Population Connectivity and Management of an Emerging Commercial Fishery

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

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

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. Santa Barbara 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

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

11. SBA NCI Thanks Mike!

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

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 Juvenile mortality Density dependent recruitment K = kelp [km2] t = time in years Tj = time until reproductively mature = age of legal size for fishery

18. Mean size (n = 1000+) Annual natural mortality rate: m = 1/mean age = 0.068 Mature: Time until mature: Tj = ~6 years (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 Juvenile mortality Density dependent recruitment K = kelp [km2] 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 Tj= 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 Juvenile mortality Density dependent recruitment K = kelp [km2] t = time in years Tj = time until reproductively mature = age of legal size for fishery

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

24. Of the total number of settlers arriving at a patch: Santa Barbara Area Northern Channel Islands Closed system: SBA NCI

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]) Profit calculated at end of each year’s harvest All whelks in system

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

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

42. Long-term optimal harvest

43. Harvest everything

44. $68,067/year Harvest everything

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

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

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

48. 90% Harvest everything

49. 90% Room for uncertainty: Plenty Little Harvest everything

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