Testing peatland testate amoeba transfer functions: appropriate methods for clustered training-sets

Transfer functions are widely used in palaeoecology to infer past environmental conditions from fossil remains of many groups of organisms. In contrast to traditional training-set design with one observation per site, some training-sets, including those for peatland testate amoeba-hydrology transfer functions, have a clustered structure with many observations from each site. Here we show that this clustered design causes standard performance statistics to be overly optimistic. Model performance when applied to independent data sets is considerably weaker than suggested by statistical cross-validation. We discuss the reasons for these problems and describe leave-one-site-out cross-validation and the cluster bootstrap as appropriate methods for clustered training-sets. Using these methods we show that the performance of most testate amoeba-hydrology transfer functions is worse than previously assumed and reconstructions are more uncertain.