Application of Moran Eigenvector Maps (MEM) to irregular sampling designs

Moran's eigenvectors maps (MEM) are attractive mathematical objects as they are fairly simple to calculate and can be used in most studies of spatially-explicit data. There is, however, an aspect of MEM analysis that still requires some investigation: the effect of irregular sampling on their modeling performance. This study investigates empirically the behavior of MEMs under different irregularity schemes. It is focusing on simulated scenarios representing sampling designs frequently encountered in ecology. We advocate that MEMs can be computed and correctly used with data coming from irregularly designed sampling surveys, given some precautions. We suggest that when the sampling sites are equally spaced but do not cover the entire study area, the MEMs can be computed directly on the coordinates of the sampling sites without any important loss of information. Whereas, when the phenomenon of interest is tackled using randomly stratified sampling designs, the MEMs should be computed on a reconstructed space of regular sampling sites followed by removal of the missing sites, before analysis. This solution of rebuilding a (regular) sampling space guarantees to capture the underlying process under study, improves the modeling results and relaxes the impact of the choice of the weighting matrix on the computation of MEMs.