Palaeoenvironmental reconstructions of lake sediment records have been greatly facilitated by statistical comparisons with microfossil assemblages from the surface sediments of modern lakes. These modern sub-fossil assemblages from different lakes, which are often referred to as "training-sets", attempt to incorporate gradients of environmental parameters, such as e.g., temperature and phosphorus, are of interest for paleoenvironmental reconstruction. One major assumption of quantitative palaeoenvironmental reconstructions requires that the environmental variable to be reconstructed is, or is linearly related to, an ecologically important determinant in the ecological system of interest, and that the joint distribution with other variables in the fossil set is the same as in the training-set. The motivation for this paper is that present-day diatom species abundances in surface-sediment samples are often influenced by several environmental gradients. Partial least squares (PLS) or weighted-averaging partial least squares (WA-PLS) regression methods can be used to adjust species optima, if the additional PLS components, which are orthogonal to previous PLS components, are included.
This paper tests a reproducible approach for reducing the influence of background variables within a diatom training-set to produce a "screened" training-set, which focuses on the variable of interest. In our example total phosphorus (TP) is the variable of interest. The initial training-set consists of modern Swiss lakes along an elevation gradient spanning 2005 m (334 to 2339 m a.s.l.), which follows a TP gradient from 522 to 3 µg L^-1. However, high-elevation lakes are not distributed equally along the TP gradient. They are meso-oligotrophic because high-elevation eutrophic lakes are rare in Switzerland. This leads to a potential confounding effect between the elevation and the nutrient gradients. These higher elevation lakes were selectively excluded, using Monte Carlo permutation tests, until the conditional effect with respect of covariables of elevation was no longer significantly related to the relative abundance of diatoms. The initial and screened inference models for log TP were applied to fossil assemblages from varved sediments at Greifensee (Switzerland), which cover the past century. The evaluation of. the reconstructions with measured TP (1954-1994) demonstrates that the smaller (screened) subset performs better than the larger, more heterogeneous, initial data-set when the same number of components are included. The slope of the relation between measured and inferred log TP changed significantly for the reconstructions using partial least squares, with one and two components, and for reconstruction using weighted averaging partial least squares with two components. According to our interpretation, the accuracy of the reconstructions improved because modern diatom abundances of the smaller subset are controlled mainly by log TP and lakes are more equally distributed along the log TP gradient. This approach of reducing the influence of background variables is applicable to other heterogeneous training-sets, such as merged training-sets, in order to homogenise the background variables and to maintain the gradient of interest.