Modelling the effect of directional spatial ecological processes at different scales

During the last 20 years, ecologists discovered the importance of including spatial relationships in models of species distributions. Among the latest developments in modelling how species are spatially structured are eigenfunction-based spatial filtering methods such as Moran's eigenvector maps (MEM) and principal coordinates of neighbour matrices (PCNM). Although these methods are very powerful and flexible, they are only suited to study distributions resulting from non-directional spatial processes. The asymmetric eigenvector map (AEM) framework, a new eigenfunction-based spatial filtering method, fills this theoretical gap. AEM was specifically designed to model spatial structures hypothesized to be produced by directional spatial processes. Water currents, prevailing wind on mountainsides, river networks, and glaciations at historical time scales are some of the situations where AEM can be used. This paper presents three applications of the method illustrating different combinations of: sampling schemes (regular and irregular), data types (univariate and multivariate), and spatial scales (metres, kilometres, and hundreds of kilometres). The applications include the distribution of a crustacean (Atya) in a river, bacterial production in a lake, and the distribution of the copepodite stages of a crustacean on the Atlantic oceanic shelf. In each application, a comparison is made between AEM, MEM, and PCNM. No environmental components were included in the comparisons. AEM was a strong predictor in all cases, explaining 59.8% for Atya distribution, 51.4% of the bacterial production variation, and 38.4% for the copepodite distributions. AEM outperformed MEM and PCNM in these applications, offering a powerful and more appropriate tool for spatial modelling of species distributions under directional forcing and leading to a better understanding of the processes at work in these systems.