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  • Open Access

Innovation-exnovation dynamics on trees and trusses

Edward D. Lee* and Ernesto Ortega-Díaz

  • *Contact author: edlee@csh.ac.at
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Phys. Rev. Research 7, 033102 – Published 31 July, 2025

DOI: https://doi.org/10.1103/ynwt-7g91

Abstract

Innovation and its complement exnovation describe the progression of realized possibilities from the past to the future, and the process depends on the structure of the underlying graph. For example, the phylogenetic tree represents the unique path of mutations to a single species. To a technology, paths are manifold, like a “truss.” We solve for the phase diagram of a model, where a population innovates while outrunning exnovation. The dynamics progress on random graphs that capture the degree of historical contingency. Higher connectivity speeds innovation but also increases the risk of system collapse. We show how dynamics and structural connectivity conspire to unleash innovative diversity or to drive it extinct.

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Phys. Rev. Research 7, 033102– Published 31 July, 2025
  • Received 5 March 2025
  • Accepted 8 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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