Biological conservation through marine protected areas in the presence of alternative stable states.
This article addresses how depleted stock can be restored by creation of marine reserve and species mobility when alternative stable states persist in a marine ecosystem. To understand the role of a marine protected area, we develop a two-patch version of an originally single-patch model. In the two-patch model, we prove that some of the locally stable equilibria are not stable equilibria from an ecological viewpoint. Similarly, some unstable equilibria determined classically from the mathematical model are no longer equilibria. It is shown that increasing reserve size may produce three alternative stable states in the presence of harvesting. Dynamic solutions have a tendency to reach an upper stable state from a lower stable state when reserve size is increased, but the opposite phenomenon (i.e., shifting to a lower stable state from an upper one) never occurs. This suggests that MPAs always have a positive effect in stock conservation even when alternative stable states inherently persist in marine ecosystems.
Department of Mathematics, National Institute of Technology Meghalaya, Bijni Complex, Shillong - 793003, Meghalaya, India. Electronic address: keshab_bg@yahoo.in.
Bapan
B
Ghosh
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah - 711103, India. Electronic address: debprasadpal@gmail.com.
Debprasad
D
Pal
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah - 711103, India. Electronic address: tkar1117@gmail.com.
T K
TK
Kar
Department of Mathematics, University of Castilla-La Mancha, 02071-Albacete, Spain. Electronic address: jose.valverde@uclm.es.
Jose C
JC
Valverde
D000818:Animals; D003247:Conservation of Natural Resources; D017753:Ecosystem; D005398:Fisheries; D008962:Models, Theoretical; D009792:Oceans and Seas
Marine reserve; Migration; Patchy model; Population dynamics; Stock recovery