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Because the land-use categories are broad averages, they can potentially obscure local heterogeneity in the rate of loss of forest cover, so it is conceivable that a rare, localized endemic species may be eliminated in one of the cleared areas. In our second scenario, species still go extinct if their range lies entirely in heavy-impact areas. However, they can also go extinct if they have ranges that lie partially or wholly within moderate- or light-impact areas. The second-scenario rule is that there is a 15% probability of extinction of each cell occupied by the species in the moderate-impact zone (because there is a 15% loss of forest cover in these areas) and a 5% probability of extinction of each cell occupied in the light-impact zone (because there is a 5% loss of forest cover in these areas). These “coin tosses” per cell are assumed to be independent Bernoulli trials, so the probability of a joint event is the product of the per-cell probabilities. If the species has no range in the unimpacted areas, and if it goes extinct in all of the cells it occupies in light- and moderate-impact areas (and it goes extinct in all heavy-impact cells), then the species goes globally extinct.

The third scenario is at the other extreme, the most conservative hypothesis, predicting the lowest extinction rates. This scenario says that even if a species is restricted to the heavy-impact zone, it has a nonzero chance of surviving. It is difficult to know what survival probability to give a species, but we assume that the larger the range of the species (more individuals), the greater the chance that some local population will survive in one of the forest fragments. For sake of argument, we assume in this scenario that a species has a 5% chance of surviving per heavy-impact cell occupied. One could run many different versions of this scenario with different survival probabilities. A species whose range lies entirely within the heavy-impact zone could nevertheless survive if it survives in at least one of the heavy-impact cells it occupies.

Given these extinction scenarios, what are the predicted extinction rates? Fig. 6.7a shows the results for the middle-of-the-road extinction scenario 1. The qualitative pattern is that the probability of extinction is a logistic function of species abundance (range size), with high extinction probabilities for rare species, dropping to essentially zero probability for species above a critical population-size threshold of ≈106 individuals. Below population sizes of ≈104 individuals, the mean probability of extinction is close to the proportion of heavy-impact areas under Laurance et al.’s (2001) optimistic and nonoptimistic deforestation scenarios. This result is not unexpected because predicted range sizes of tree species with <104 individuals are small, <24 km2. Under the nonoptimistic deforestation scenario 3,656 tree species (32.6%) are predicted to go extinct, but only 354 of these species have population sizes of >105 individuals, and only 42 species predicted to go extinct have population sizes of >106 individuals. But even under the optimistic deforestation scenario, 2,228 tree species

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