Marine reserves and fishery profit: practical designs offer optimal solutions.

1. Marine reserves and fishery profit: practical designs offer optimal solutions. Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of California – Santa Barbara

2. Larval export No Fishing

3. When is larval export maximized? What reserve design (size and spacing) maximizes larval export to fishable areas? Do reserves benefit fisheries? Is fishery yield/profit greater under optimal reserve design than attainable without reserves?

4. When is larval export maximized? Research Question: To maximize larval export (and thus benefit fisheries) should reserves be… …few and large, …or many and small? SLOSS debate

5. Coastal fish & invert life history traits in model • Adults are sessile, reproducing seasonally (e.g. Brouwer et al. 2003, Lowe et al. 2003, Parsons et al. 2003) • Larvae disperse, mature after 1+ yrs (e.g. Dethier et al. 2003, Grantham et al. 2003) • Larva settlement and/or recruitment success decreases with increasing adult density at that location (post-dispersal density dependence) (e.g. Steele and Forrester 2002, Lecchini and Galzin 2003)

6. An integro-difference model describing coastal fish population dynamics: Adult abundance at location x during time-step t+1 Fecundity Number of adults harvested Larval survival Larval dispersal (Gaussian)(Siegel et al. 2003) Natural mortality of adults that escaped being harvested Larval recruitment at x Number of larvae that successfully recruit to location x

7. Incorporating Density Dependence Post-dispersal: Larva settlement and/or recruitment success decreases with increasing adult population density at that location.

8. SEVERAL SMALL RESERVES FEW LARGE RESERVES

9. θ Cost of catching one fish = Density of fish at that location θ = 5 θ = 0

10. θ Cost of catching one fish = Density of fish at that location Bottom line for fishermen: Profit = Revenue - cost θ = 5 θ = 0

11. θ Cost of catching one fish = Density of fish at that location Bottom line for fishermen: Profit = Revenue - cost θ = 20 θ = 0

12. SEVERAL SMALL RESERVES FEW LARGE RESERVES

13. Scale bar = 100 km

14. Scale bar = 100 km

15. Scale bar = 100 km

26. Max Yield without Reserves

27. Max Yield without Reserves

28. Max Yield without Reserves

29. Max Yield without Reserves

30. Max Yield without Reserves

31. Max Yield without Reserves

32. Max Yield without Reserves

33. Max Yield without Reserves

34. Max Yield without Reserves

35. A spectrum of high-profit scenarios Max Yield without Reserves

36. Cost = θ/density A spectrum of high-profit scenarios Max Yield without Reserves

37. Cost = θ/density (Stop fishing when cost = $1) A spectrum of high-profit scenarios Max Yield without Reserves

38. Cost = θ/density (Stop fishing when cost = $1) Escapement = % of virgin K (K = 50) A spectrum of high-profit scenarios Max Yield without Reserves

39. Cost = θ/density (Stop fishing when cost = $1) Escapement = % of virgin K (K = 50) Zero-profit escapement level = θ/K = 40% A spectrum of high-profit scenarios Max Yield without Reserves

40. Cost = θ/density (Stop fishing when cost = $1) Escapement = % of virgin K (K = 50) Zero-profit escapement level = θ/K = 40% A spectrum of high-profit scenarios Max Yield without Reserves

41. θ/K = 15/50 = 30% A spectrum of high-profit scenarios Max Yield without Reserves

42. θ/K = 10/50 = 20% A spectrum of high-profit scenarios Max Yield without Reserves

43. θ/K = 5/50 = 10% A spectrum of high-profit scenarios Max Yield without Reserves

44. Summary • Post-dispersal density dependence generates larval export. • Larval export varies with reserve size and spacing. • Fishery yield and profit maximized via… • Less than ~15% coastline in reserves …Any reserve spacing option. • More than ~15% coastline in reserves …Several small or few medium-sized reserves.

45. Summary 4. Reserves benefit fisheries when escapement is moderate to low (E < ~35%*K) 5. Reserves become more beneficial as fish become easier to catch (low θ)

46. Summary • Given optimal reserve spacing, a near-maximum profit is maintained across a spectrum of reserve and harvest scenarios: Many None/few Reserves High Escapement Low

47. Summary • Given optimal reserve spacing, a near-maximum profit is maintained across a spectrum of reserve and harvest scenarios: Many None None/few Reserves High Escapement Low Along this spectrum exists an optimal reserve network scenario, based on the fisheries’ self-regulated escapement, that maximizes profits to the fishery.

48. THANK YOU! University of California – Santa Barbara National Science Foundation

49. Logistic model: post-dispersal density dependence No reserves: Nt+1 = Ntr(1-Nt) Yield = Ntr(1-Nt)-Nt MSY = max{Yield} dYield/dN = r – 2rN – 1 = 0 N = (r – 1)/2r MSY = Yield(N = (r – 1)/2*r) = (r – 1)2 / 4r

50. Logistic model: Scorched earth outside reserves post-dispersal density dependence Reserves: Nt+1 = crNr(1-Nr) Nr* = 1 – 1/cr Yield = crNr(1 – c)(1 – No) Yield(Nr* = 1 – 1/cr) = -rc2 + cr + c – 1 dYield/dc = -2cr + r + 1 = 0 c = (r + 1)/2r MSY = Yield(c = (r + 1)/2r) = (r – 1)2 / 4r