Research tools


, Volume 269, Issue 1, pp 485-502

First online:

Weighted averaging partial least squares regression (WA-PLS): an improved method for reconstructing environmental variables from species assemblages

  • Cajo J. F. ter BraakAffiliated withAgricultural Mathematics Group-DLODLO-Institute for Forestry and Nature Research
  • , Steve JugginsAffiliated withEnvironmental Change Research Centre, Department of Geography, University College LondonBotanical Institute, University of Bergen

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Weighted averaging regression and calibration form a simple, yet powerful method for reconstructing environmental variables from species assemblages. Based on the concepts of niche-space partitioning and ecological optima of species (indicator values), it performs well with noisy, species-rich data that cover a long ecological gradient (>3 SD units). Partial least squares regression is a linear method for multivariate calibration that is popular in chemometrics as a robust alternative to principal component regression. It successively selects linear components so as to maximize predictive power. In this paper the ideas of the two methods are combined. It is shown that the weighted averaging method is a form of partial least squares regression applied to transformed data that uses the first PLS-component only. The new combined method, ast squares, consists of using further components, namely as many as are useful in terms of predictive power. The further components utilize the residual structure in the species data to improve the species parameters (‘optima’) in the final weighted averaging predictor. Simulations show that the new method can give 70% reduction in prediction error in data sets with low noise, but only a small reduction in noisy data sets. In three real data sets of diatom assemblages collected for the reconstruction of acidity and salinity, the reduction in prediction error was zero, 19% and 32%.

Key words:

diatoms gradient analysis indicator values palaeo-environments partial least squares regression PLS species-environment calibration transfer function