Variance partitioning and spatial eigenvector analyses with large macroecological datasets

Abstract

Macroecological data are usually structured in space, so taking into account spatal autocorrelation in regression and correlation analyses is essental for a beter understanding of patterns and processes. Many methods are available to deal with spatal autocorrelation, but there are some difficulties when one is dealing with huge geographical extents and fine-scale data. So, we propose a relatively simple and fast computer-intensive approach to deal with Principal Coordinate of Neighbor Matrices (PNCM)/ Moran’s Eigenvector Mapping (MEM) analyses for large datasets, using global richness patern of sharks as a model. We performed a variance partitioning approach by regressing species richness against environmental variables and spatal eigenvectors derived from PCNM. Due to the large number of ocean grid cells (> 9000), we ran the analyses 1000 times by randomly subsampling each time 50 to 4500 cells and compared the distribution of the variance partitioning components, as well as the slopes of the environmental variables. We also estimated Moran’s I coefficients for regression residuals to check if spatal eigenvectors took into account spatal autocorrelation. Comparing statistics of analyses with different sample sizes, we note that although the environmental component increases linearly, other components (unique space and shared) of the most important variables stabilize with about 1000 cells, whereas all other smaller effects tend to stabilize between 2500 and 3000 cells. Besides that, PCNM eigenvectors were able to control spatal autocorrelation very well. We showed that shark richness patterns are strongly and positively correlated with temperature range, according to the well-known patern of distribution for the taxon, and strong negatively correlated with oxygen supplies, which are higher in polar zones where ice acts as a barrier to sharks. Our approach clearly shows that it is possible to perform a robust evaluation of global patterns of diversity using eigenvector approaches based on a resampling strategy and allows effective computation of the variance partitioning even when dealing with large datasets.