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

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 SWM s (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 SWM s 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 SWM s 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.