Relativistic Ecological Dynamics: An Empirical Investigation of its Geometric Properties

Sebastián Vallejo, Richard A Fariña

The foundational models of population dynamics, such as those by Lotka and Volterra, presuppose a static, Euclidean phase space where interactions are governed by fixed forces. The theory of Biorelativity challenges this, positing that dynamics are better described as geodesics on a manifold whose geometry is actively shaped by the system’s state and external forcings. This study gives operational form to this concept by framing the choice between classical and biorelativistic models as an empirical question about the underlying geometry of ecological interactions. A model tournament was conducted across three predator-prey datasets, confronting classical models with a key formalisation of Biorelativity: a climate-driven ecological clock that modulates the metric of the phase space. While simple Euclidean models proved sufficient for systems dominated by internal dynamics, the climate-driven ecological clock (BR-Z) was the decisive winner for the externally forced Isle Royale system. This result provides strong empirical evidence that a geometric, non-static description of ecological dynamics is not only more accurate but also more parsimonious, vindicating the core tenets of Biorelativity.