it does not report extinction rates or the numbers of species that are threatened. Despite its posturing, it deals with a different issue. The paper is riddled with false statements. For instance:

The paper states: “Estimates of extinction rates based on (the species-area) method are almost always much higher than those actually observed.” It is unequivocally false. One reference used to support this (Pimm and Askins) uses a species-area relationship to predict 4.5 bird extinctions following deforestation in Eastern North America and then notices that four species went extinct and one is threatened.

There are dozens of other studies of many taxa around the world that find equally compelling agreements between predicted and observed extinctions. A small selection of them follows.

So what does the paper model — and why does it poorly address the issue of extinctions? Imagine destruction that wipes out 95% of the habitat in an area metaphorically “overnight”. How many species have disappeared “the following morning”? The paper tells you. It is not many, just those wholly restricted to the 95% (and absent from the 5% where they would survive). The important question is …
How many of additional species living lonely lives in their isolated patches (the 5%) would become extinct eventually because their population sizes are too small to be viable? A different species-area curve applies — the one for islands, which are isolated. It is a much larger number of extinctions, of course, and the one used in the studies mentioned above that find such compelling agreement between predicted against observed extinctions.
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A response will be submitted to Nature shortly.
Stuart

Pimm, S. L. & Askins, R. A. Forest losses predict bird extinctions in eastern North America. Proc. Natl Acad. Sci. USA 92, 9343–9347 (1995).

Brooks, T. M. et al. Habitat loss and extinction in the hotspots of biodiversity. Conserv. Biol. 16, 909–923 (2002).

Grelle, C. E. de V., Fonseca, G. A. B., Fonseca, M. T. & Costa, L. P. The question of scale in threat analysis: a case study with Brazilian mammals. Animal Conserv. 2, 149–152 (1999).

Brooks, T. & Balmford, A. Atlantic forest extinctions. Nature 380, 115 (1996).

Cowlishaw, G. Predicting the pattern of decline of African primate diversity: an extinction debt from historical deforestation. Conserv. Biol. 13, 1183–1193 (1999).

Brook, B. W., Sodhi, N. S. & Ng, P. K. L. Catastrophic extinctions follow deforestation in Singapore. Nature 424, 420–423 (2001)

Brooks, T. M., S. L. Pimm, V. Kapos and C. Ravilious 1999. Threat from deforestation to montane and lowland birds and mammals in insular Southeast Asia. J. Anim. Ecol. 68: 1061-1078

Brooks, T. M., Pimm, S. L., & Oyugi, J. O. Time lag between deforestation
and bird extinction in tropical forest fragments. Conserv. Biol. 13, 1140-1150
(1999).

A full discussion of species area curves appears in

Rosenzweig, M.L. Species diversity in space and time. (Cambridge Univ.
Press, 1995)