2.6. Patterns of co‐occurrence of sensitive and tolerant species away from pines

To determine whether species within a pine response category were more or less likely to co‐occur than expected by chance in areas away from pines, we pruned the species × plot matrix for each site to include only those species belonging to one of the two pine response categories and only those plots away from pines. We then used the resulting matrix to generate a Bray‐Curtis distance (dissimilarity) matrix using species (rather than plots) as observations. The result provided a matrix of distances among species with respect to their occurrence in plots away from pines for each site. The matrix was then subjected to a multivariate dispersion test (using betadisper in R), wherein we calculated the distance of each species from its category centroid (i.e., either the tolerant category centroid or the sensitive category centroid). We then calculated the mean and standard deviation of distances separately for tolerant and sensitive species to generate a standardized average distance (dispersion) for each site (Disp _(tolerant) and Disp _(sensitive)). We compared the observed average distance for each response category to that expected by chance by randomizing occurrences of each species 1,000 times using permatswap and then calculating the average distance of each species to its response category centroid using betadisper. For each response category, an observed average distance that was greater than expected by chance indicated that species within a response category (e.g., sensitive species) were less likely to co‐occur in areas away from pines than expected by chance. Such a response would support the hypothesis that species in the same response category are not likely to co‐occur, perhaps because they occupy similar niches (Figure 2a). In contrast, an observed average distance that was less than expected by chance indicated that species within a response category were more likely to co‐occur than expected by chance. Such a response would support the hypothesis that species in the same response category are likely to co‐occur perhaps because of similar fitness (competitive abilities) and/or abiotic requirements (Figure 2b).