Modelling the Impact of Marine Reserves on a Population with Depensatory Dynamics

Bulletin of Mathematical Biology

Volumn 76, Issue 9, 2014, Pages 2122-2143

  Chan, Matthew H ^a   Kim, Peter S ^a  

^a UNIVERSITY OF SYDNEY   (Australia)

Author keywords

Depensation; Marine reserve; Population dynamics; Stage structure; Strong Allee effect

Indexed keywords

ANIMAL; ECONOMICS; ENVIRONMENTAL PROTECTION; FISH; FISHERY; GROWTH, DEVELOPMENT AND AGING; POPULATION DYNAMICS; PROCEDURES; THEORETICAL MODEL;

ANIMALS; CONSERVATION OF NATURAL RESOURCES; FISHERIES; FISHES; MODELS, THEORETICAL; POPULATION DYNAMICS;

EID: 84927170129     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-014-0003-2     Document Type: Article

References (58)

1. Abesamis RA, Russ GR (2005) Density-dependent spillover from a marine reserve: long-term evidence. Ecol Appl 15(5):1798–1812
2. Ban NC, Klein CJ (2009) Spatial socioeconomic data as a cost in systematic marine conservation planning. Conserv Lett 2(5):206–215
3. Botsford LW, Kaplan DM, Hastings A (2004) Sustainability and yield in marine reserve policy. Am Fish Soc Symp 42:75–86
4. Botsford LW, Micheli F, Hastings A (2003) Principles for the design of marine reserves. Ecol Appl 13:25–31
5. Bundy A, Fanning LP (2005) Can Atlantic cod (Gadus morhua) recover? Exploring trophic explanations for the non-recovery of the cod stock on the eastern Scotian Shelf, Canada. Can J Fish Aquat Sci 62(7):1474–1489
6. Clark CW (1976) Pure and applied mathematics., Mathematical bioeconomics: the optimal management of renewable resourcesWiley-Interscience, New York
7. Costello C, Ovando D, Hilborn R, Gaines SD, Deschenes O, Lester SE (2012) Status and solutions for the worlds unassessed fisheries. Science 338(6106):517–520
8. Côté IM, Mosqueira I, Reynolds JD (2001) Effects of marine reserve characteristics on the protection of fish populations: a meta-analysis. J Fish Biol 59:178–189
9. Courchamp F, Clutton-Brock T, Grenfell BT (1999) Inverse density dependence and the Allee effect. Trends Ecol Evol 14(10):405–410
10. Dubey B, Chandra P, Sinha P (2003) A model for fishery resource with reserve area. Nonlinear Anal Real 4(4):625–637
11. Frank KT, Brickman D (2000) Allee effects and compensatory population dynamics within a stock complex. Can J Fish Aquat Sci 57(3):513–517
12. Gaylord B, Gaines SD, Siegel DA, Carr MH (2005) Marine reserves exploit population structure and life history in potentially improving fisheries yields. Ecol Appl 15(6):2180–2191
13. Gell FR, Roberts CM (2003) Benefits beyond boundaries: the fishery effects of marine reserves. Trends Ecol Evol 18(9):448–455
14. Gerber LR, Andelman SJ, Botsford LW, Gaines SD, Hastings A, Palumbi SR, Possingham HP (2003) Population models for marine reserve design: a retrospective and prospective synthesis. Ecol Appl 13:47–S64
15. Grafton QR, Kompas T, Pham VH (2006) The economic payoffs from marine reserves: resource rents in a stochastic environment. Econ Rec 82:469–480
16. Grafton RQ, Kompas T, Lindenmayer D (2005) Marine reserves with ecological uncertainty. Bull Math Biol 67(5):957–971
17. Grüss A, Kaplan D, Guenette S, Roberts CM, Botsford LW (2011) Consequences of adult and juvenile movement for marine protected areas. Biol Cons 144:692–702
18. Halpern B, Warner R (2002) Marine reserves have rapid and lasting effects. Ecol Lett 5:361–366
19. Halpern BS (2003) The impact of marine reserves: do reserves work and does reserve size matter? Ecol Appl 13:117–137
20. Hannesson R (1998) Marine reserves: what would they accomplish? Mar Resour Econ 13:159–170
21. Hannesson R (2008) The economics of marine reserves. Nat Resour Model 15:273–290
22. Harrison HB, Williamson DH, Evans RD, Almany GR, Thorrold SR, Russ GR, Feldheim KA, van Herwerden L, Planes S, Srinivasan M, Berumen ML, Jones GP (2012) Larval export from marine reserves and the recruitment benefit for fish and fisheries. Curr Biol 22(11):1023–1028
23. Hart, DR, Sissenwine MP (2009) Marine reserve effects on fishery profits: a comment on white et al. (2008) Ecol Lett 12(3):E9–E11
24. Hastings A, Botsford LW (1999) Equivalence in yield from marine reserves and traditional fisheries management. Science 284(5419):1537–1538
25. Holland DS, Brazee RJ (1996) Marine reserves for fisheries management. Mar Resour Econ 11:157–172
26. Horwood JW, Nichols JH, Milligan S (1998) Evaluation of closed areas for fish stock conservation. J Appl Ecol 35(6):893–903
27. Huo HF, Jiang HM, Meng XY (2012) A dynamic model for fishery resource with reserve area and taxation. J Appl Math. doi:10.1155/2012/794719
28. Hutchings JA (2013) Renaissance of a caveat: Allee effects in marine fish. ICES J Mar Sci. doi:10.1093/icesjms/fst179
29. Hutchings JA, Myers RA (1994) What can be learned from the collapse of a renewable resource? Atlantic cod, Gadus morhua, of Newfoundland and Labrador. Can J Fish Aquat Sci 51(9):2126–2146
30. Lauck T, Clark CW, Mangel M, Munro GR (1998) Implementing the precautionary principle in fisheries management through marine reserves. Ecol Appl 8:S72–S78
31. Liermann M, Hilborn R (2001) Depensation: evidence, models and implications. Fish Fish 2(1):33–58
32. Myers RA, Barrowman NJ, Hutchings JA, Rosenberg A (1995) Population dynamics of exploited fish stocks at low population levels. Science 269(5227):1106–1108
33. Naidoo R, Balmford A, Ferraro PJ, Polasky S, Ricketts TH, Rouget M (2006) Integrating economic costs into conservation planning. Trends Ecol Evol 21(12):681–687
34. Nehlsen W, Williams JE, Lichatowich JA (1991) Pacific salmon at the crossroads: stocks at risk from California, Oregon, Idaho, and Washington. Fisheries 16(2):4–21
35. Neubert MG (2003) Marine reserves and optimal harvesting. Ecol Lett 6(9):843–849
36. Parrish R (1999) Marine reserves for fisheries management: why not? Calif Coop Ocean Fish 40:77–86
37. Price MHH, Darimont CT, Temple NF, MacDuffee SM (2008) Ghost runs: management and status assessment of Pacific salmon (Oncorhynchus spp.) returning to British Columbia’s central and north coasts. Can J Fish Aquat Sci 65(12):2712–2718
38. Ralston S, OFarrell MR (2008) Spatial variation in fishing intensity and its effect on yield. Can J Fish Aquat Sci 65(4):588–599
39. Ricard D, Minto C, Jensen OP, Baum JK (2012) Examining the knowledge base and status of commercially exploited marine species with the ram legacy stock assessment database. Fish Fish 13(4):380–398
40. Roberts CM, Hawkins JP, Gell FR (2005) The role of marine reserves in achieving sustainable fisheries. Phil Trans R Soc B 360(1453):123–132
41. Rowe S, Hutchings JA, Bekkevold D, Rakitin A (2004) Depensation, probability of fertilization, and the mating system of atlantic cod (Gadus morhua L.). ICES J Mar Sci 61(7):1144–1150
42. Russ GR (2002) Yet another review of marine reserve as reef fishery management tools. In: Sale PF (ed) Coral reef fishes: dynamics and diversity in a complex ecosystem. Academic Press, San Diego
43. Russ GR, Alcala AC (2011) Enhanced biodiversity beyond marine reserve boundaries: the cup spillith over. Ecol Appl 21:241–250
44. Shelton PA, Healey BP (1999) Should depensation be dismissed as a possible explanation for the lack of recovery of the northern cod (Gadus morhua) stock? Can J Fish Aquat Sci 56(9):1521–1524
45. Sinclair AF (2001) Natural mortality of cod (Gadus morhua) in the Southern Gulf of st Lawrence. ICES J Mar Sci J du Conseil 58(1):1–10
46. Stephens PA, Sutherland WJ, Freckleton RP (1999) What is the allee effect? Oikos 87(1):185–190
47. Stoner AW (1997) The status of queen conch, strombus gigas, research in the caribbean. Mar Fish Rev 59(3):14–33
48. Stoner AW, Davis MH, Booker CJ (2012) Negative consequences of allee effect are compounded by fishing pressure: comparison of queen conch reproduction in fishing grounds and a marine protected area. Bull Mar Sci 88:89–104
49. Stoner AW, Lipcius RN, Marshall LS, Bardales AT (1988) Synchronous emergence and mass migration in juvenile queen conch. Mar Ecol Prog Ser 49(1–2):51–55
50. Sumaila UR (1998) Protected marine reserves as fisheries management tools: a bioeconomic analysis. CMI working papers. Chr. Michelsen Institute
51. Taylor CM, Hastings A (2005) Allee effects in biological invasions. Ecol Lett 8(8):895–908
52. Tetreault I, Ambrose RF (2007) Temperate marine reserves enhance targeted but not untargeted fishes in multiple no-take mpas. Ecol Appl 17(8):2251–2267
53. Walters CJ, Kitchell JF (2001) Cultivation/depensation effects on juvenile survival and recruitment: implications for the theory of fishing. Can J Fish Aquat Sci 58(1):39–50
54. White C, Kendall BE (2007) A reassessment of equivalence in yield from marine reserves and traditional fisheries management. Oikos 116(12):2039–2043
55. White C, Kendall BE, Gaines SD, Siegel DA, Costello CJ (2008) Marine reserve effects on fishery profit. Ecol Lett 11:370–379
56. Wicklund RI, Hepp LA, Wenz GA (1991) Preliminary studies on the early life history of the queen conch (strombus gigas) in the exuma cays, bahamas. In: Proceedings of the Gulf and Caribbean Fisheries Institute, vol 40. Gulf and Caribbean Fisheries Institute, pp 283–298
57. Willis TJ, Millar RB, Babcock RC, Tolimieri N (2003) Burdens of evidence and the benefits of marine reserves: putting descartes before des horse? Environ Conserv 30(2):97–103
58. Worm B, Hilborn R, Baum JK, Branch TA, Collie JS, Costello C, Fogarty MJ, Fulton EA, Hutchings JA, Jennings S, Jensen OP, Lotze HK, Mace PM, McClanahan TR, Minto C, Palumbi SR, Parma AM, Ricard D, Rosenberg AA, Watson R, Zeller D (2009) Rebuilding global fisheries. Science 325(5940):578–585