Dynamics of a birth-death process based on combinatorial innovation

JOURNAL OF THEORETICAL BIOLOGY

卷:491

Article

Steel, Mike¹  Hordijk, Wim²  Kauffman, Stuart A.³ 

[1] Univ Canterbury, Biomath Res Ctr, Christchurch, New Zealand

[2] Konrad Lorenz Inst Evolut & Cognit Res, Klosterneuburg, Austria

[3] Inst Syst Biol, Seattle, WA USA

关键词: Birth-death process;    Explosive growth;    Extinction;    Combinatorial formation;   

DOI  :  10.1016/j.jtbi.2020.110187

来源: Elsevier

【 摘 要 】

A feature of human creativity is the ability to take a subset of existing items (e.g. objects, ideas, or techniques) and combine them in various ways to give rise to new items, which, in turn, fuel further growth. Occasionally, some of these items may also disappear (extinction). We model this process by a simple stochastic birth-death model, with non-linear combinatorial terms in the growth coefficients to capture the propensity of subsets of items to give rise to new items. In its simplest form, this model involves just two parameters (P, alpha). This process exhibits a characteristic 'hockey-stick' behaviour: a long period of relatively little growth followed by a relatively sudden 'explosive' increase. We provide exact expressions for the mean and variance of this time to explosion and compare the results with simulations. We then generalise our results to allow for more general parameter assignments, and consider possible applications to data involving human productivity and creativity. (C) 2020 Elsevier Ltd. All rights reserved.

【 授权许可】

Free