### Functional Equations VIII: Measuring Biodiversity

#### Posted by Tom Leinster

Posts entitled “Such-and-Such Part 8” can be intimidating…! But in this week’s instalment of the functional equations course, we just began a new topic. So if you’ve been interested in this course at a distance, without having actually dived in, now is a decent entry point.

This week, I introduced the difficult conceptual question of how to quantify biological diversity. A partial answer is given by what ecologists call the Hill numbers, which are the exponentials of what others call the Rényi entropies. I explained what these are, how they behave, and how they’re linked to other mathematical concepts.

There were hardly any actual functional equations this week, but they’ll come back soon! This week was mainly just background and intuition.

You can find the notes from this week’s session on pages 30–34 of the notes so far.

Posted at March 29, 2017 2:32 AM UTC
## Re: Functional Equations VIII: Measuring Biodiversity

What do you think of the work of Tomas Veloz and others to use Chemical Organization Theory (COT) to measure and quantify biodiversity?

https://www.pims.math.ca/scientific-event/170111-mbstv

http://users.minet.uni-jena.de/csb/prj/ot/