The 2019 International Congress for Conservation Biology conference in Kuala Lumpur had a plenary talk, Rarefaction and Extrapolation: Standardizing Samples to Make Fair Comparisons of Biodiversity among Multiple Assemblages on nearly this exact subject:
In this talk, two types of standardization methods are reviewed: (1) Sample-size-based rarefaction and extrapolation methods aim to compare diversity estimates for equally-large samples determined by samplers. (2) Coverage-based rarefaction and extrapolation methods aim to compare diversity estimates for equally-complete samples; the sample completeness in this method is measured by sample coverage (the proportion of the total number of individuals that belong to the species detected in the sample), a concept originally developed by Alan Turing and I. J. Good in their cryptographic analysis during World War II. Contrary to intuition, sample coverage for the observed sample, rarefied samples, and extrapolated samples can be accurately estimated by the observed data themselves. These two types of standardization methods allow researchers to efficiently use all available data to make robust and detailed inferences about the sampled assemblages, and also to make objective comparisons among multiple assemblages. Hypothetical and real examples are presented for illustrating the use of the online software iNEXT (iNterpolation/EXTrapolation) to compute and plot seamless rarefaction/extrapolation sampling curves based on several diversity measures.
Look up Anne Chao’s work.