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On the Statistical Mechanics of Alien Species Distribution

1
Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
2
Department of Zoology, University of Oxford, South Parks Road, Oxford OX1 3PS, UK
3
Department of Integrative Biology, University of South Florida, Tampa, FL 33620, USA
*
Authors to whom correspondence should be addressed.
Entropy 2017, 19(12), 674; https://doi.org/10.3390/e19120674
Received: 20 November 2017 / Revised: 6 December 2017 / Accepted: 8 December 2017 / Published: 9 December 2017
(This article belongs to the Special Issue Applications of Information Theory in the Geosciences II)
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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. View Full-Text
Keywords: statistical mechanics; resource partitioning; stochastic processes; population dynamics statistical mechanics; resource partitioning; stochastic processes; population dynamics
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Bowler, M.G.; Kelly, C.K. On the Statistical Mechanics of Alien Species Distribution. Entropy 2017, 19, 674.

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