Probabilistic Measures for Biological Adaptation and Resilience

TL;DR

This paper develops a probabilistic framework for measuring ecological resilience in noisy biological systems, emphasizing adaptation to environmental stress using concepts from statistical mechanics and stochastic response theory.

Contribution

It introduces a novel probabilistic resilience measure tailored for noisy, adaptive biological systems, integrating stochastic dynamics and ensemble averages.

Findings

Resilience can be quantified through ensemble averages of system states.

The proposed measure accounts for randomness and variability in biological responses.

Illustrative example demonstrates the measure's interpretability and potential applications.

Abstract

This paper introduces a novel approach to quantifying ecological resilience in biological systems, particularly focusing on noisy systems responding to episodic disturbances with sudden adaptations. Incorporating concepts from non-equilibrium statistical mechanics, we propose a measure termed `ecological resilience through adaptation,' specifically tailored to noisy, forced systems that undergo physiological adaptation in the face of stressful environmental changes. Randomness plays a key role, accounting for model uncertainty and the inherent variability in the dynamical response among components of biological systems. Our measure of resilience is rooted in the probabilistic description of states within these systems, and is defined in terms of the dynamics of the ensemble average of a model-specific observable quantifying success or well-being. Our approach utilizes stochastic linear response theory to compute how the expected success of a system, originally in statistical equilibrium, dynamically changes in response to a environmental perturbation and a subsequent adaptation. The resulting mathematical derivations allow for the estimation of resilience in terms of ensemble averages of simulated or experimental data. Finally, through a simple but clear conceptual example, we illustrate how our resilience measure can be interpreted and compared to other existing frameworks in the literature. The methodology is general but inspired by applications in plant systems, with the potential for broader application to complex biological processes.