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Addressing global environmental crises such as anthropogenic climate change requires the consistent adoption of proenvironmental behavior by a large part of a population. Here, we develop a mathematical model of a simple behavior-environment feedback loop to ask how the individual assessment of the environmental state combines with social interactions to influence the consistent adoption of proenvironmental behavior, and how this feeds back to the perceived environmental state. In this stochastic individual-based model, individuals can switch between two behaviors, ‘active’ (or actively proenvironmental) and ‘baseline’, differing in their perceived cost (higher for the active behavior) and environmental impact (lower for the active behavior). We show that the deterministic dynamics and the stochastic fluctuations of the system can be approximated by ordinary differential equations and a Ornstein-Uhlenbeck type process. By definition, the proenvironmental behavior is adopted consistently when, at population stationary state, its frequency is high and random fluctuations in frequency are small. We find that the combination of social and environmental feedbacks can promote the spread of costly proenvironmental behavior when neither, operating in isolation, would. To be adopted consistently, strong social pressure for proenvironmental action is necessary but not sufficient—social interactions must occur on a faster timescale compared to individual assessment, and the difference in environmental impact must be small. This simple model suggests a scenario to achieve large reductions in environmental impact, which involves incrementally more active and potentially more costly behavior being consistently adopted under increasing social pressure for proenvironmentalism.

应对人为气候变化等全球环境危机，需要大量人口持续采纳亲环境行为（proenvironmental behavior）。本研究构建了一个简单的行为-环境反馈环路数学模型，旨在探究个体对环境状态的评估与社会互动如何共同影响亲环境行为的持续采纳，以及这一过程如何反向作用于个体感知到的环境状态。
在该基于个体的随机模型（stochastic individual-based model）中，个体可在两种行为间切换：‘主动型’（即主动亲环境行为）与‘基准型’，二者在感知成本（主动型行为成本更高）与环境影响（主动型行为环境影响更低）上存在差异。研究表明，系统的确定性动力学与随机涨落可分别通过常微分方程（ordinary differential equations）与奥恩斯坦-乌伦贝克类过程（Ornstein-Uhlenbeck type process）进行近似。
根据定义，当种群处于稳态时，若亲环境行为的占比较高且其频率的随机涨落较小，则该行为可被视为持续被采纳。研究发现，当单独的社会反馈或环境反馈均无法推动高成本亲环境行为的传播时，二者的结合可促进此类行为的扩散。若要实现亲环境行为的持续采纳，针对亲环境行动的强社会压力是必要非充分条件——社会互动的时间尺度必须快于个体评估的时间尺度，且不同行为的环境影响差异需较小。
这一简单模型提出了一种可大幅降低环境影响的实现路径：随着亲环境主义的社会压力不断提升，逐步持续采纳愈发主动且潜在成本更高的行为。