Critical habitat size of organisms diffusing with stochastic resetting

The persistence of populations depends on the minimum habitat area required for survival, known as the critical patch size. While most studies assume purely diffusive movement, additional movement components can significantly alter habitat requirements. Here, we investigate how critical patch sizes are affected by stochastic resetting, where each organism intermittently returns to a common fixed location, modeling behaviors such as homing, refuge-seeking, or movement toward essential resources. We analytically derive the total population growth over time and the critical patch size. Our results are validated by agent-based simulations, showing excellent agreement. Our findings demonstrate that stochastic resetting can either increase or decrease the critical patch size, depending on the reset rate, reset position, and external environmental hostility. These results highlight how intermittent relocation shapes ecological thresholds and may provide insights for ecological modeling and conservation planning, particularly in fragmented landscapes such as deforested regions.