Marine reserves and fishery profit: practical designs offer optimal solutions.

Marine reserves and fishery profit: practical designs offer

optimal solutions.

Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of California – Santa Barbara

Larval export

No Fishin

g

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?

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

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)

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ty

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tx

tx

tx

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1tx RLK)FH(A)HM(AHAA

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

Incorporating Density Dependence

Post-dispersal: )Hc(Ao

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1tx RLK)FH(A)HM(AHAA

Larva settlement and/or recruitment success decreases with increasing adult population density at that location.

FEW LARGE RESERVES

SEVERAL SMALL RESERVES

θ = 5

θ = 0

Cost of catching one fish

= Density of fish at that location

θ

θ = 5

θ = 0

Bottom line for fishermen:

Profit = Revenue - cost



θ

θ = 20

θ = 0

Bottom line for fishermen:

Profit = Revenue - cost



θ

FEW LARGE RESERVES

SEVERAL SMALL RESERVES

Scale bar = 100 km

Scale bar = 100 km

Scale bar = 100 km

Max Yield without Reserves









A spectrum of high-profit scenariosMax Yield without Reserves

A spectrum of high-profit scenarios

Cost = θ/density



Cost = θ/density (Stop fishing when cost = $1)




Escapement = % of virgin K (K = 50)





Zero-profit escapement level = θ/K = 40%





Zero-profit escapement level = θ/K = 40%


A spectrum of high-profit scenariosθ/K = 15/50 = 30%






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.

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)

Summary 4. Given optimal reserve spacing, a near-maximum

profit is maintained across a spectrum of reserve and harvest scenarios:

ReservesNone/few

Many

EscapementHigh Low

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

EscapementHigh Low

None/few

University of California – Santa Barbara

National Science Foundation

THANK YOU!

Logistic model:

post-dispersal density dependence

No reserves:

Nt+1 = Ntr(1-Nt)

Yield = Ntr(1-Nt)-Nt

MSY = max{Yield}

dYield/dN = r – 2rN – 1 = 0

N = (r – 1)/2r

MSY = Yield(N = (r – 1)/2*r) = (r – 1)2 / 4r

Logistic model:

Scorched earth outside reserves


Reserves:

Nt+1 = crNr(1-Nr)

Nr* = 1 – 1/cr

Yield = crNr(1 – c)(1 – No)

Yield(Nr* = 1 – 1/cr) = -rc2 + cr + c – 1

dYield/dc = -2cr + r + 1 = 0

c = (r + 1)/2r

MSY = Yield(c = (r + 1)/2r) = (r – 1)2 / 4r

Ricker model:


No reserves:

Nt+1 = rNte-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

Ricker model:

Reserves:

Nr = crNre-gNr

Nr* = Log[cr] / g

Recruitment to fishable domain =

Yield = crNr(1 – c)e-gNo

Yield(Nr* = 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

Older, bigger fish produce many more young

Channel Islands

0 500 1000 15000

10

20

30

40

50Optimal Reserve Spacing

Distance between reserve centers [km]

Mea

n H

arv

est

Den

sity

[#

fis

h/k

m]

Reserve = 50% of the coastline

0 500 1000 15000

10

20

30

40

50Optimal Reserve Spacing

Distance between reserve centers [km]

Mea

n H

arv

est

Den

sity

[#

fis

h/k

m]

Dd = 100 kmDd = 200 kmDd = 300 km

Reserve = 50% of the coastline

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.

Scale bar = 100 km

Scale bar = 100 km

Marine reserves and fishery profit: practical designs offer

optimal solutions.

Crow White, Bruce Kendall, Dave Siegel, and Chris Costello University of California – Santa Barbara

Can Marine Reserves bolster fishery

yields?

NO RESERVES

RESERVES (E = 0% outside)

Larvae-on-larvae density dependence

equal

0.2

0

0

0

00

Fraction protected

d/L

= 0

.01

d/L

= 0

.03

d/L

= 0

.1d

/L =

0.3

Traditional 3-Reserve network

Pre-dispersal

nand

Pre- or post-

dispersaln andN

0.4

0.4 0.8 0 0.4 0.8 0 0.4 0.8

Two size classes

Yie

ld

0.2

0.4

0.2

0.4

0.2

0.4

Post-dispersal

nand

Short disperser

Long disperser

Marine reserves can exploit population structure and life history in improving potential fisheries yieldsBrian 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.

Logistic model:


No reserves:

Nt+1 = Ntr(1-Nt)

Yield = Ntr(1-Nt)-Nt

MSY = max{Yield}

dYield/dN = r – 2rN – 1 = 0

N = (r – 1)/2r

MSY = Yield(N = (r – 1)/2*r) = (r – 1)2 / 4r

Logistic model:

Scorched earth outside reserves


Reserves:

Nt+1 = crNr(1-Nr)

Nr* = 1 – 1/cr

Yield = crNr(1 – c)(1 – No)

Yield(Nr* = 1 – 1/cr) = -rc2 + cr + c – 1

dYield/dc = -2cr + r + 1 = 0

c = (r + 1)/2r

MSY = Yield(c = (r + 1)/2r) = (r – 1)2 / 4r

Ricker model:


No reserves:

Nt+1 = rNte-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

Ricker model:

Reserves:

Nr = crNre-gNr

Nr* = Log[cr] / g

Recruitment to fishable domain =

Yield = crNr(1 – c)e-gNo

Yield(Nr* = 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

Comparing MSYs:

MSYreserve = max{crLog[cr](1 – c) / g}

MSYfishable = max{ rNe-gN – N}

dYfishable/dN = re-gN – grNe-gN – 1 = 0

n 1 ProductLog

r

g

ProductLog[z] = w is the solution for z = wew

INCREASE

Costello and Ward. In Review.

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Marine reserves and fishery profit: practical designs offer optimal solutions.

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