Weighted averaging partial least squares (WA-PLS)

Like the Modern Analogue Technique (and calibration with CABFAC), WA-PLS is a method for reconstructing past environmental parameters (temperature, pH) from a fossil assemblage, based on a training set of modern samples. First described by ter Braak & Juggins (1993) and ter Braak et al. (1993), WA-PLS is considered by some as the overall most accurate calibration method.

The (single) environmental variable, usually temperature, enters in the first column, and taxa in consecutive columns. All the modern sites, with known values for the environmental variable, go in the first rows, followed by all the downcore samples (these should have question marks in the environmental column).

The plot on the first tab shows all the modern samples, with the observed temperature (for example) versus the reconstructed temperature. This does not use cross-validation. The RMSE (Root Mean Square Error) is based on these values.

The method is also cross-validated with the leave-one-out procedure (jackknifing), which is basis for the RMSEP value (Root Mean Square Error of Prediction). The number of PLS components should be set in order to minimize the RMSEP. Sometimes the minimal value is obtained already with only one component, when the method is equivalent to two-way weighted averaging (WA).

The implementation of WA-PLS in Past is based on the algorithm of ter Braak & Juggins (1993), see the Past manual for details.


ter Braak, C.J.F. 1987. Ordination. Pp. 91-173 in: Jongman, R.H.G., ter Braak, C.J.F., van Tongeren, O.F.R. (eds), Data Analysis in Community and Landscape Ecology, Pudoc.

ter Braak, C.J.F., Juggins, S., Birks, H.J.B., van der Voet, H. 1993. Weighted Averaging Partial Least Squares regression (WA-PLS): definition and comparison with other methods for species-environment calibration. Pp. 525-560 in: Patil, G.P. & Rao, C.R. (eds), Multivariate Environmental Statistics, Elsevier.

ter Braak, C.J.F., Juggins, S. 1993. Weighted averaging partial least squares (WA-PLS): an improved method for reconstructing environmental variables from species assemblages. Hydrobiology 269/270: 485-502.

Published Aug. 31, 2020 10:05 PM - Last modified Aug. 31, 2020 10:05 PM