Modelling the effect of directional spatial ecological processes at different scales

Abstract

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.

Similar Resilience Attributes in Lakes with Different Management Practices

“…For an outline of the approach see the flow chart in Appendix S1 and Angeler et al [45]. We used temporal variables extracted by Asymmetric Eigenvector Maps (AEM) analysis [55], [56]. Briefly, the AEM analysis produces a set of orthogonal temporal variables that are derived from the linear time vector that comprises the length of the study period (i.e., 39 time steps for each lake) and that can be used as explanatory variables to model temporal relationships in community data.…”

“…The type of AEM variables computed in the present study was designed for spatial analysis to account for linear trends in the response variables. As time comprises a directional process, AEM is better suited to model linear trends relative to other methods (Principal Coordinates of Neighbor Matrices and Moran Eigenvector Maps [56]). This procedure yielded AEM variables with positive Eigenvalues, each of which corresponds to a specific temporal structure and scale: the first AEM variable models linear trends and the subsequent variables capture temporal variability from slow to increasingly shorter fluctuation frequencies in the community data [57].…”

Particulate Organic Matter Distribution along the Lower Amazon River: Addressing Aquatic Ecology Concepts Using Fatty Acids

“…Spatial vectors were derived using: 1) principal coordinates of neighbor matrices (PCNMs) which is a well-suited method to detect spatial trends across a wide range of scales [37]–[39] and 2) asymmetric eigenvector maps (AEMs) which is mainly designed to assess spatial structures in flow system (i.e. asymmetric forcing process)[40], [41]. As recommended by Blanchet et al [41], the use of both methods helps to better understand the spatial structure in the systems that are not fully directional [41].…”

Statistical methods for temporal and space–time analysis of community composition data

“…AEMs are suitable for the analysis of time series because the processes associated with time are directional: changes occur from time 1 to time 2, not the reverse. The calculation of AEM eigenfunctions, described in [1,7,13], is simpler than that of MEM. One constructs a matrix E representing a graph with nodes (times or sites) as rows and edges (directional connexions between nodes) as columns.…”

“…In matrix E, E0, which has the value 1 for all times, does not play any role; that column can be removed in time-series analysis. In applications of AEM analysis to directional spatial processes, the edges joining sites to the origin may play a meaningful role (see [7,13]). Nine AEM eigenfunctions were produced by PCA or SVD of matrix E shown in figure 4.…”