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arXiv · 2609.22368

Fitness, predictability and equilibrium in biological dynamics

Rolando Rebolledo·Mauricio Tejo·Mara A. Freilich·Pablo Marquet
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Abstract

Understanding eco-evolutionary dynamics presents significant mathematical challenges, particularly regarding predictability, equilibrium, and the mathematical representation of fitness. Using Open System Dynamics and Stochastic Analysis, we develop a theoretical framework to characterize fitness change and its relationship with predictability. We explore the limiting behavior of biomass abundances modeled by stochastic processes, deriving continuous-time diffusion counterparts from discrete-time models. Focusing on neutrality and the search for equilibrium, we analyze diffusions in two distinct state spaces. For relative abundances on a d-dimensional simplex, we demonstrate the central role of orthogonal polynomials in model construction. For non-proportional abundances in the positive orthant of d-dimensional space, we detail two specific families of models. Finally, we address statistical inference by presenting numerical examples for relative abundances, illustrating how orthogonal polynomials facilitate maximum likelihood parameter estimation.

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Rolando Rebolledo, Mauricio Tejo, Mara A. Freilich, Pablo Marquet. 2026-09-17. Fitness, predictability and equilibrium in biological dynamics. https://arxiv.org/abs/2609.22368

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