For organisms that diffuse and randomly reset to a fixed location, the critical patch half-width is ℓc = arccos(r cos(xr/√(1−r))) / √(1−r) in a lethal exterior, and resetting can either raise or lower the required habitat size.
Fahrig, Effects of habitat fragmentation on biodiver- sity, Annual review of ecology, evolution, and systematics 34, 487 (2003)
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Critical habitat size of organisms diffusing with stochastic resetting
For organisms that diffuse and randomly reset to a fixed location, the critical patch half-width is ℓc = arccos(r cos(xr/√(1−r))) / √(1−r) in a lethal exterior, and resetting can either raise or lower the required habitat size.