Quantification of the spatial co-occurrences of ecological boundaries

In this paper, we investigate spatial relationships between vegetation boundaries and environmental boundaries from a second-growth forest in southwestern Quebec, Canada. Four statistics that quantify the amount of direct spatial overlap and the mean minimum distance between boundaries are introduced and used to compute the degree of spatial co-occurrences between boundaries. The significance of these statistics is determined using randomized and restricted permutation tests. Boundaries based on tree species density are found to significantly overlap the locations of boundaries delineated by the environmental data at the study site. Significant overlap is also found using boundaries defined by tree presence-absence data and environmental variables. Vegetation boundaries based on tree species density and on tree presence-absence data are not, however, at the same locations. This suggests that for the study site the two types of vegetation boundaries (tree density and presence-absence) reflect different responses to underlying environmental processes. Vegetation boundaries determined using species diversity and species richness, although spatially related to the presence-absence boundaries, did not overlap the environmental boundaries. Results of the two permutation tests (randomized and restricted) agree only when the spatial relationship between the two boundary types is strong. Overall, randomization is found to be a more conservative test for detecting boundary spatial relationships, rejecting the null hypothesis of no spatial relationship fewer times than the restricted permutation test.