Learning to outgrow the competition: Reaction-diffusion systems that adapt to time-dependent environments

A fundamental challenge in both biology and engineering is understanding how adaptation can emerge from simple physical or chemical building blocks. Biological adaptation appears to rely on two key capabilities: information processing, to enable learning of complex tasks, and reproduction, to give such learning its value through reproductive success. Creating and coordinating these capabilities poses both a formidable engineering challenge and a fundamental evolutionary puzzle. Here, we propose a model in which learning and reproduction emerge jointly from simple, nonequilibrium chemical systems, without prior design or evolution. The model's essential features are that it supports many steady states and spatial heterogeneities, upon which adaptation arises solely from exposure to time-varying influxes of reactants, without any predesigned program or memory. The adaptive response is specific to the temporal sequence of environmental changes, yet general enough to extend to related sequences. Learning manifests in several forms: It is reinforced through repeated exposure to the same environmental sequence, representing a form of self-learning, and enhanced through spatial interactions, corresponding to a form of collective learning. Moreover, an adapted state can accelerate adaptation in nearby regions, providing a mechanism akin to teacher-guided learning. By coupling environmental variations to stochastic reaction-diffusion dynamics, our model establishes a minimal physical framework in which learning of complex environments and selective amplification of the states that encode them arise directly from nonequilibrium chemical processes.