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A first principles derivation of animal group size distributions
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2011 (English)In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 283, no 1, 35-43 p.Article in journal (Refereed) Published
##### Abstract [en]

Several empirical studies have shown that the animal group size distribution of many species can be well fit by power laws with exponential truncation. A striking empirical result due to Niwa is that the exponent in these power laws is one and the truncation is determined by the average group size experienced by an individual. This distribution is known as the logarithmic distribution. In this paper we provide first principles derivation of the logarithmic distribution and other truncated power laws using a site-based merge and split framework. In particular, we investigate two such models. Firstly, we look at a model in which groups merge whenever they meet but split with a constant probability per time step. This generates a distribution similar, but not identical to the logarithmic distribution. Secondly, we propose a model, based on preferential attachment, that produces the logarithmic distribution exactly. Our derivation helps explain why logarithmic distributions are so widely observed in nature. The derivation also allows us to link splitting and joining behavior to the exponent and truncation parameters in power laws.

##### Place, publisher, year, edition, pages
2011. Vol. 283, no 1, 35-43 p.
##### Keyword [en]
Truncated power law, The logarithmic distribution, Merge and split dynamics
Natural Sciences
##### Identifiers
ISI: 000298526600005OAI: oai:DiVA.org:uu-167671DiVA: diva2:487939
Available from: 2012-02-01 Created: 2012-01-31 Last updated: 2017-12-08Bibliographically approved

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Ma, QiSumpter, David J. T.

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Analysis and Applied Mathematics
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Cite
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