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Population Connectivity and Management of an Emerging Commercial Fishery. Crow White ESM 242 Project May 31, 2007. Kellet’s whelk Kelletia kelletii. Adult (15 cm) Recruits. Focus of developing fishery Sold to US domestic Asian market (mostly in LA)
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Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 Project May 31, 2007
Kellet’s whelk Kelletia kelletii Adult (15 cm) Recruits
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
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?
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
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
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
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
SBA NCI Thanks Mike!
Pattern supported by lobster/Kellet’s whelk fisherman (John Wilson, per. comm. 16 May 2007) (N = 4) (N = 4)
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
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.)
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
Kellet’s whelk, Kelletia kelletii 1000+ larvae per egg capsule
Density dependence coefficient Given each patch is a closed system and Tj= 1: N* = virgin carrying capacity.
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
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!
Of the total number of settlers arriving at a patch: Santa Barbara Area Northern Channel Islands Closed system: SBA NCI
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 ∫
Choke price = max(Price [1979-2005]) Profit calculated at end of each year’s harvest All whelks in system
mr = mc = θ / density, when density = 0.1*min(SBA* or NCI*)
mr, given supply = 1 mt Marginal profit calculated during harvest
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.
Higher Lower
NPV = ∑ π(t) = $1,279,900 ~$32,000/year
H(t) = H* + U[-v/2, +v/2](H*) NPV 10,000 simulations: H* - (v/2)(H*) H* H* + (v/2)(H*)
H(t) = H* + U[-v/2, +v/2](H*) NPV 10,000 simulations: H* - (v/2)(H*) H* H* + (v/2)(H*) 90% NPV
$68,067/year Harvest everything
40-year horizon and r = 0.05: ~$31,000/year $68,067/year Harvest everything
40-year horizon and r = 0.05: ~$31,000/year $68,067/year Harvest everything
40-year horizon and r = 0.05: ~$31,000/year $68,067/year Harvest everything
90% Harvest everything
90% Room for uncertainty: Plenty Little Harvest everything
90% NCI reserve constraint NCI used as a source, regardless of regulation! Harvest everything