SPATIAL MODELING IN ECOLOGY: THE FLEXIBILITY OF EIGENFUNCTION SPATIAL ANALYSES

TLDR

Eigenfunction‑based spatial modeling has recently been proposed to explicitly incorporate spatial predictors into ecological analyses, with two main approaches: distance‑based eigenvector maps and topology‑based spatial filtering. The goal is to generate spatial predictors that can be readily integrated into conventional regression models. The study demonstrates the usefulness of eigenfunctions in ecological spatial modeling, showing equivalencies and differences between the two implementations, and highlights their advantage of enabling full general and generalized linear modeling in the presence of spatial autocorrelation.

Abstract

Recently, analytical approaches based on the eigenfunctions of spatial configuration matrices have been proposed in order to consider explicitly spatial predictors. The present study demonstrates the usefulness of eigenfunctions in spatial modeling applied to ecological problems and shows equivalencies of and differences between the two current implementations of this methodology. The two approaches in this category are the distance-based (DB) eigenvector maps proposed by P. Legendre and his colleagues, and spatial filtering based upon geographic connectivity matrices (i.e., topology-based; CB) developed by D. A. Griffith and his colleagues. In both cases, the goal is to create spatial predictors that can be easily incorporated into conventional regression models. One important advantage of these two approaches over any other spatial approach is that they provide a flexible tool that allows the full range of general and generalized linear modeling theory to be applied to ecological and geographical problems in the presence of nonzero spatial autocorrelation.