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. Research Question: To maximize larval export (and thus benefit fisheries) should reserves be… …few and large, When is larval export maximized? …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 Number of adults harvested Natural mortality of adults that escaped being harvested Fecundity Larval survival Larval dispersal (Gaussian) (Siegel et al. 2003) 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. FEW LARGE RESERVES SEVERAL SMALL RESERVES

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

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

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

12. FEW LARGE RESERVES SEVERAL SMALL RESERVES

13. Scale bar = 100 km

26. Max Yield without Reserves

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

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

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

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

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

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

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

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

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

44. Summary 1.Post-dispersal density dependence generates larval export. 2.Larval export varies with reserve size and spacing. 3.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 4.Given optimal reserve spacing, a near-maximum profit is maintained across a spectrum of reserve and harvest scenarios: ReservesNone/few Many EscapementHighLow

47. Summary Along this spectrum exists an optimal reserve network scenario, based on the fisheries’ self-regulated escapement, that maximizes profits to the fishery. 4.Given optimal reserve spacing, a near-maximum profit is maintained across a spectrum of reserve and harvest scenarios: ReservesNone Many EscapementHighLow None/few

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

49. Logistic model: post-dispersal density dependence No reserves: N t+1 = N t r(1-N t ) Yield = N t r(1-N t )-N t 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: N t+1 = crN r (1-N r ) N r * = 1 – 1/cr Yield = crN r (1 – c)(1 – N o ) Yield(N r * = 1 – 1/cr) = -rc 2 + cr + c – 1 dYield/dc = -2cr + r + 1 = 0 c = (r + 1)/2r MSY = Yield(c = (r + 1)/2r) = (r – 1) 2 / 4r

51. Ricker model: post-dispersal density dependence No reserves: N t+1 = rN t e -gNt Surplus growth = Yield = rNe -gN – N dYield/dN = re -gN – grNe -gN – 1 = 0 1. Find N for dYield/dN = 0 2. Plug N into Yield(N,r,g) = MSY

54. Ricker model: Reserves: N r = crN r e -gNr N r * = Log[cr] / g Recruitment to fishable domain = Yield = crN r (1 – c)e -gNo Yield(N r * = Log[cr] / g) = crLog[cr](1 – c) / g dYield/dc = (rLog[cr] + r – 2crLog[cr] – cr) / g = 0 1. Find c for dYield/dc = 0 2. Plug c into Yield(c,r,g) = MSY

59. Older, bigger fish produce many more young

61. Channel Islands

64. FUTURE RESEARCH 1.Evaluate under post-dispersal dd where larvae recruitment success depends on sympatric larvae density. 2.Conduct analysis within a finite domain. 3.Add size structure to the fish population.

67. Scale bar = 100 km

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

70. Can Marine Reserves bolster fishery yields?

71. NO RESERVES RESERVES (E = 0% outside) Larvae-on- larvae density dependence equal

73. Short disperser Long disperser Marine reserves can exploit population structure and life history in improving potential fisheries yields Brian Gaylord, Steven D. Gaines, David A. Siegel, Mark H. Carr. In Press. Ecol. Apps. Post-dispersal density dependence: survival of new recruits decreases with increasing density of adults at settlement location.

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

76. Logistic model: Scorched earth outside reserves post-dispersal density dependence Reserves: N t+1 = crN r (1-N r ) N r * = 1 – 1/cr Yield = crN r (1 – c)(1 – N o ) Yield(N r * = 1 – 1/cr) = -rc 2 + cr + c – 1 dYield/dc = -2cr + r + 1 = 0 c = (r + 1)/2r MSY = Yield(c = (r + 1)/2r) = (r – 1) 2 / 4r

78. Ricker model: post-dispersal density dependence No reserves: N t+1 = rN t e -gNt Surplus growth = Yield = rNe -gN – N dYield/dN = re -gN – grNe -gN – 1 = 0 1. Find N for dYield/dN = 0 2. Plug N into Yield(N,r,g) = MSY

81. Ricker model: Reserves: N r = crN r e -gNr N r * = Log[cr] / g Recruitment to fishable domain = Yield = crN r (1 – c)e -gNo Yield(N r * = Log[cr] / g) = crLog[cr](1 – c) / g dYield/dc = (rLog[cr] + r – 2crLog[cr] – cr) / g = 0 1. Find c for dYield/dc = 0 2. Plug c into Yield(c,r,g) = MSY

85. Comparing MSYs: MSY reserve = max{crLog[cr](1 – c) / g} MSY fishable = max{ rNe -gN – N} dY fishable /dN = re -gN – grNe -gN – 1 = 0 ProductLog[z] = w is the solution for z = we w

86. INCREASE

87. Costello and Ward. In Review.