First Case: The Original Ranking Does Not Mean Support

Posadas et al. (2001) evaluated the conservation ranking in southern South America areas. They found that depending on the index used, the selected area changed, as the best area could be: Santiago (D), Ñuble (F), Valdivia (H), or the Malvinas islands (K). Also, for a single index, the values could be misleading, as the differences between the W index values are quite small, and the ranking could be an artifact rather than a real result (Table 1). I reanalyzed their dataset and found that the best index for this analysis is Is (Fig. 2) as this index that has the highest jack-knife frequency.

The most stable area using Is or raw W (the second best index), was the Malvinas islands, a candidate to be the best area (Fig. 3). The high uncertainty in the area chosen is eliminated when the support is included in the selection of the best area. Santiago has the highest number of species and harbors the highest number of endemic species, but it was not placed as the highest priority, while Malvinas island, the second most endemic area has the highest priority. The inferences based on the

Table 1 First area in the ranking proposed by Posadas et al. (2001). For raw W the index values are 52.62/52.58/52.05. Labels follow Posadas et al. (2001)

I

W

raw

Malvinas islands (K)

Valdivia (H) or Santiago (D) or Ñuble (F)

e

Malvinas islands (K)

Malvinas islands (K)

s

Santiago (D)

Ñuble (F)

es

Malvinas islands (K)

Ñuble (F)

Fig. 2 For each index, the number of hits with a delete value of 0.32 or 0.5 for j.topol and three j.tip values of 0.32, 0.5, and 1 (in the last situation, the whole topology is deleted). Species endemism and richness (number of species) are included for comparative purposes (Data from Posadas et al. (2001)). (a) Number of hits with a j.topol value of 0.32 (b) Number of hits with a j.topol value of 0.5

Fig. 3 Number of times an area is recovered as the first (number 1), second (number 2), or third area (number 3). These are the lowest (a) and the highest (b) delete probabilities used in this analysis. Acronyms for areas follow Posadas et al. (2001) and table 1. (a) Probabilities of j.topol = 0.32, j.tip = 0.32 (b) Probabilities of j.topol = 0.5, j.tip = 1

un-sampled data set might be misleading, while jack-knifing could help to decide which is the most supported solution.

Second Case: The Support for the Original Ranking

There are two main approaches to define amazonian areas of endemism, eight areas from Bates et al. (1998) and Da Silva et al. (2005) or 16 areas from Da Silva and Oren (1996). López-Osorio and Miranda-Esquivel (2010), used both ways to establish conservation priorities for Amazonia's areas of endemism.

Using Bates et al. (1998) areas, they found that Guiana and Inambari are the first and second priority areas. Inambari is the richest area while Guiana presents the highest endemicity value. Their inferences were based on Wes, on theoretical grounds as the index includes endemicity and standardization (López-Osorio and MirandaEsquivel 2010).

The reanalysis showed that the best index is either Wes, We or Ws (Fig. 4). These three indices select Guiana as the first area and Inambari as the second area (Fig. 5), as stated in the original paper. In this example the re-sampling reinforces the original findings, giving a stronger support to the areas chosen as first and second in the ranking.

Using the areas from Da Silva and Oren (1996), López-Osorio and MirandaEsquivel (2010) found that depending on the index, either Guiana2 or Rondonia could be the highest priority area, while the second area could be Guiana3, Inamambari2 or even Rondonia or Guiana2. Therefore, the first question is, which is the best index for conservation in Amazonia? and given that index, which are the areas chosen as the first and second priority?.

López-Osorio and Miranda-Esquivel (2010) found that most indices selected the same area Guiana2, which could be seen as there is no difference given the index. The reanalysis showed that in general Is and Ws are more stable than any other index, and Is behaves better than Ws. As the size of the topologies is different and some large topologies with more nodes may have more impact than smaller topologies, standard I and W indices are not stable (Fig. 6). The first area is Guiana2 in all indices used, while the second area varies: Rondonia, Guiana3 or Inamambari2 (Fig. 7). These results are similar to those found by López-Osorio and Miranda-Esquivel (2010). Here the re-sampling helped to resolve the initial discrepancy as the highest priority is Guiana2 and not Rondonia, that could be a possible candidate. The second area could be any of the three initially considered, so the evidence is not misleading but inconclusive to define the second area, even after re-sampling the data. These brief examples show that the confidence of the original ranking should be evaluated using re-sampling, as an un-sampled ranking analysis could be unstable when some information (phylogenies or species) is deleted. The results may render any output, from a different answer from the original ranking to a congruent answer with the original ranking. Only after the re-sampling analysis, the quality of the answer could be stated without hesitation. Even if we only calculate the support for

Fig. 4 Number of hits with a delete value of 0.32 or 0.5 for j.topol and three j.tip values of 0.32, 0.5, and 1 (in the last situation, the whole topology is deleted) (Data from López-Osorio and Miranda-Esquivel (2010). Areas from Bates et al. (1998)). (a) Number of hits with a j.topol value of 0.32 (b) Number of hits with a j.topol value of 0.5

Fig. 5 Number of times an Area is recovered as the first (number 1), second (number 2), or third area (number 3). These are the lowest (a) and the highest (b) delete probabilities used in this analysis. (a) Probabilities of j.topol = 0.32, j.tip = 0.32 (b) Probabilities of j.topol = 0.5, j.tip = 1

Fig. 6 Number of hits with a delete value of 0.32 or 0.5 for j.topol and three j.tip values of 0.32, 0.5, and 1 (in the last situation, the whole topology is deleted) (Data from López-Osorio and Miranda-Esquivel (2010). Areas from Da Silva and Oren (1996)). (a) Number of hits with a j.topol value of 0.32 (b) Number of hits with a j.topol value of 0.5

Fig. 7 Number of times an Area is recovered as the first (number 1), second (number 2), or third area (number 3). These are the lowest (a) and the highest (b) delete probabilities used in this analysis (Data from López-Osorio and Miranda-Esquivel (2010). Areas from Da Silva and Oren (1996)). (Acronyms A = Guiana3, B = Guiana2, C = Guiana1, D = Imeri2, E = Imeri1, F = Napo3, G = Napo2, H = Napo1, I = Inambari1, J = Inambari2, K = Inambari3, L = Inambari4, M = Rondonia, N = Tapajos, O = Xingu, P = Belen). (a) Probabilities of j.topol = 0.32, j.tip = 0.32 (b) Probabilities of j.topol = 0.5, j.tip = 1

a given ranking, the results after re-sampling would give a clue of the situation when the information is perturbed.

Acknowledgements I am grateful to Roseli Pellens for her kind invitation to participate in the book. Two anonymous referees helped to improve my perspective about Jack-knife and Conservation. I am indebted to División de Investigación y Extensión, Facultad de salud (project 5658), and Facultad de Ciencias, Universidad Industrial de Santander (project 5132) for their financial support.

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