Optimizing the choice of a spatial weighting matrix in eigenvector‐based methods

Abstract

Eigenvector-mapping methods such as Moran's eigenvector maps (MEM) are derived from a spatial weighting matrix (SWM) that describes the relations among a set of sampled sites. The specification of the SWM is a crucial step, but the SWM is generally chosen arbitrarily, regardless of the sampling design characteristics. Here, we compare the statistical performances of different types of SWMs (distance-based or graph-based) in contrasted realistic simulation scenarios. Then, we present an optimization method and evaluate its performances compared to the arbitrary choice of the most-widely used distance-based SWM. Results showed that the distance-based SWMs generally had lower power and accuracy than other specifications, and strongly underestimated spatial signals. The optimization method, using a correction procedure for multiple tests, had a correct type I error rate, and had higher power and accuracy than an arbitrary choice of the SWM. Nevertheless, the power decreased when too many SWMs were compared, resulting in a trade-off between the gain of accuracy and the loss of power. We advocate that future studies should optimize the choice of the SWM using a small set of appropriate candidates. R functions to implement the optimization are available in the adespatial package and are detailed in a tutorial.

Landscape genetic analyses of Cervus elaphus and Sus scrofa: comparative study and analytical developments

“…select" function from the R package "adespatial" . Specifically, we used the minimisation of Moran's I in the residuals (MIRs) approach (Bauman et al 2018) to identify the set of MEMs removing spatial autocorrelation in the residuals so that the Moran's I statistic was not significant at a threshold α = 0.1. Any environmental predictor acting as a cross-over suppressor in presence of retained spatial predictors was discarded (see below for details about statistical suppression) and the MIR optimisation procedure was repeated.…”

Past human disturbances and soil fertility both influence the distribution of light‐demanding tree species in a Central African tropical forest

“…The MSR uses information on the spatial connectivity among sampling points obtained when selecting Moran's Eigenvector Maps (MEMs; Dray, Legendre, & Peres‐Neto, 2006) which are commonly used to model multiscale spatial structures in ecological data. Connections among plots were defined using a Gabriel's graph which has been shown appropriate in the case of highly irregular sampling design (Bauman, Drouet, Fortin, & Dray, 2018a). The selection of MEMs was optimised following a forward selection procedure (Blanchet, Legendre, & Borcard, 2008) that has been shown to provide correct type I error rate for the selection of spatial eigenvectors (Bauman, Drouet, Dray, & Vleminckx, 2018b).…”

Avaliação De Gradiente Pedoambiental Usando Análise De Componentes Principais (Pca) Na Antártica Marítima

“…Matrix B was generated using three graph-based connection schemes (Gabriel = gab, relative neighbourhood = rel and minimum spanning tree = mst). Weighting matrices A were derived from three functions: f bin = binary, based only on topology and reflecting a neutrality in the weight; f lin = 1-(d/dmax), linear, and f con = 1-(d/dmax) 0.5 , nonlinear, both weighted by the inverse of the power of Euclidean distances (d and dmax) between two sampling sites (BAUMAN et al, 2018). The selection of matrix W among the nine candidate matrices and the subset of significant MEMs was conducted using the optimization method (listw.candidates function) available in the adespatial package (DRAY et al, 2019), considering only MEMs associated with positive eigenvalues.…”