Evolution’s hidden architecture: a non-lipschitz theory of creation and catastrophe
File(s)
Published version
Author(s)
Duran Olivencia, Miguel Angel
Duran Olivencia, Miguel Angel
Type
Journal Article
Abstract
Background
Models of evolutionary dynamics have long been dominated by a paradigm of gradualism, yet the fossil record consistently points to a history defined by punctuation. This disconnect between theory and data has left major macroevolutionary events, such as punctuated equilibria, explosive radiations, and mass extinctions, without a unified first-principles explanation. We argue that this gap stems from a subtle ubiquitous assumption in theoretical models: that the underlying fitness landscapes are mathematically smooth (Lipschitz continuous).
Results
We develop a theoretical framework based on relaxing this assumption, showing that non-Lipschitz dynamics are sufficient to make punctuation the default mode of evolution. We demonstrate that non-Lipschitz singularities, which arise naturally from known biological mechanisms like developmental constraints and ecological tipping points, provide a formal dynamical-systems basis for speciation as a bifurcation event and extinction as a finite-time singularity. Furthermore, we show that these dynamics are universal, appearing in contexts ranging from viral quasispecies to global biotas.
Conclusion
Our framework provides a new generative engine for macroevolutionary theory. It makes specific quantitative predictions for paleontological patterns, including the decoupling of disparity and diversity during adaptive radiations, and for the genomic signatures of lineages that undergo rapid evolution. By replacing the assumption of smoothness with non-Lipschitz continuity, we offer a rigorous mathematical reconciliation between gradualist models and the punctuated nature of the fossil record.
Models of evolutionary dynamics have long been dominated by a paradigm of gradualism, yet the fossil record consistently points to a history defined by punctuation. This disconnect between theory and data has left major macroevolutionary events, such as punctuated equilibria, explosive radiations, and mass extinctions, without a unified first-principles explanation. We argue that this gap stems from a subtle ubiquitous assumption in theoretical models: that the underlying fitness landscapes are mathematically smooth (Lipschitz continuous).
Results
We develop a theoretical framework based on relaxing this assumption, showing that non-Lipschitz dynamics are sufficient to make punctuation the default mode of evolution. We demonstrate that non-Lipschitz singularities, which arise naturally from known biological mechanisms like developmental constraints and ecological tipping points, provide a formal dynamical-systems basis for speciation as a bifurcation event and extinction as a finite-time singularity. Furthermore, we show that these dynamics are universal, appearing in contexts ranging from viral quasispecies to global biotas.
Conclusion
Our framework provides a new generative engine for macroevolutionary theory. It makes specific quantitative predictions for paleontological patterns, including the decoupling of disparity and diversity during adaptive radiations, and for the genomic signatures of lineages that undergo rapid evolution. By replacing the assumption of smoothness with non-Lipschitz continuity, we offer a rigorous mathematical reconciliation between gradualist models and the punctuated nature of the fossil record.
Date Issued
2026-01-15
Date Acceptance
2025-12-01
Citation
BMC Ecology and Evolution, 2026, 26
ISSN
2730-7182
Publisher
BMC
Journal / Book Title
BMC Ecology and Evolution
Volume
26
Copyright Statement
© The Author(s) 2025. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Publication Status
Published
Article Number
5
Date Publish Online
2025-12-24