Resource and population dynamics in an agent-environment interaction model

In any ecosystem, the conditions of the environment and the characteristics of the species that inhabit it are entangled, coevolving in space and time. We introduce a model that couples active agents with a dynamic environment, interpreted as a nutrient source. Agents are persistent random walkers that gather food from the environment and store it in an inner energy depot. This energy is used for self-propulsion, metabolic expenses, and reproduction. The environment is a two-dimensional surface divided into patches, each of them producing food. Thus, population size and resource distribution become emergent properties of the system. Combining simulations and an analytical framework to analyze limiting cases, we show that the system exhibits distinct phases separating quasistatic and highly motile regimes. We observe that, in general, population sizes are inversely proportional to the average energy per agent. Furthermore, we find that, counterintuitively, reduced access to resources or increased metabolic expenditure can lead to a larger population size. The proposed theoretical framework provides a link between active matter and movement ecology, allowing to investigate short versus long-term strategies to resource exploitation and rationing, as well as sedentary versus wandering strategy. The introduced approach may serve as a tool to describe real-world ecological systems and to test environmental strategies to prevent species extinction.