Download - Population Connectivity and Management of an Emerging Commercial Fishery

Population Connectivity and Management of an Emerging

Commercial Fishery

Crow White ESM 242 Project May 31, 2007

Adult (15 cm)

Recruits

Kellet’s whelk

Kelletia kelletii

Focus of developing fishery

Sold to US domestic Asian market (mostly in LA)

Mean price = $1.43/kg = ~$0.15/whelk

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ltin

e-N

eils

on

et

al.

200

6

Caught as by-catch by commercial trap fishermen

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?

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

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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

CONSTRAINTS:

tt NH 0Harvest in a patch must be equal or greater than zero, as well as equal or less than the current stock in that patch

*, 2.0 BBH tBt

In Northern Channel Islands patch harvest may not reduce stock below 20% of its virgin size

12 reserves constituting ~20% of the NCI coastline

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Juvenile mortality

t = time in years


SBA

NCI

Thanks Mike!

SBA NCI

0.00

0.20

0.40

0.60

0.80D

en

sit

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E [

#/m

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(N = 4) (N = 4)

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

Protected in reserves

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Juvenile mortality

t = time in years


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.)

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Juvenile mortality

t = time in years


Kellet’s whelk, Kelletia kelletii

1000+ larvae per egg capsule

mLog

K

Ng

1*

Density dependence coefficient

Given each patch is a closed system and Tj = 1:

N* = virgin carrying capacity.

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Juvenile mortality

t = time in years


Csource-destination:

CSBA-SBA = 0.15

CSBA-NCI = 0.34

CNCI-NCI = 0.35

CNCI-SBA = 0.27

Gastropod larva K. kelletia settler

(OIPL 2007) (Koch 2006)

SBA

NCI

Thanks James!

Of the total number of settlers arriving at a patch:

Santa Barbara Area Northern Channel Islands

SBA NCI

Closed system:

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])

All whelks in system

Profit calculated at end of each year’s harvest

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 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.

Short-term (40-year) optimal harvest path

Harvest path is variable and different in the two patches

HigherLower

Initial spike in harvest

Harvest limited by NCI reserve constraint

Harvest until mr = mc

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

NPV = ∑ π(t) = $1,279,900

~$32,000/year

10,000 simulations:NPV

H*H* - (v/2)(H*) H* + (v/2)(H*)

H(t) = H* + U[-v/2, +v/2](H*)

10,000 simulations:

90% NPVH*H* - (v/2)(H*) H* + (v/2)(H*)

NPV

H(t) = H* + U[-v/2, +v/2](H*)

Long-term optimal harvest

Harvest everything

Harvest everything

$68,067/year

Harvest everything

$68,067/year

40-year horizon and r = 0.05: ~$31,000/year

Harvest everything

90%

90%

Harvest everything

Plenty

Room for uncertainty:

Little

90%

NCI reserve constraint

Harvest everything

NCI used as a source, regardless of regulation!

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.

Currents

Oceanographic boundaries

(Gaylord & Gaines 2000)

Central CA

Southern CA

US

Mexico

Borders dividing fishery management jurisdictions

Is cooperation in cross-border management part of the optimal solution?

Thank you!

10,000 simulations:

90% net present value

H*H* - U[1-v,1+v](H*)

H* + U[1-v,1+v](H*)

Southern hemisphere cetaceans (Hilborn et al. 2003)

“Rapid worldwide depletion of predatory fish” (Myers &

Worm 2003)

Mean size (n = 1000+)

m = 1/mean age = 0.068

Annual natural mortality rate:

Excellent for lawn art (match gnomes beautifully!)

Thank you!