Optimal control policies for evolutionary dynamics with environmental feedback

TL;DR

This paper develops optimal control strategies for managing population behaviors and opinions to sustain environmental resources, revealing oscillatory dynamics that pose both opportunities and risks for resource conservation.

Contribution

It introduces a novel framework combining population dynamics, environmental feedback, and opinion influence, with numerical solutions for optimal control policies in complex socio-environmental systems.

Findings

Control strategies can successfully increase resource levels

Optimal policies induce oscillations between resource states

Oscillating dynamics pose risks but may have beneficial average effects

Abstract

We study a dynamical model of a population of cooperators and defectors whose actions have long-term consequences on environmental "commons" - what we term the "resource". Cooperators contribute to restoring the resource whereas defectors degrade it. The population dynamics evolve according to a replicator equation coupled with an environmental state. Our goal is to identify methods of influencing the population with the objective to maximize accumulation of the resource. In particular, we consider strategies that modify individual-level incentives. We then extend the model to incorporate a public opinion state that imperfectly tracks the true environmental state, and study strategies that influence opinion. We formulate optimal control problems and solve them using numerical techniques to characterize locally optimal control policies for three problem formulations: 1) control of incentives, and control of opinions through 2) propaganda-like strategies and 3) awareness campaigns. We show numerically that the resulting controllers in all formulations achieve the objective, albeit with an unintended consequence. The resulting dynamics include cycles between low and high resource states - a dynamical regime termed an "oscillating tragedy of the commons". This outcome may have desirable average properties, but includes risks to resource depletion. Our findings suggest the need for new approaches to controlling coupled population-environment dynamics.