Geometry and scale in species–area relationships

Last year, I blogged about a Nature paper by Fangliang He and Stephen Hubbell, which claims that conventional extinction predictions based on species-area relationships are overestimated. They suggest extinction-area relationships as more appropriate to estimate extinction risk from habitat loss. My old post can be found here.

After two short replies by Brooks and colleagues and Evans and colleagues that were published immediately after the original paper, nothing had happened for quite some time, although it was clear that many people had sent technical responses regarding that paper to Nature. Yesterday, however, Nature published two technical comments along with a response by He and Hubbel.

One comment is from Chris Thomas and Mark Williamson, who mainly reemphasizes some points that have also been made earlier by other people in the news and on blogs (see my previous post), namely that many, if not most current estimates of global species extinction rates are not exclusively based on SAR slopes, and that currently observed extinction rates are not generally lower than predicted.

The comment by Pereira and colleagues, “Geometry and scale in species–area relationships” concentrates on the geometry of habitat destruction that was assumed in the original paper. Their argument relates to a fact on which I already commented on in my earlier post: if species clumping is the reason for the difference between SAR and EAR, then the geometry of habitat destruction can not be inconsequential. For example, consider completely random habitat destruction, where one random individual after the other is removed – in this case, spatial clumping of species is completely inconsequential, each individual is removed with the same probability regardless of its position. Pereira et al. concentrate their reply on another case: they concede that EAR is the correct model, assuming that SAR curves were generated nestedly, (outwards in the picture below), and assuming habitat destruction occurs with the same geometry. However, if the destruction would appear with a different geometry than the SAR/EAR sampling model, e.g. completely opposite (inwards in the picture), one would expect that inverse SAR estimates (inverse EAR) should be more appropriate.

Figure: Different geometries of habitat destructions, from Pereira et al.

The reply by He and Hubbel agrees to the points made by Chris Thomas, but rejects the arguments of Pereira et al. They raise serveral points, but I think the main one is that they simply think that one should assume the same geometry for habitat destruction than for statistical sampling. To avoid misinterpreting them, here’s the direct quote:

Pereira et al.1 commit a statistical error by confusing a specific configuration of landscape destruction with the statistical expectation. The SAR is a macroecological pattern defined as the expected number of species as a function of area. The word ‘always’ in the title of our paper2 refers to the fact that the expectation of extinction rate is always biased too high if one uses the backward power-law SAR method. One certainly cannot trust any single specific case of the extinction rate estimated in this manner to be reliable, and our result is a general proof that shows that the average extinction rate so estimated is always an overestimate.

I can understand this argument to a certain extent – clearly, if only one particular, very unlikely geometry of habitat destruction would change their results, this could be neglected. Yet, I don’t think it is likely that habit destruction is random in general. Rather, it clusters along roads, coastal zones etc. (e.g. Seabloom, 2002), so the geometry is usually non-random. I guess I would like to see more evidence still to be convinced that the geometry of habitat destruction is really inconsequential for estimating extinction rates.


He, F. & Hubbell, S. P. (2011) Species-area relationships always overestimate extinction rates from habitat loss. Nature, 473, 368-371.

Pereira, H. M.; Borda-de-Agua, L. & Martins, I. S. (2012) Geometry and scale in species-area relationships. Nature, 482, E3-E4.

Thomas, C. D. & Williamson, M. (2012) Extinction and climate change. Nature, 482, E4-E5.

He, F. & Hubbell, S. P. (2012) He and Hubbell reply. Nature, 482, E5-E6.

Seabloom, E. W.; Dobson, A. P. & Stoms, D. M. (2002) Extinction rates under nonrandom patterns of habitat loss. Proceedings of the National Academy of Sciences, 99, 11229-11234.


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