Species–area relationships always overestimate extinction rates from habitat loss

Fangliang He & Stephen P. Hubbell
Nature 473, 368–371 (19 May 2011) doi:10.1038/nature09985

My guess (intuition and ignorance mixed together) is that the estimator is asymptotically unbiased and an n=3 is to small a sample for its bias to get small.

That sounds right. Theorem 1 in the paper by Macallister and Schapire seems to say this estimator is asymptotically unbiased. (My main uncertainty here is that I’m just guessing the official definition of ‘asymptotically unbiased
estimator’. The theorem certainly gives a sense in which the estimator gets less biased as the sample size increases.)

By the way, after having gone to different restaurants for 4 days, I skipped lunch on the 5th, but the rest of the gang went to yet another new restaurant.

Meanwhile, I see 20/20 hindsight - a phenomenon acknowledged enough to get a nickname - as proof that people don’t generally understand the contemplation of the past to involve similar gear-reversals.

1. Select a series of nested pieces of land (of some type) increasing size and “count” the number of species in each. (The estimation in the count doesn’t really matter.) From this construct a curve of how the number of species varies with area.

2. Take an existing area with a “counted” number of species and a projected area reduction and use the curve to produce an estimate of the new number of species.

The argument was that an implied reversibility symmetry isn’t there: species are more “robust to loss in the presence of declining area” than they are “prone to speciation in the presence of increasing area”, so simple reversing doesn’t work. The scientist wasn’t claiming that biodiversity loss wasn’t happening, just that many numerical predictions were dramatic overestimates.

(Alert readers will have spotted that this isn’t an exact reversal; ideally step 1 would actively expand the area and watch speciation happen rather than just be a “measurement artifact”. The radio piece, which I was half listening to while stripping wallpaper, did stress that a non-applicable reversibility was being assumed in standard models.)

15, 10, 8, 6, 1, 1, 1 (15)
14, 11, 8, 6, 1, 1, 1 (11)
14, 10, 9, 6, 1, 1, 1 (9)
14, 10, 8, 7, 1, 1, 1 (7)
14, 10, 8, 6, 2, 1, 1 (2)
14, 10, 8, 6, 1, 1, 1, 1 (4)

So you estimate P(43rd orchid is a new species) = 4/48 = 1/12. This is not What Good does, but is not far off, and seems reasonable. If you have observed N different species, the estimate is (N+1)/(N+3). This gives 2/3 in the restaurant example, which I think is better than 1.