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1
Sustainable and Optimum
Fishery Yield
Takashi Matsuishi At SERD, AIT, Thailand 24Feb-14Mar, 2014
Surplus Production Model
2
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
5
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:
6
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
9
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
11
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
42
E
CPU
E CPUE=a-bE
12
Example
King 1995
Per Recruit Analysis
13
14
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
15
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
16
Instantaneous Catch
Yw:Yield
F: Fishing mortality
Nt: Population in number
wt: weight per fish
ttw wNF
dt
dY
17
Nt Population dynamics
Nt: Population
F:Fishing mortality
M:Natural mortality
tt NMF
dt
dN)(
18
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
19
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
20
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
21
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
22
YPR Contour
H
L Winf 14.8 K 0.19 t0 -0.73 M 0.25 tr 2 tl 10
23
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
24
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
26
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
27
YPR Contour
H
L F=0.5
28
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
29
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
30
H
L
Winf 14.8 K 0.19 t0 -0.73 M 0.25 tr 2 tl 10
31
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
32
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 + -
33
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
34
%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
35
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)
36
37
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
38
Price Curve of Kichiji
39
VPR and YPR
40
VPR Merit and Perspective
Bioeconomic Analysis
Including the size dependency of the price
Does not include the yield dependency
Equilibrium analysis
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