Navigating Uncertainty: Risk-Averse vs. Risk-Prone Strategies in Populations Facing Demographic and Environmental Stochasticity

TL;DR

This paper investigates how different risk strategies affect the invasion success of mutants in populations facing environmental and demographic randomness, revealing conditions favoring risk-averse or risk-prone behaviors.

Contribution

It introduces a game-theoretical model combining environmental and demographic stochasticity to analyze strategy effectiveness in mutant invasion.

Findings

Variance aversion reduces invasion probability under high environmental change rates.

Risk-prone strategies can capitalize on transient favorable conditions, increasing fixation chances.

The model clarifies how environmental dynamics influence optimal risk strategies.

Abstract

Strategies aimed at reducing the negative effects of long-term uncertainty and risk are common in biology, game theory, and finance, even if they entail a cost in terms of mean benefit. Here, we focus on the single mutant's invasion of a finite resident population subject to fluctuating environmental conditions. Thus, the game-theoretical model we analyze integrates environmental and demographic randomness, i.e., the two leading sources of stochasticity and uncertainty. We use simulations and mathematical analysis to study if and when strategies that either increase or reduce payoff variance across environmental states can enhance the mutant fixation probability. Variance aversion implies that the mutant pays insurance in terms of mean payoff to avoid worst-case scenarios. Variance-prone or gambling strategies, on the other hand, entail specialization, allowing the mutant to capitalize on transient favorable conditions, leading to a series of ``boom-and-bust'' cycles. Our analyses elucidate how the rate of change of environmental conditions and the shape of the probability distribution of possible states affect the possible most convenient strategies. We discuss how our results relate to the bet-hedging theory, which aims to reduce fitness variance rather than payoff variance. We also describe the analogies and differences between these similar yet distinct approaches.