1. Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007

2. Adult (15 cm) Recruits Kellet’s whelk Kelletia kelletii

3. Focus of developing fishery Sold to US domestic Asian market (mostly in LA) Mean price = $1.43/kg = ~$0.15/whelk Aseltine-Neilson et al. 2006

4. Caught as by-catch by commercial trap fishermen

5. Research questions:  What is the optimal harvest path that maximizes net present value of the Kellet’s whelk fishery?  Short-term.  Long-term.  How do they differ?

6. SBA NCI Focus on Santa Barbara area Two patches: SBA: Santa Barbara mainland NCI: Northern Channel Islands Patches differ with respect to: Habitat area, stock size & density Intra- and inter-patch dispersal dynamics Protection in reserves Santa Barbara

7. EQUATION OF MOTION (patch A): Adult stock [mt]Growth rate“Connectivity” = probability of dispersal Harvest [mt]Annual natural mortality rate Density dependent recruitment K = kelp [km2] Juvenile mortality t = time in years Tj = time until reproductively mature = age of legal size for fishery

8. CONSTRAINTS: Harvest in a patch must be equal or greater than zero, as well as equal or less than the current stock in that patch In Northern Channel Islands patch harvest may not reduce stock below 20% of its virgin size

9. 12 reserves constituting ~20% of the NCI coastline

10. EQUATION OF MOTION (patch A): Adult stock [mt]Growth rate“Connectivity” = probability of dispersal Harvest [mt]Annual natural mortality rate Density dependent recruitment K = kelp [km2] Juvenile mortality t = time in years Tj = time until reproductively mature = age of legal size for fishery

11. SBA NCI Thanks Mike!

14. (N = 4) Pattern supported by lobster/Kellet’s whelk fisherman (John Wilson, per. comm. 16 May 2007)

16. Protected in reserves

17. EQUATION OF MOTION (patch A): Adult stock [mt]Growth rate“Connectivity” = probability of dispersal Harvest [mt]Annual natural mortality rate Density dependent recruitment K = kelp [km2] Juvenile mortality t = time in years Tj = time until reproductively mature = age of legal size for fishery

18. Mean size (n = 1000+) m = 1/mean age = 0.068 Tj = ~6 years Annual natural mortality rate: Time until mature: Mature: (Growth data from D. Zacherl 2006 unpub. Res.)

19. EQUATION OF MOTION (patch A): Adult stock [mt]Growth rate“Connectivity” = probability of dispersal Harvest [mt]Annual natural mortality rate Density dependent recruitment K = kelp [km2] Juvenile mortality t = time in years Tj = time until reproductively mature = age of legal size for fishery

20. Kellet’s whelk, Kelletia kelletii 1000+ larvae per egg capsule

21. Density dependence coefficient Given each patch is a closed system and T j = 1: N* = virgin carrying capacity.

22. EQUATION OF MOTION (patch A): Adult stock [mt]Growth rate“Connectivity” = probability of dispersal Harvest [mt]Annual natural mortality rate Density dependent recruitment K = kelp [km2] Juvenile mortality t = time in years Tj = time until reproductively mature = age of legal size for fishery

23. C source-destination: C SBA-SBA = 0.15 C SBA-NCI = 0.34 C NCI-NCI = 0.35 C NCI-SBA = 0.27 Gastropod larva K. kelletia settler (OIPL 2007) (Koch 2006) SBA NCI Thanks James!

24. Of the total number of settlers arriving at a patch: Santa Barbara AreaNorthern Channel Islands SBANCI Closed system:

25. Economics:  Revenue based on demand curve:  revenue(t) = choke price – (Harvest[t])(slope)  Cost based on stock effect:  cost(t) = θ / stock density  π(t) = (revenue[t] – cost[t])(1 – r)^-t  r = discount rate = 0.05 ∫

26. Choke price = max(Price [1979-2005]) All whelks in system Profit calculated at end of each year’s harvest

27. mr = mc = θ / density, when density = 0.1*min(SBA* or NCI*)

28. mr, given supply = 1 mt Marginal profit calculated during harvest

29. Optimization procedure  Short-term: 40 years of harvest  Let un-harvested system equilibrate  Search for optimal harvest path: employ constrained nonlinear optimization function (derivative-based algorithm) in program Matlab.  Goal: find optimal H that maximizes NPV = ∑ π(t)  Long-term: Steady state (t → ∞)  Iterative exploration of all combinations of constant escapement (A – H ≈ 0 – 100%) in each patch.  run until system equilibrates  Goal: identify escapement combination that maximizes π at t = final.

30. Short-term (40-year) optimal harvest path

32. Harvest path is variable and different in the two patches

33. Higher Lower

34. Initial spike in harvest

35. Harvest limited by NCI reserve constraint

36. Harvest until mr = mc

37. Harvest path is semi-cyclic: due to delayed development?

38. NPV = ∑ π(t) = $1,279,900 ~$32,000/year

40. 10,000 simulations: NPV H* H* - (v/2)(H*)H* + (v/2)(H*) H(t) = H* + U[-v/2, +v/2](H*)

41. 10,000 simulations: 90% NPV H* H* - (v/2)(H*)H* + (v/2)(H*) NPV H(t) = H* + U[-v/2, +v/2](H*)

42. Long-term optimal harvest

43. Harvest everything

44. $68,067/year

45. Harvest everything $68,067/year 40-year horizon and r = 0.05: ~$31,000/year

46. Harvest everything $68,067/year 40-year horizon and r = 0.05: ~$31,000/year

47. Harvest everything $68,067/year 40-year horizon and r = 0.05: ~$31,000/year

48. Harvest everything 90%

49. Harvest everything Plenty Room for uncertainty: Little

50. 90% NCI reserve constraint Harvest everything NCI used as a source, regardless of regulation!

51. Future research: 1.Improve accuracy in parameter estimates (e.g., λ, population density) and re-run analysis. 1.Relevance of NCI reserve constraint? 2.Incorporate known variability (e.g., connectivity across years) and uncertainty (e.g., in λ and form of density dependence function) into analysis. 3.Apply model to a variety of systems characterized by different levels of connectivity.

52. Currents Oceanographic boundaries (Gaylord & Gaines 2000)

53. Central CA Southern CA US Mexico Borders dividing fishery management jurisdictions Is cooperation in cross- border management part of the optimal solution?

54. Thank you!

56. 10,000 simulations: 90% net present value H* H* - U[1-v,1+v](H*) H* + U[1-v,1+v](H*)

57. Southern hemisphere cetaceans (Hilborn et al. 2003)

58. “Rapid worldwide depletion of predatory fish” (Myers & Worm 2003)

59. Mean size (n = 1000+) m = 1/mean age = 0.068 Annual natural mortality rate:

60. Excellent for lawn art (match gnomes beautifully!)

61. Thank you!