Of priors and prejudice

TL;DR

This paper explores how simple birth-death processes lead to a log series distribution in species abundance, analyzing the role of priors in maximum entropy methods through various mathematical approaches.

Contribution

It provides new insights into the derivation of species abundance distributions and clarifies the role of priors in maximum entropy modeling.

Findings

Birth-death processes produce a log series distribution.

Different mathematical methods yield consistent results.

Clarifies the role of priors in MaxEnt models.

Abstract

If species abundance distributions are dominated by the simple processes of individuals in a community giving birth and death independently, the result is a log series distribution. I calculate this in a number of different ways, using both master equations and also the combinatoric methods of elementary statistical mechanics. Considerable light is shed on the nature and role of 'priors' in the language of MaxEnt.