CASA Working Paper 135

Evolution and turnover in scaling systems

Scaling has been discovered in the long tails of size distributions characterizing a variety of diverse systems, many of which evolve in terms of the size of their components through competition. Such time-invariant macro distributions, however, often obscure the micro-dynamics of change, such as continual turnover in the rank order of the constituents.

Here we show how a model drawn from evolutionary theory can explain this change, such that the time spent in the top ranked constituents is finite and also characterized by longtailed distributions. To show the broad applicability of this model, we compare typical model runs to real-world examples including US boys' names, UK Number One for pop albums, journal article keywords, and city sizes.

This working paper is available as a PDF. The file size is 395KB.

Authors: Michael Batty, Alex Bentley, Paul Ormerod

Publication Date: 1/5/2008

Download working paper No. 135.