Dynamics of a birth-death process based on combinatorial innovation.
Publication Title
Journal of theoretical biology
Document Type
Article
Publication Date
4-21-2020
Keywords
Birth–death process; Combinatorial formation; Explosive growth; Extinction
Abstract
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, α). 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.
Specialty/Research Institute
Institute for Systems Biology
