Calculation of species pools

We calculated regional species pools as probabilistic dispersal pools (REF). To each woody forest species s in our data set, we assigned probabilities of being part of each region i's species pool pi, based on the distances between s' occurrences in all intermediate-grain regions within the conterminous US and the focal region. We assumed that s's probability of being part of piPs-pi, would be equal to the joint probability that i can be colonized by s through dispersal from any of s's  intermediate-grain-region occurrences osPs-i. We assumed that the simple probability of s to disperse to from osPos-i, declined with increasing distance between oand iDos-i (as measured by great-circle distance between region centroids). Due to insufficient data on the dispersal abilities of individual plant species, we explored five different global distance-decay functions between Pos-i and Dos-i , and chose the one where the resultant species pool had the highest correlation with species richness. We set the scaling coefficients of these distance-decay functions such that Pos-i for occurrences in 'adjacent' regions to i would be 0.975, 0.95, 0.90, 0.80 or 0.60, respectively. We defined 'adjacent' as the mean minimum distance between all regions and their respective closest regions. By definition, species within i form part of pi (Ps-pi = 1; they form part of the 'actual species pool' \cite{Zobel_1997}). Finally, we calculated pi as the sum of all Ps-i across all species. Due to long computation times, we assumed that species pools of fine-grain regions (i.e. FIA plots) were equal to the species pools of the intermediate-grain regions in which they are nested. To calculate species pools of coarse regions, we then summed all Ps-pi across all constituent counties of a given coarse unit. For coarse-grain regions, we calculated Ps-i as the joint probability that s can disperse from any its os to any of the intermediate-grain regions nested within coarse region i.