Evaluating Extinction Risk Transformations

We assigned the five main IUCN risk levels to the tips of 100 100-species birth death trees (b = 0.1, d = 0.06), in the same proportion per level as mean for the birds and mammals of the world [12] , [13] ; see our Table 1. We then converted each species' level to a probability of extinction under each of five transformations: one where each increase in level corresponds to a doubling of extinction risk [12] three transformations corresponding to the official IUCN designations, but scaled to 50, 100, and 500 year windows, and a pessimistic transformation of our choosing. The IUCN has not designated prob(extinction) for the two lowest categories, and these had to be interpolated. Partly in order to produce contrasting scales, we set prob(extinction) for the ‘least concern’ species to 0.01% [13] , equivalent to assuming that at most 1 of the 7600 bird species in this category would go extinct over the next 100 years; the Near Threatened category was given a prob(extinction) 100 times this, in accord with the interpolation used in [13] .
For each tree and assignment, we calculated the EDGE and HEDGE scores using the Tuatara module [26] of the Mesquite package [27] . We asked how often the top ranked species differed as one moved between transformations. When the ranks differed between transformations, we also recorded the degree of this difference by taking the sum of the differences in ranks. For example, if the top five species under the Isaac transformation {1,2,3,4,5} are ranked {1,5,3,10,2} under the IUCN100 transformation, this contributes 12 (0+3+0+6+3) to the sum, and if the top five species under the IUCN100 transformation {1,2,3,4,5} are ranked {1,5,3,8,2} under the Isaac et al. transformation, this contributes 10 {0+3+0+4+3}, giving a summed difference score of 22. We considered four measures of sensitivity to transformation. For the top five- and for the top 20-ranked species under a transformation, we recorded the proportion of the simulated trees that showed any difference, and also the average across trees of the sum of these differences in ranks.