Null hypothesis and randomization test

Raw values of RPE are not highly informative because the magnitude of PE is clearly affected by the number of terminal taxa present. Therefore, we calculated standardized effect size scores of RPE (SES_RPE) as:

where RPE_obs represents the observed value for a particular ecoregion, and RPE_null is a null distribution of RPE values generated by randomizing the actual site-by-species matrix 999 times (Kembel, 2009), following an ‘independent swap’ scheme with 10 000 iterations (Gotelli, 2000). This null model retains both species occurrence frequency and sample species richness as those of the actual site-by-species matrix, which has been demonstrated to minimize the risk of type II errors (Gotelli and Ulrich, 2012; Ulrich and Gotelli, 2013). We repeated this procedure for each species-level tree topology (n = 1000), and used the arithmetic mean of the resultant SES_RPE values as an approximation to the ‘true’ values.