Inferring a single variable from an assemblage with multiple controls: getting into deep water with cladoceran lake-depth transfer functions

Transfer functions have proved very useful for quantitative reconstruction of past environments. Inferring values of a single parameter based on changes in a community with multiple controls may result in unreliable inferences. To assess this unreliability cladoceran surface sediment assemblages from 53 lakes in Greenland, which have substantial variations in lake depth and fish abundance, both of which shape cladoceran communities, were analysed in this study. Redundancy analysis (RDA) revealed that maximum lake depth and either fish abundance or fish presence/absence exerted substantial and significant control on the cladoceran assemblage. Partial RDA showed that maximum lake depth and fish abundance uniquely explained 7.9 and 5.1%, respectively, with 5.3% variance being shared. A transfer function to infer lake depth from cladoceran sub-fossils was constructed and performed moderately well [coefficient of determination (r ²) = 0.65; root mean square error of prediction (RMSEP) = 0.32 log maximum depth] on the full dataset. When outliers, defined by a bootstrapped prediction error greater than 25% of the total depth gradient, were excluded, the model performed well (r ² = 0.74, RMSEP = 0.25 log maximum depth). The improved transfer function was then applied to sedimentary assemblage from a sediment core from Lake Boresø, in North-eastern Greenland, covering 9,000 years. A large increase in lake depth was inferred around 6250 bp. Whilst the climate was wetter at that time, the inferred changes in depth likely reflect the alteration of the food web, which resulted from the arrival of fish in the lake. This highlights the risks of using single-variable inference models for hindcasting change in lake physical and/or food web structure when there are other important co-variables.