On the Statistical Mechanics of Alien Species Distribution

Michael Bowler,Colleen Kelly

doi:10.3390/e19120674

Abstract

Many species of plants are found in regions to which they are alien. Their global distributions are characterised by a family of exponential functions of the kind that arise in elementary statistical mechanics (an example in ecology is MacArthur’s broken stick). We show here that all these functions are quantitatively reproduced by a model containing a single parameter—some global resource partitioned at random on the two axes of species number and site number. A dynamical model generating this equilibrium is a two-fold stochastic process and suggests a curious and interesting biological interpretation in terms of niche structures fluctuating with time and productivity, with sites and species highly idiosyncratic. Idiosyncrasy implies that attempts to identify a priori those species likely to become naturalised are unlikely to be successful. Although this paper is primarily concerned with a particular problem in population biology, the two-fold stochastic process may be of more general interest.

Highlights

The study of macro-ecology has benefited from the application of methods from the physical sciences
Species abundance distributions have been addressed with methods of statistical mechanics [3,4,5,6,7]
A more general review of the application of statistical mechanics in biology is given by Frank [11]

Summary

Introduction

The study of macro-ecology has benefited from the application of methods from the physical sciences. Species abundance distributions have been addressed with methods of statistical mechanics [3,4,5,6,7]. We apply statistical mechanics to a very different problem in macro-ecology, the distribution of alien species (as opposed to individuals of those species) over the globe. The first is that the number of species found alien at n sites is, for n > 1, exponentially distributed. The first is that the number of species found alien at n sites is, for n > 1, exponentially distributed with n with n S(n) = =S0Sexp( − βn) (1).

Methods

Discussion

Conclusion