1

Sustainable and Optimum

Fishery Yield

Takashi Matsuishi At SERD, AIT, Thailand 24Feb-14Mar, 2014

Surplus Production Model

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3

Surplus Production Model

Calculate Sustainable Yield from Russell’s Equation

Ye: Sustainable Yield V: Natural Growth

V depends on Biomass

V= 0 if B= 0

B have the upper limit K. V=0 at K

Ye =V will have a maximum point between B=0 and B= K

Maximum Sustainable Yield / MSY

MGAVYe

MSY and MSYL

4

K 0

V

B

MSY

MSYL

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Assumption of the Model

1. Equilibrium condition: Factors affecting the Population

dynamics is stable

2. Single Population: Population is single and closed

3. Fishable population constant：The variance of age

composition can be Ignored

4. Constant catchability

5. No time lag:

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The formulation of the Model

Without Fishing

rtae

KtB

1

K

BrB

dt

dB1

B(t

)

t

7

With Fishing

Basic Equation

r: intrinsic growth rate

B:Biomass

K：Carrying Capacity

q：Catchability Coefficient

E:Fishing Effort

At Sustainable Yield

qEBK

BrB

dt

dB

1

K

BrBqEBSY

dt

dB

1

0

quP

PqXYu e

/

V

B

SY

K

BrB 1

8

CPUE and E at equilibrium

r

qEKB

r

qE

K

B

K

B

r

qE

K

BrqE

K

BrBqEBY

1

1

1

1

1

Er

KqqK

E

Y

Er

KqqKEY

r

qEqEKqEBY

2

22

1

Er

KqqKCPUE

2

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Effort and SY

K

BrBqEBSY 1

Biomass

Sust

ainab

le Y

ield

Surp

lus

Pro

duct

ion

Fishing Effort

22

Er

KqqKESY

10

MSY

22

Er

KqqKESY

E vsSY

SY

E

B vs SY

K

BrBSY 1

B

SY

K

2K

4rK

qr 2

4rK

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Estimation of MSY from CPUE

Er

KqqKCPUE

Er

KqqKESY

2

22

bEaCPUE

brKq

aqK

2

b

a

Kq

rqK

q

rE

b

a

rKq

qKrKMSY

MSY22

1

2

444

2

2

2

2

baE

baMSY

MSY 2

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E

CPU

E CPUE=a-bE

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Example

King 1995

Per Recruit Analysis

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Overfishing

Overfishing

A form of overexploitation in which fish stocks are depleted to unacceptable levels

Growth overfishing

Biomass is depleted because fish are caught in small size.

Mainly the age at first capture is too small.

Recruit Overfishing

Biomass is depleted because the spawning stock size is too small to make a sufficient next generation

Mainly the fishing mortality (fishing effort) is too large

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Yield per Recruit Analysis

Yield per Recruit analysis is mainly for evaluate the stock

is in the state of Growth overfishing or not

It can be calculated from

Growth curve parameters

natural mortality

age at first capture

fishing mortality

small YPR means growth overfishing

It does not consider the spawning biomass.

use with SPR analysis

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Instantaneous Catch

Yw:Yield

F: Fishing mortality

Nt: Population in number

wt: weight per fish

ttw wNF

dt

dY

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Nt Population dynamics

Nt: Population

F:Fishing mortality

M:Natural mortality

tt NMF

dt

dN)(

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wt weight growth

w∞: Asymptotic average maximum body size

K: growth rate coefficient

t0: hypothetical age which the species has zero length

3)()1( 0ttK

t eww

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Yw Lifetime Yield

t

t

ww

cdt

dt

dYY

1,3,3,1

3,2,1,0

nA

n

)( 0ttMw

ceFRWY

3

0

))(()(

10

n

ttnKMFttnK

n c

c

enKMF

eA

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YPR

Parameters

)( rc ttMw eFWR

YYPR

3

0

))(()(

10

n

ttnKMFttnK

n c

c

enKMF

eA

W∞, K, t0: Growth Curve Parameter

M : Natural Mortality

tr: age at recruit

tλ: max age

Calculation in Excel

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2

3

4

5

6

7

8

9

10

0 0.2 0.4 0.6 0.8 1 1.2 1.4

tc

F

2-2.2

1.8-2

1.6-1.8

1.4-1.6

1.2-1.4

1-1.2

0.8-1

0.6-0.8

0.4-0.6

0.2-0.4

0-0.2

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YPR Contour

H

L Winf 14.8 K 0.19 t0 -0.73 M 0.25 tr 2 tl 10

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2

4

6

8

10

0 0.2 0.4 0.6 0.8

1 1.2 1.4 1.6 1.8

2 2.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4

tc

YP

R

F

2-2.2

1.8-2

1.6-1.8

1.4-1.6

1.2-1.4

1-1.2

0.8-1

0.6-0.8

0.4-0.6

0.2-0.4

0-0.2

2

3

4

5

6

7

8

9

10

0 0.2 0.4 0.6 0.8 1 1.2 1.4

tc

F

2-2.2

1.8-2

1.6-1.8

1.4-1.6

1.2-1.4

1-1.2

0.8-1

0.6-0.8

0.4-0.6

0.2-0.4

0-0.2

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YPR Contour

H

L tc=2.5

25

0

0.5

1

1.5

2

0 0.5 1 1.5

YP

R

F

tc=2.5

θ Fmax

MSY/R

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0

0.5

1

1.5

2

0 0.5 1 1.5

YP

R

F

tc=2.5

θ Fmax F0.1

θ/10

2

3

4

5

6

7

8

9

10

0 0.2 0.4 0.6 0.8 1 1.2 1.4

tc

F

2-2.2

1.8-2

1.6-1.8

1.4-1.6

1.2-1.4

1-1.2

0.8-1

0.6-0.8

0.4-0.6

0.2-0.4

0-0.2

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YPR Contour

H

L F=0.5

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0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2 4 6 8 10

YP

R

tc

F=0.5 MSY/R

tcmax

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YPR/F

F∝E

Y/X=CPUE∝N

YPR/F ∝CPUE∝N in equilibrium

2

3

4

5

6

7

8

9.5

0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5

tc

F

9-10

8-9

7-8

6-7

5-6

4-5

3-4

2-3

1-2

0-1

YPR/F

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H

L

Winf 14.8 K 0.19 t0 -0.73 M 0.25 tr 2 tl 10

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7.3ct

Right fig. : YPR contour

Left fig. : Section at tc=3.7

MSY at F=0.22 if recruit is constant

growth over fishing at F>0.22

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Increase biomass and catch together

• Simplified graph

• Curves at P(tc=3.7, F=0.73)

Area Yw/R Yw/RF

A + + B - + C - - D + -

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SPR(Index for recruit overfishing)

Spawning stock Per Recruitment

SSB×RPS=Recruit

(SSB=Spawning Stock Biomass)

Recuirt×SPR=SSB

If SPR×RPS=1 then stable.

%SPR= SPRF=Fcurrent / SPRF=0

30%SPR or more is recommended

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%SPR Contour

0

1

2

3

4

5

6

7

8

9

10

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

tc

F

90%-100%

80%-90%

70%-80%

60%-70%

50%-60%

40%-50%

30%-40%

20%-30%

10%-20%

0%-10%

H

L

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0

3.5

7 0%

10% 20% 30% 40% 50% 60% 70% 80% 90%

100% 0

0.2

0.4

0.6

0.8

1

1.2

1.4

tc

F

90%-100%

80%-90%

70%-80%

60%-70%

50%-60%

40%-50%

30%-40%

20%-30%

10%-20%

0%-10%

Value per recruit analysis Pavarot, Matsuishi et al. (2011 FS)

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VPR (Pavarot, Matsuishi et al. 2011)

Value per Recruit

Value = Yield x Unit price

Consider the price by size

max1 t

tttt

c

dtNFpR

VPR

max

c

exp11

t

ta

aaa NMFMF

Fp

RVPR

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Price Curve of Kichiji

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VPR and YPR

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VPR Merit and Perspective

Bioeconomic Analysis

Including the size dependency of the price

Does not include the yield dependency

Equilibrium analysis