Marine reserve spacing and fishery yield: practical designs offer optimal solutions.

 

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

2 = # reserves at a given site

Larval export

No Fishin

g

Research Question:

To maximize larval export (and fishery yield) should reserves be… …few and large,

When is larval export maximized?

…or many and small?

SLOSS debate

Reaction Diffusion model

Adults move and reproduce simultaneously

Larvae mature into adults instantaneously

Real coastal fish & invert population dynamics 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 success inversely proportional to adult density at settlement location (post-dispersal density dependence) (e.g. Lorenzen and Enberg 2002, Steele and Forrester 2002)

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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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FEW LARGE RESERVES

SEVERAL SMALL RESERVES

FEW LARGE RESERVES

SEVERAL SMALL RESERVES

Scale bar = 100 km

Scale bar = 100 km

Scale bar = 100 km

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 = 10% 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]

Reserve = 10% of the coastline

20%

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 = 10% of the coastline

20%

30%

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 = 10% of the coastline

20%

30%

40%

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 = 10% of the coastline

20%

30%

40%

50%

CHANNEL ISLANDS MARINE PROTECTED AREAS

~20% coastline into 10 no-take reserves

All < 15 km wide

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 = 20% 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]

Reserve = 10% of the coastline

20%

30%

40%

50%

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

5

10

15

20

25

30

35

40

45When is Yield Fully Maximized?

% Coastline Dedicated to Reserve Status

Me

an Y

ield

[#

/km

], g

iven

Op

tim

al

Res

erv

e S

pac

ing

10% escapement

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

5

10

15

20

25

30

35

40

45When is Yield Fully Maximized?

% Coastline Dedicated to Reserve Status

Me

an Y

ield

[#

/km

], g

iven

Op

tim

al

Res

erv

e S

pac

ing

10% escapement

20%

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

5

10

15

20

25

30

35

40

45When is Yield Fully Maximized?

% Coastline Dedicated to Reserve Status

Me

an Y

ield

[#

/km

], g

iven

Op

tim

al

Res

erv

e S

pac

ing

10% escapement

20%

30%

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

5

10

15

20

25

30

35

40

45When is Yield Fully Maximized?

% Coastline Dedicated to Reserve Status

Me

an Y

ield

[#

/km

], g

iven

Op

tim

al

Res

erv

e S

pac

ing

10% escapement

20%

30%

40%

Summary 1. Post-dispersal density dependence generates larval

export.

Summary 1. Post-dispersal density dependence generates larval

export.

2. Larval export varies with reserve size and spacing.

Summary 1. Post-dispersal density dependence generates larval

export.

2. Larval export varies with reserve size and spacing.

3. Yield maximized via…

Summary 1. Post-dispersal density dependence generates larval

export.

2. Larval export varies with reserve size and spacing.

3. Yield maximized via…

Less than ~15% coastline in reserves

…Any reserve spacing option.

Summary 1. Post-dispersal density dependence generates larval

export.

2. Larval export varies with reserve size and spacing.

3. Yield maximized via…

Less than ~15% coastline in reserves

…Any reserve spacing option.SLOSS

Summary 1. Post-dispersal density dependence generates larval

export.

2. Larval export varies with reserve size and spacing.

3. Yield maximized via…

Less than ~15% coastline in reserves

…Any reserve spacing option.SLOSS

Summary 1. Post-dispersal density dependence generates larval

export.

2. Larval export varies with reserve size and spacing.

3. Yield 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.

SLOSS

Summary 1. Post-dispersal density dependence generates larval

export.

2. Larval export varies with reserve size and spacing.

3. Yield 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.

SLOSS

SLOSS

Summary 1. Post-dispersal density dependence generates larval

export.

2. Larval export varies with reserve size and spacing.

3. Yield 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.

SLOSS

SLOFMOSSSLOSS

Summary 1. Post-dispersal density dependence generates larval

export.

2. Larval export varies with reserve size and spacing.

3. Yield 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.

SLOSS

SLOFMOSSSLOSS

Summary 1. Post-dispersal density dependence generates larval

export.

2. Larval export varies with reserve size and spacing.

3. Yield 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.

SLOSS

SLOFMOSSSLOSS4. Yield may be maximized when reserves constitute

a large fraction of the coastline, and fishing elsewhere is intensive.

University of California – Santa Barbara

National Science Foundation

THANK YOU!