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Weighted Averaging Partial Least Squares regression (WA-PLS): definition and comparison with other methods for species-environment calibration

(1993). Weighted averaging partial least squares regression (WA-PLS): definition and comparison with other methods for species-environment calibration. ABSTRACT A multivariate calibration method is proposed that relates to correspondence analysis as partial least squares (PLS) relates to principal components analysis. The new method extends and improves the weighted averaging (WA) method for inferring values of environmental variables from biological species compositions, hence the name weighted averaging partial least squares (WA-PLS). WA-PLS is designed to cope with the special features of ecological data, namely, large numbers of species, many zero-abundance values and the non-linear, often unimodal response of species to environmental variables. In simulations of such data in which the species response is governed by two environmental variables, one of which is the variable of interest and the other a nuisance variable, the standard error of prediction (SEP) was reduced by a factor of ca. 0.5 by using WA-PLS instead of WA. The length of gradient of the data (between 2 and 8 SD-units) had little influence on the relative performance as had the nuisance variable, except for a short calibration gradient (2 SD). Further comparisons were made with PLS and a maximum likelihood method (MLM) based on the Gaussian response model for compositional data. WA-PLS outperformed PLS and MLM in all cases, the difference with MLM being small if the nuisance variable was unimportant. WA-PLS also compared favourably on a real data example from Imbrie & Kipp (1971) in which sea-surface temperature is reconstructed from fossil foraminiferal composition.