Population persistence under two conservation measures: Paradox of habitat protection in a patchy environment

Anthropogenic modification of natural habitats is a growing threat to biodiversity and ecosystem services. The protection of biospecies has become increasingly important. Here, we pay attention to a single species as a conservation target. The species has three processes: reproduction, death and movement. Two different measures of habitat protection are introduced. One is partial protection in a single habitat (patch); the mortality rate of the species is reduced inside a rectangular area. The other is patch protection in a two-patch system, where only the mortality rate in a particular patch is reduced. For the one-patch system, we carry out computer simulations of a stochastic cellular automaton for a "contact process". Individual movements follow random walking. For the two-patch system, we assume an individual migrates into the empty cell in the destination patch. The reaction-diffusion equation (RDE) is derived, whereby the recently developed "swapping migration" is used. It is found that both measures are mostly effective for population persistence. However, comparing the results of the two measures revealed different behaviors. ⅰ) In the case of the one-patch system, the steady-state densities in protected areas are always higher than those in wild areas. However, in the two-patch system, we have found a paradox: the densities in protected areas can be lower than those in wild areas. ⅱ) In the two-patch system, we have found another paradox: the total density in both patches can be lower, even though the proportion of the protected area is larger. Both paradoxes clearly occur for the RDE with swapping migration.