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Extrapolation of rarefaction

Posted by arose on 10 Aug 2011 at 09:58 GMT

A very nice and comprehensive paper with a lot of efforts and interesting data.
A short remark: It is permissible to interpolate species numbers of rarefaction curves in order to compare stations at a minimum N sampled at all stations. But this needs to meet some basic assumptions (Simberloff 1979: e.g., same sampling methods; sampling effort must be representative for the sampling area; interpolated S is overestimated with more patchy distributions of organisms, etc).
Leaving aside this, according to Simberloff (1979) (also to Sanders 1968) "it is not permissible to extrapolate a rarefaction curve beyond the number of individuals" actually found, since "there is no distribution-free, statistically sound way to do so. If one assumes an underlying distribution of individuals into species, [...] such extrapolation is possible, but one must then justify deductively the use of the specified distribution."

There are more appropriate methods available for estimating species numbers which might have provided different results: Chao 1 & 2, Jackknife 1 & 2, lognormal distributions, species-area curves, and many other. These were extensively tested and reviewed by Palmer (1990, 1991), Baltanás (1992), Soberón & Llorente (1993), Colwell & Coddington (1994), and others. I would suggest to use one of these, e.g. Chao2.

Sanders, H. L. (1968): Marine benthic diversity: a comparative study. - American Naturalist 102 (925): 243-282.
Simberloff, D. (1979): Rarefaction as a distribution-free method of expressing and estimating diversity. - in: J. F. Grassle, G. P. Patil, W. Smith & C. Taillie (eds.): Ecological Diversity in Theory and Practice. International Co-operative Publishing House, Fairland, Maryland, pp 159-176.

Palmer, M. W. (1990): The estimation of species richness by extrapolation. - Ecology 71 (3): 1195-1198.

Palmer, M. W. (1991): Estimating Species Richness - The 2nd Order Jackknife Reconsidered. - Ecology 72 (4): 1512-1513.

Baltanás, A. (1992): On the use of some methods for the estimation of species richness. - Oikos 65 (3): 484-492.

Soberón M., J. & J. Llorente B. (1993): The use of species accumulation functions for the prediction of species richness. - Conservation Biology 7 (3): 480-488.

Colwell, R. K. & J. A. Coddington (1994): Estimating Terrestrial Biodiversity Through Extrapolation. - Philosophical Transactions of the Royal Society of London Series B - Biological Sciences 345 (1311): 101-118.

No competing interests declared.