1. Fishing pressure and marine reserve management (Claire W. Armstrong* and Anders Skonhoft**: Marine Reserves: A bioeconomic model with asymmetric density dependent migration Ecological Economics 2006) *University of Tromsø, Norway **Norwegian University of Science and Technology, Trondheim, Norway

2. Background Biodiversity in oceans threatened by overfishing, habitat reduction (trawlers...) and destructionBiodiversity in oceans threatened by overfishing, habitat reduction (trawlers...) and destruction Problems input control, output controlProblems input control, output control Latest solutions: property rights: ITC; Rights to catch or stock??Latest solutions: property rights: ITC; Rights to catch or stock?? And reserves.And reserves.

3. More than 5% of the earth’s land surface is covered by conservation zones.More than 5% of the earth’s land surface is covered by conservation zones. But… less than 0.5% of the ocean is closed to utilisation.But… less than 0.5% of the ocean is closed to utilisation. Marine motivation: preserve species and habitat within reserve, increase/secure exploitation outside reserve.Marine motivation: preserve species and habitat within reserve, increase/secure exploitation outside reserve.

4. help preserve habitat and conserve fish deal with overfishing and attendant problems hedge against the risk from fishing => protect economic benefits may be particularly useful in multi-species or bycatch fisheries supplement to conventional fisheries management enforcement… reduce management costs reduce conflict Why apply marine reserves?

5. Literature Large biological literature both terrestrial and marineLarge biological literature both terrestrial and marine Bioeconomics marine:Bioeconomics marine: –Holland and Brazee 1996, Conrad 1999, Hannesson 1998, Pezzey, et. al. 2000, Sanchirico and Wilen 1999, 2001, Smith and Wilen 2003 and Sumaila 1998, Armstrong and Skonhoft 2006, and many others..

6. Standard models RESERVE Harvesting Perfect control Different management options Migration Density dependent

7. Model Two-patch; reserve and neighbouring areaTwo-patch; reserve and neighbouring area Marine reserve area fixedMarine reserve area fixed Fishing activity in neighbouring area onlyFishing activity in neighbouring area only Static modelStatic model General model that opens for asymmetric density dependent dispersal between reserve and neighbouring areaGeneral model that opens for asymmetric density dependent dispersal between reserve and neighbouring area

8. dX 1 /dt = F(X 1 ) - M(X 1,X 2 ) = r 1 X 1 (1 - X 1 /K 1 ) - m(ßX 1 /K 1 - X 2 /K 2 ) dX 2 /dt =G(X 2 ) + M(X 1,X 2 ) - h =r 2 X 2 (1 - X 2 /K 2 ) + m(ßX 1 /K 1 - X 2 /K 2 ) - h X i = population size in i=1; the protected area, and i=2; the outside area F(.) and G(..) = the accompanying logistic natural growth functions M = dispersion between the two areas K i = carrying capacities m = degree of dispersion, m>0 ß = density dispersion parameter, ß>0 h = harvesting in outside area

9. Asymmetric dispersion M(X 1,X 2 ) = m(ßX 1 /K 1 - X 2 /K 2 ) ß  1; dispersion due to different predator-prey relations, competition or habitat differences between the two areas. ß >1; circumstances inside reserve are detrimental, creating greater potential migration out of the reserve. 0<ß<1; circumstances outside the reserve are detrimental, creating less potential migration out of the reserve.

10. Finding a vehicle for analysis; The Induced Sustainable Yield Function; Solving for ecological equilibrium; dX 1 /dt = dX 2 /dt = 0 =>X 2 =K 2 X 1 (β/K 1 -(r 1 /m)(1-X 1 /K 1 ))=R(X 1 ) Using this in the harvest function, we obtain h = M(X 1,X 2 )+G(X 2 ) = F(X 1 )+G(X 2 ) = F(X 1 )+G(R(X 1 )) = h(X 1 ) which we call the Induced Sustainable yield Function (ISYF) ISYF gives the relationship between the fish abundance in the reserve, and the harvesting taking place outside.

11. h(X 1 ),F(X 1 ) X1X1 F(X 1 ) K1K1 h(X 1 ) G(R(X 1 )) The Induced Sustainable Yield Curve; ISYF h(X 1 ) (β<1) F>0; reserve is a source F<0; reserve is a sink Fishable area detrimental

12. Management regimes 1.Maximum harvest; h msy 2.Maximum current profit; h mey 3.Open access; h  4.Maximum sustainable yield in reserve, or maximum dispersal out; h mm

13. h(X 1 ),F(X 1 ) X1X1 F(X 1 ) K1K1 h(X 1 ) a) Maximum harvest; h msy h msy

14. Maximum current profit; h mey Assume a Schaefer harvest function; h =qEX q is the catchability coefficient and E is the effort used in harvesting Current profit is described as P= (p-c/qX 2 )h where p and c are unit landing price and effort cost, respectively, assumed to be fixed. Wish to maximise  with subject to h=h(X 1 )

15. h(X 1 ),F(X 1 ) X1X1 F(X 1 ) K1K1 h(X 1 ) h msy b) Maximum current profit ; h mey Isoprofit curve  h mey

16. h(X 1 ),F(X 1 ) X1X1 F(X 1 ) K1K1 h(X 1 ) h msy c) Open access ; h  Isoprofit curve  h mey R(X 1 ) =c/pq hh => 0 profit

17. h(X 1 ),F(X 1 ) X1X1 F(X 1 ) K1K1 h(X 1 ) h msy K 1 /2 d) Maximum sustainable yield in the reserve, or maximum dispersal out; h mm Isoprofit curve  h mey R(X 1 ) =c/pq hh h mm Max dispersal equals max growth, since dX1/dt=0 gives F(X 1 )=M. => Reserve stock level equals K 1 /2

18. Numerical analysis of North-East Atlantic cod stock harvest Equal sized areas, and intrinsic growth rates High dispersion m Norwegian trawl cost and price data Density dependence over life-cycle – spawning, recruitment and cannibalism Look at β=1 (symmetry), β=1.5 (the reserve is detrimental) and β=0.5 (the fishable area is detrimental)

19. Some results of the numerical analysis Case d) max dispersal gives negative profits, lowest harvest and the smallest stock size when fishable area is detrimental (β=0.5) Profits are reduced overall and show greater variation when fishable area is detrimental (β=0.5) Critical to assume symmetric density dependent dispersal when β=0.5 is the case, as harvest levels would be set too high for all management options. If the manager chooses option a) max harvest, b) max profit or d) max dispersal; closing the detrimental area is optimal. If manager chooses option c) max employment; closing the the ecologically most attractive area is the best option.

20. Some conclusions If ecological conditions outside the reserve are detrimental, assuming symmetry will lead to overharvesting. Many reserves are imposed in order to protect unique or highly productive habitats, hence this seems of relevance. Focus on maximum yield in the reserve may be especially economically critical if the fishable area is detrimental. If economic efficiency is the goal (as is claimed to be the case for the N-E Atlantic cod), then optimal closing of a detrimental area is preferable, and probably politically most acceptable (though probably less desireable from the biologist’s point of view?)