response curves used in the simulations varied from simple Gaussian form with equal maxima and tolerances to complex multimodal curves with varying maxima and tolerances. Simulations were conducted both with and without noise. When species response curves are smooth, and a reasonable initial configuration is provided, principal curve gradient analysis can succeed even when the curves are complex and beta diversity is high. Principal curves can also be adapted for direct gradient analysis in order to relate species composition to environmental variables. Although ordination techniques are used both to uncover ecological gradients and to represent species composition, it is argued that these two aims are distinct. Hence, a single ordination technique cannot generally achieve both objectives simultaneously. However, by superimposing a principal curve on a principal components biplot, joint representation of an ecological gradient and species composition can be achieved. Information from either an indirect or direct principal curve gradient analysis can be added to the biplot, thereby relating environmental variables to species composition and locations of sites on the gradient. Two ecological data sets, comprising abundances of hunting spiders and species of grasses, are analyzed using principal curve gradient analysis. The results are contrasted with previous analyses, using canonical-correspondence analysis and canonical-correlation analysis, and indicate that principal curve gradient analysis can find one-dimensional gradients that explain species composition as well as, or better than, higher dimensional solutions from other techniques. This, in turn, can lead to a more succinct representation and better understanding of ecological systems.