Modelling singularities in macroevolution

Abstract

Macroevolutionary dynamics often display sudden, explosive surges, where systems remain relatively stable for extended periods before experiencing dramatic acceleration that frequently exceeds traditional exponential growth. This pattern is evident in biological evolution, cultural shifts, and technological progress and is often referred to as the emergence of singularities. Despite their widespread occurrence, these explosions arise from distinct underlying mechanisms in different domains. In this context, we present a unified framework that captures these dynamics through a theory of combinatorial innovation. Building on the Theory of the Adjacent Possible, we model macroevolutionary change as a process driven by recombining pre-existing elements within a system. By formalising these qualitative insights, we provide a mathematical structure that explains the emergence of these explosive phenomena, facilitates comparisons across different systems, and enables predictive insights into future evolutionary trajectories. Moreover, by comparing discrete and continuous formalisations of the theory, we emphasise that the occurrence and observation of these presumed singularities should be carefully considered, as they arise from the continuous limit of inherently discrete models.