Following the expected behavior in an optimal condition, first I evaluated the index. I considered the best index as the one that recovered most times the same original ranking -first to third areas-, as an ordered ranking. Then, using the selected index, I evaluated the best area, as the one found most often in the first place.
I tested six scenarios by modifying j.topol and j.tip values as follows: j.topol values of 0.50 and 0.32, and j.tip values of 1, 0.50 and 0.32. These values are just used to introduce the concept, but they are similar to strong, mild and relaxed tests. A value of 1 to delete a species means that all areas for that species will be deleted, while a value of 0.32 means that one out of three will be deleted. Smaller values as
0.01 are discarded, it would make no difference, as the perturbation to the data would be unimportant.
The effect of deleting areas is related to the number of areas inhabited. If the species is in an endemic area, the effect of deleting an area would be as deleting the whole species, while in a widespread species, the effect should be minimal with indices as Ie/We or Ies/Wes, but we can not define which is the best index as the four indices have similar properties. In all cases the probability of deleting areas was 1, therefore I tested the effect of the topology and species but not the effect of the distribution.
Number of Replicates
Hedges (1992) presented the number 1825 as the number of replicates needed to obtain an accuracy of ±1 % for a bootstrapping proportion of 95 %. Although the higher the number of replicates the higher the accuracy of the estimation of the bootstrap or jack-knife value, Pattengale et al. (2010) introduced a stopping criteria that yield lower figures as 500 replicates to get robust bootstrapping values for a 2500 taxa analysis. I randomized each scenario 10,000 times, that could be considered intuitively an appropriate number of replicates to estimate the jack-knife proportion for conservation purposes.
For these analyses, I used a modified version of the program Richness (Posadas et al. 2001) to randomize the data and to perform the index calculations [Jrich: available from https://github.com/Dmirandae/jrich], while the data analyses were performed using the software R (R Core Team 2013) and the figures were prepared using the library ggplot2 (Wickham 2009).