Butterfly and Moth Biodiversity

Do you have any idea how many moth species live in the Pikes Peak Region? Take a guess. A hundred? A thousand? Ten thousand? Well, it turns out, if you have data like I have, a reasonable estimate can be made. I used the Clench equation, taken from Harry K. Clench’s paper* on estimating butterfly biodiversity on reserves. It is useful after a few years (or hours) of data points are available. If you want the answer, you can skip the math and go to the case study, below. But in case you’re interested…

The equation shows that the eventual number of species (Se) in a locality can be estimated as a function of a constant, K, and the number of hours spent in the field (N).


As K approaches zero, N + K approaches N, and Se = S. In this equation, S represents the number of species taken at any given time and N represents the number of years (or hours) afield. Simplified, the equation looks like this:


Data that show a positive curve will not apply, of course. This can result if the first expedition is poor but the second is extraordinary. But as more data accumulate, a negative curve is generated, and any two points roughly on the curve can be used to estimate the asymptote, which is equivalent to Se.

Let us assume that after two years, 62 species have been cataloged (2, 62), and that after an additional 2 years, a total of 81 have been recorded (4, 81). Using these to create a system of equations allows us to calculate K, and then Se, as follows.

2Se = (2)(62) + 62K

4Se = (4)(81) + 81K

multiplying the first equation by –2 yields this pair:

– 4Se = –248 – 124K

4Se =   324 + 81K

eliminating the Se term,

0 = 76 – 43K

– 76 = –43K

K = 1.77

Substituting into the original equation yields an estimate of

Se = 124 + 110 = 234 species


screen-shot-2017-01-14-at-1-20-43-pm*Clench, H. K. 1979 How to make regional lists of butterflies: some thoughts. Journ. Lepid Soc 33(4) 216-231


Author: Samuel A. Johnson

This blog is about hiking, thinking, and writing.

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