A Two-Species Model for a Fishing System with Marine Protected Areas
A model of a system concerning one species of demersal
(inshore) fish and one of pelagic (offshore) fish undergoing fishing
restricted by marine protected areas is proposed in this paper. This
setup was based on the FISH-BE model applied to the Tabina fishery
in Zamboanga del Sur, Philippines. The components of the model
equations have been adapted from widely-accepted mechanisms in
population dynamics. The model employs Gompertz-s law of growth
and interaction on each type of protected and unprotected subpopulation.
Exchange coefficients between protected and unprotected
areas were assumed to be proportional to the relative area of the
entry region. Fishing harvests were assumed to be proportional to
both the number of fishers and the number of unprotected fish. An
extra term was included for the pelagic population to allow for the
exchange between the unprotected area and the outside environment.
The systems were found to be bounded for all parameter values. The
equations for the steady state were unsolvable analytically but the
existence and uniqueness of non-zero steady states can be proven.
Plots also show that an MPA size yielding the maximum steady state
of the unprotected population can be found. All steady states were
found to be globally asymptotically stable for the entire range of
parameter values.
[1] White, A.T., Ali˜no, and Meneses, A.B.T., Creating and Managing
Marine Protected Areas in the Philippines. Cebu City, Philippines:
University of the Philippines Marine Science Institute, 2006
[2] Salm, R.V., and Clark, J.R., Marine and Coastal Protected Areas, A
Guide for Planners and Managers. 3rd ed., Gland, Switzerland:
International Union for Conservation of Nature and Natural Resources,
2000
[3] Roberts, C.M., McClean, C.J., Veron J.E.N., Hawkins, J.P., Allen,
G.R., McAllister D.E., Mittermeier, C.G., Schueler, F.W., Spalding, M.,
Wells, F., Vynne, C., Werner, T.B., "Marine Biodiversity Hotspots and
Conservation Priorities for Tropical Reefs," Science, V295, pp. 1280-
1284, 2002
[4] Licuanan, W.Y., Ali˜no, P.M., Campos, W.I., Castillo, G.B. and Juinio-
Me˜nez, M.A., "A Decision Support Model for Determining Sizes of
Marine Protected Areas: Biophysical Considerations," The Philippine
Agricultural Scientist, V89(1), pp. 509-520, 2006
[5] Russ, G.R. and Alcala, A.C. "Do marine reserves export adult fish
biomass? Evidence from Apo Island, central Philippines" Marine Ecology
Progress Series, V132, pp. 1-9, 1996
[6] Alcala, A.C. and Luchavez, T. "Fish Yields of a Coral Reef Surrounding
Apo Island, Central Visayas," Proceedings of the 4th International Coral
Reef Symposium, V1, pp. 69-73, 1981
[7] Oracion, E.G., Miller, M.L. and Christie, P. "Marine Protected Areas for
whom? Fisheries, Tourism, and Solidarity in a Philippine Community,"
Ocean and Coastal Management, V48, pp. 393-410, 2005
[8] Castillo, G.B., Licuanan, W.Y., Ali˜no, P.M., Campos, W. and Juinio-
Me˜nez, A., "Fisheries Bio-Economic Model: A Decision Support Model
for Local Fisheries Management," Philippine Environmental Governance
Project,(Technical Report) Department of Environment and Natural
Resources - United States Agency for International Development, 2004
[9] Baskett, M.L., Micheli, F. and Levin, S.A., "Designing Marine Reserves
for Interacting Species: Insight from Theory," Biological Conservation,
V137, pp. 163-179, 2007
[10] Dubey, B., Chandra, P. and Sinha, P. "A Model for Fishery Resource
with Reserve Area" Nonlinear Analysis: Real World Applciations, V4,
pp. 625-637, 2003
[11] Kar, T.K. and Misra, S. "Influence of Prey Reserve in a Prey-Predator
Fishery" Nonlinear Analysis, V65, pp. 1725-1735, 2006
[12] Greenville, J. and MacAulay, T.G., "Protected Areas in Fisheries: a
two-patch, two-species population model" The Australian Journal of
Agricultural and Resource Economics, V50, pp. 207-226, 2006
[13] Kar, T.T. "Influence of Environmental Noises on the Gompertz Model of
Two Species Fishery" Ecological Modelling, V173, pp. 283-293, 2004
[14] Pradhan, T. and Chaudhuri, K.S. "Bioeconomic Modeling of a Single-
Species Fishery with Gompertz Law of Growth" Journal of Biological
Systems, V6(4), pp. 393-409, 1998
[15] Shirai, Y. and Harada, Y., "Evaluation of the Advantage of Marine
Protected Areas over the Reduction of the Fishing Mortality Coefficient,"
Fisheries Science, V69, pp. 465-472, 2003
[16] Armstrong, C.W. and Skonhoft, A. "Marine reserves: A bio-economic
model with asymmetric density dependent migration" Ecological Economics,
V57, pp. 466-476, 2006
[17] Roberts, C.M., Bohnsack, J.A., Gell, F., Hawkins, J.P. and Goodridge,
R. "Effects of Marine Reserves on Adjacent Fisheries" Science, V294,
pp. 1920-1923, 2001
[18] Pezzey, J.C.V., Reoberts, C.M. and Urdal, B.T. "A Simple Bioeconomic
Model of a Marine Reserve" Ecological Economics, V33, pp. 77-91,
2000
[19] Nowlis, J.S., "Short-and Long-term Effects of Three Fishery-
Management Tools on Depleted Fisheries" Bulletin of Marine Science,
V66(3), pp. 651-662, 2000
[1] White, A.T., Ali˜no, and Meneses, A.B.T., Creating and Managing
Marine Protected Areas in the Philippines. Cebu City, Philippines:
University of the Philippines Marine Science Institute, 2006
[2] Salm, R.V., and Clark, J.R., Marine and Coastal Protected Areas, A
Guide for Planners and Managers. 3rd ed., Gland, Switzerland:
International Union for Conservation of Nature and Natural Resources,
2000
[3] Roberts, C.M., McClean, C.J., Veron J.E.N., Hawkins, J.P., Allen,
G.R., McAllister D.E., Mittermeier, C.G., Schueler, F.W., Spalding, M.,
Wells, F., Vynne, C., Werner, T.B., "Marine Biodiversity Hotspots and
Conservation Priorities for Tropical Reefs," Science, V295, pp. 1280-
1284, 2002
[4] Licuanan, W.Y., Ali˜no, P.M., Campos, W.I., Castillo, G.B. and Juinio-
Me˜nez, M.A., "A Decision Support Model for Determining Sizes of
Marine Protected Areas: Biophysical Considerations," The Philippine
Agricultural Scientist, V89(1), pp. 509-520, 2006
[5] Russ, G.R. and Alcala, A.C. "Do marine reserves export adult fish
biomass? Evidence from Apo Island, central Philippines" Marine Ecology
Progress Series, V132, pp. 1-9, 1996
[6] Alcala, A.C. and Luchavez, T. "Fish Yields of a Coral Reef Surrounding
Apo Island, Central Visayas," Proceedings of the 4th International Coral
Reef Symposium, V1, pp. 69-73, 1981
[7] Oracion, E.G., Miller, M.L. and Christie, P. "Marine Protected Areas for
whom? Fisheries, Tourism, and Solidarity in a Philippine Community,"
Ocean and Coastal Management, V48, pp. 393-410, 2005
[8] Castillo, G.B., Licuanan, W.Y., Ali˜no, P.M., Campos, W. and Juinio-
Me˜nez, A., "Fisheries Bio-Economic Model: A Decision Support Model
for Local Fisheries Management," Philippine Environmental Governance
Project,(Technical Report) Department of Environment and Natural
Resources - United States Agency for International Development, 2004
[9] Baskett, M.L., Micheli, F. and Levin, S.A., "Designing Marine Reserves
for Interacting Species: Insight from Theory," Biological Conservation,
V137, pp. 163-179, 2007
[10] Dubey, B., Chandra, P. and Sinha, P. "A Model for Fishery Resource
with Reserve Area" Nonlinear Analysis: Real World Applciations, V4,
pp. 625-637, 2003
[11] Kar, T.K. and Misra, S. "Influence of Prey Reserve in a Prey-Predator
Fishery" Nonlinear Analysis, V65, pp. 1725-1735, 2006
[12] Greenville, J. and MacAulay, T.G., "Protected Areas in Fisheries: a
two-patch, two-species population model" The Australian Journal of
Agricultural and Resource Economics, V50, pp. 207-226, 2006
[13] Kar, T.T. "Influence of Environmental Noises on the Gompertz Model of
Two Species Fishery" Ecological Modelling, V173, pp. 283-293, 2004
[14] Pradhan, T. and Chaudhuri, K.S. "Bioeconomic Modeling of a Single-
Species Fishery with Gompertz Law of Growth" Journal of Biological
Systems, V6(4), pp. 393-409, 1998
[15] Shirai, Y. and Harada, Y., "Evaluation of the Advantage of Marine
Protected Areas over the Reduction of the Fishing Mortality Coefficient,"
Fisheries Science, V69, pp. 465-472, 2003
[16] Armstrong, C.W. and Skonhoft, A. "Marine reserves: A bio-economic
model with asymmetric density dependent migration" Ecological Economics,
V57, pp. 466-476, 2006
[17] Roberts, C.M., Bohnsack, J.A., Gell, F., Hawkins, J.P. and Goodridge,
R. "Effects of Marine Reserves on Adjacent Fisheries" Science, V294,
pp. 1920-1923, 2001
[18] Pezzey, J.C.V., Reoberts, C.M. and Urdal, B.T. "A Simple Bioeconomic
Model of a Marine Reserve" Ecological Economics, V33, pp. 77-91,
2000
[19] Nowlis, J.S., "Short-and Long-term Effects of Three Fishery-
Management Tools on Depleted Fisheries" Bulletin of Marine Science,
V66(3), pp. 651-662, 2000
@article{"International Journal of Engineering, Mathematical and Physical Sciences:54544", author = "Felicia Magpantay and Kenzu Abdella", title = "A Two-Species Model for a Fishing System with Marine Protected Areas", abstract = "A model of a system concerning one species of demersal
(inshore) fish and one of pelagic (offshore) fish undergoing fishing
restricted by marine protected areas is proposed in this paper. This
setup was based on the FISH-BE model applied to the Tabina fishery
in Zamboanga del Sur, Philippines. The components of the model
equations have been adapted from widely-accepted mechanisms in
population dynamics. The model employs Gompertz-s law of growth
and interaction on each type of protected and unprotected subpopulation.
Exchange coefficients between protected and unprotected
areas were assumed to be proportional to the relative area of the
entry region. Fishing harvests were assumed to be proportional to
both the number of fishers and the number of unprotected fish. An
extra term was included for the pelagic population to allow for the
exchange between the unprotected area and the outside environment.
The systems were found to be bounded for all parameter values. The
equations for the steady state were unsolvable analytically but the
existence and uniqueness of non-zero steady states can be proven.
Plots also show that an MPA size yielding the maximum steady state
of the unprotected population can be found. All steady states were
found to be globally asymptotically stable for the entire range of
parameter values.", keywords = "fisheries modelling, marine protected areas, sustainablefisheries, Gompertz Law", volume = "2", number = "4", pages = "241-10", }
