Spatially explicit predictions using spatial eigenvector maps

Abstract In this paper, we explain how to obtain sets of descriptors of the spatial variation, which we call “predictive Moran's eigenvector maps” (pMEM), that can be used to make spatially explicit predictions for any environmental variables, biotic or abiotic. It unites features of a method called “Moran's eigenvector maps” (MEM) and those of spatial interpolation, and produces sets of descriptors that can be used with any other modelling method, such as regressions, support vector machines, regression trees, artificial neural networks and so on. The pMEM are the predictive eigenvectors produced by using a distance‐weighting function (DWF) in the construction of MEM. Seven types of pMEM, each associated with one of seven different DWFs, were defined and studied. We performed a simulation study to determine the power of different types of pMEM eigenfunctions at making accurate predictions for spatially structured variables. We exemplified the application of the method to the prediction of the spatial distribution of 35 Oribatid mites living in a peat moss ( Sphagnum ) mat on the shore of a Laurentian lake. We also provide an R language package called pMEM to make calculations easily available to end users. The results indicate that anyone of the pMEMs obtained from the different DWFs could be the best suited one to predict spatial variability in a given data set. Their application to the prediction of mite distributions highlights the capability of pMEMs for predicting distributions, and for providing spatially explicit estimates of environmental variables that are useful for predicting distributions.