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

Nariyuki Nakagiri; Hiroki Yokoi; Yukio Sakisaka; Kei-ichi Tainaka; Nariyuki Nakagiri; Hiroki Yokoi; Yukio Sakisaka; Kei-ichi Tainaka

doi:10.3934/mbe.2022429

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 9: 9244-9257. doi: 10.3934/mbe.2022429

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

1.
School of Human Science and Environment, University of Hyogo, Himeji 670-0092, Japan
2.
Fisheries Resources Institute, Japan Fisheries Research and Education Agency, Yokohama 236-8648, Japan
3.
Division of Early Childhood Care and Education, Nakamura Gakuen University Junior College, Fukuoka 814-0198, Japan
4.
Institute of Preventive and Medicinal Dietetics, Nakamura Gakuen University, Fukuoka 814-0198, Japan
5.
Department of Mathematical and Systems Engineering, Shizuoka University, Hamamatsu 432-856, Japan

Academic Editor: Jerome Goddard II

Received: 29 March 2022 Revised: 08 June 2022 Accepted: 09 June 2022 Published: 23 June 2022

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.
- habitat conservation,
- stochastic cellular automaton,
- contact process,
- reaction-diffusion equation,
- swapping migration,
- birth and death processes,
- metapopulation model
Citation: Nariyuki Nakagiri, Hiroki Yokoi, Yukio Sakisaka, Kei-ichi Tainaka. Population persistence under two conservation measures: Paradox of habitat protection in a patchy environment[J]. Mathematical Biosciences and Engineering, 2022, 19(9): 9244-9257. doi: 10.3934/mbe.2022429

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Abstract

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.

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