Modelling directional spatial processes in ecological data

Distributions of species, animals or plants, terrestrial or aquatic, are influenced by numerous factors such as physical and biogeographical gradients. Dominant wind and current directions cause the appearance of gradients in physical conditions whereas biogeographical gradients can be the result of historical events (e.g. glaciations). No spatial modelling technique has been developed to this day that considers the direction of an asymmetric process controlling species distributions along a gradient or network. This paper presents a new method that can model species spatial distributions generated by a hypothesized asymmetric, directional physical process. This method is an eigenfunction-based spatial filtering technique that offers as much flexibility as the Moran's eigenvector maps (MEM) framework; it is called asymmetric eigenvector maps (AEM) modelling. Information needed to construct eigenfunctions through the AEM framework are the spatial coordinates of the sampling or experimental sites, a connexion diagram linking the sites to one another, prior information about the direction of the hypothesized asymmetric process influencing the response variable(s), and optionally, weights attached to the edges (links). To illustrate how this new method works, AEM is compared to MEM analysis through simulations and in the analysis of an ecological example where a known asymmetric forcing is present. The ecological example reanalyses the dietary habits of brook trout (Salvelinus fontinalis) sampled in 42 lakes of the Mastigouche Reserve, Québec.