How to test the significance of the relation between spatially autocorrelated data at the landscape scale: A case study using fire and forest maps

To better understand the relationship between wildfire and forest regeneration in the boreal forest, we quantify their degree of relationship by means of correlation. Given that wildfires in the boreal forest can cover large areas, such correlation needs also to be computed for large areas (i.e., 33,000 km(2) in northern Quebec). At this landscape scale, both variables (fire and forest) show strong and significant positive spatial autocorrelation. The presence of spatial autocorrelation in the two variables, however, can affect the statistical significance and the interpretation of their degree of correlation. In this paper, we compare different approaches that have been proposed to solve this problem: a parametric test that corrects for the presence of autocorrelation by adjusting the effective sample size (Dutilleul's modified t test); a complete randomization test; a restricted randomization test based on a toroidal shift; the Mantel test that controls for the relative spatial locations among sampling: and the partial Mantel test that controls for the spatial distances among sampling sites. A positive correlation between the two variables was found significant by the parametric test and complete randomization test. but not significant when the restricted randomization test, Dutilleul's modified t test, and the Mantel test were used. Conversely, a negative correlation was found by the partial Mantel test. Hence, to control for the presence of spatial autocorrelation, either a restricted randomization test or the Dutilleul method is recommended, while to control for the spatial relative position of the data, the Mantel and partial Mantel tests should be used. A firm understanding of these statistical tests and their respective assumptions regarding the spatial structure of the data is crucial to any valid ecological understanding and interpretation.