Zipf's, Heaps' and Taylor's laws are determined by the expansion into the adjacent possible

Abstract

Zipf's, Heaps' and Taylor's laws are ubiquitous in many different systems where innovation processes are at play. Together, they represent a compelling set of stylized facts regarding the overall statistics, the innovation rate and the scaling of fluctuations for systems as diverse as written texts and cities, ecological systems and stock markets. Many modeling schemes have been proposed in literature to explain those laws, but only recently a modeling framework has been introduced that accounts for the emergence of those laws without deducing the emergence of one of the laws from the others or without ad hoc assumptions. This modeling framework is based on the concept of adjacent possible space and its key feature of being dynamically restructured while its boundaries get explored, i.e., conditional to the occurrence of novel events. Here, we illustrate this approach and show how this simple modelling framework, instantiated through a modified Polya's urn model, is able reproduce Zipf's, Heaps' and Taylor's laws within a unique self-consistent scheme. In addition the same modelling scheme embraces other less common evolutionary laws (Hoppe's model and Dirichlet processes) as particular cases.

arXiv commentThis article belongs to the Special Issue Economic Fitness and Complexity

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Cited by in corpus (9)

• Interacting discovery processes on complex networks
• The exploration of the Adjacent Possible explains the emergence and evolution of social networks
• Taylor's law in innovation processes
• Interacting Innovation processes: case studies from Reddit and Gutenberg
• Damping effect in innovation processes: case studies from Twitter
• On the dual nature of adoption processes in complex networks
• Time-Dependent Urn Models reproduce the full spectrum of novelties discovery
• Modelling Singularities in Macroevolution
• Central limit theorems for interacting innovation processes, related statistical tools and general results