Quantifying Extinction by Quantifying Biodiversity

Saving biodiversity from extinction is of fundamental importance to people everywhere. Biodiversity must be quantified to demonstrate that mass extinctions have occurred. Diversity estimation turns out to be very difficult because most inventories of communities are too small to catch all of the species. The problem is so hard that researchers continue to use strongly disagreeing strategies. Most aren't helpful. For example, randomly drawing the data down to a least common denominator of data set size (rarefaction) only yields relative diversity estimates. Like most approaches, it is highly inaccurate when most individuals belong to just a few species (so a distribution is uneven). Hill numbers such as Shannon's H and Simpson's D are designed to overweight evenness and minimise the signal of richness. Simple equations called richness indices, such as Chao 1, usually just don't work. I discuss two good solutions to the problem. First, I use simple algebra to derive an equation called the geometric series index. Applying it to a large set of species inventories shows that it has no sample size bias. Second, I discuss properties of an unpublished model of relative abundances that also yields richness estimates. These too are unbiased, but more precise. The distribution is simple, has good theoretical properties, and describes real data accurately. It therefore seems to describe the population dynamics of most ecological communities. The field of biodiversity estimation has been at an impasse for many decades, hindering our understanding of mass extinctions - but unification of the field now seems possible.