Stochastic analysis of the extra clustering model for animal grouping

Michael Drmota, Michael Fuchs*, Yi Wen Lee

*Corresponding author for this work

研究成果: Article

1 引文 斯高帕斯(Scopus)

摘要

We consider the extra clustering model which was introduced by Durand et al. (J Theor Biol 249(2):262–270, 2007) in order to describe the grouping of social animals and to test whether genetic relatedness is the main driving force behind the group formation process. Durand and François (J Math Biol 60(3):451–468, 2010) provided a first stochastic analysis of this model by deriving (amongst other things) asymptotic expansions for the mean value of the number of groups. In this paper, we will give a much finer analysis of the number of groups. More precisely, we will derive asymptotic expansions for all higher moments and give a complete characterization of the possible limit laws. In the most interesting case (neutral model), we will prove a central limit theorem with a surprising normalization. In the remaining cases, the limit law will be either a mixture of a discrete and continuous law or a discrete law. Our results show that, except of in degenerate cases, strong concentration around the mean value takes place only for the neutral model, whereas in the remaining cases there is also mass concentration away from the mean.

原文English
頁(從 - 到)123-159
頁數37
期刊Journal of Mathematical Biology
73
發行號1
DOIs
出版狀態Published - 1 七月 2016

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