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Training course in fish stock
assessment and fisheries
management
National Institute of Oceanography and Fisheries
Fish population Dynamics Lab
10-14 November, 2013ns
Surplus Production models
(Biomass Dynamic Models)
Prof. Dr. Sahar Fahmy Mehanna
Head of fish population dynamics lab
National Institute of Oceanography and
Fisheries
Surplus Production models
• The level of the biomass of a population at
time t+1 will depend to different
phenomena.
• While recruitment and individual
growth contribute to its increase
• mortality due to both natural causes and
removals by fishing activity will
contribute to its decline
Surplus Production models
Bt+1 = Bt + Recruitment + Growth effects Natural Mortality – Catch
When there is no fishing, the combination of
recruitment and growth is called Production
Bt+1 = Bt + Production (P) - Natural
Mortality (M)
Surplus Production models
In the case P>M, the population will grow.
The “Surplus Production” is defined as the
increased amount of the population
biomass in the absence of fishing or the
amount of catch that can be harvested
keeping biomass constant.
Bt+1 = Bt + Surplus Production – Catch
in the case Catch > Surplus Production,
the biomass will decrease.
Surplus Production models
Data requirements
• In general use data on catch and effort
• Equilibrium
• Problems with quantification of
effective effort
• Multispecies-multigear fisheries (target,
spatial and temporal changes…)
Some definitions
Catch= landed fraction + discards + undefined
incidental deaths
Effort: Fishing effort (f) is the labour, vessels,
skill and technology used in catching fish.
One unit of fishing effort removes a certain
constant fraction of a stock
this effort is directly related to the fishing
mortality (F) through a constant called
catchability coefficient (q)
Is catchability constant along time?
Some definitions
F = qf
q is the fraction of F produced by a unit of effort
hence q may be a different value depending on
which unit of effort is used!
The choice of a suitable unit of effort
Catch
Annual catches (avoidance of errors) due to:
• Under-reporting (critical for management with TAC’s)
• Discard at sea
(individuals under legal size)
• Not quantified incidental deaths (fish that is able to
escape but successively will die due to bad conditions)
Effort
• Definition of effort for such gear (trawlers, gill
nets, hooks, traps)
• Partitioning among species and fisheries
• Standardization by vessels characteristics
• Technological improvements along time
The more classical relationship between stock
biomass and surplus production
450
400
Surplus Prod.
350
300
250
200
150
100
50
0
0
500
1000
B
1500
2000
In general, there is no available information
on Biomass, but on an abundance index as
CPUE (Catch per unit of effort).
The most popular versions of production models
use data of catch and fishing effort in order to
define which is the yield that is likely to be
produced at different levels of exploitation.
Fishing effort
2400
Fishing effort
FISHING
Fishing
effort
4000
3600
3200
EFFORT
5600
5200 5600
5600
4800 5200
5600
5200
4800
4400
PELLA &
TOMLINSON
4000
3.5
4400 4800
5200
3600
3200
2800
2400
2000
1600
4
4000
4800
4400
4400
3600
4000
3200
3600
2800 2800
3200
2800
2400
2000
0
1200
2
2400
2000
1600
0.5
800
1.5
1600
2000
1
1200
1
400
1.5
1200
2.5
2.5
1600
0.5
0
3
800
400
800
C/f
3
1200
C/f
2
800
0
400
400
0
0
0
C/f
Ye
5000
4500
4000
3500
3
3000
2500
2.5
2000
2
1500
1.5
1000
1
500
0.50
SCHAEFER
FOX
PELLA & TOMLINSON
FOX
SCHAEFER
0
PRODUCTION MODEL
SCHAEFER (1954)
Bt+1=Bt + rBt (1-Bt/K)-Ct - t+1
FOX (1970)
Bt+1=Bt + rBt (1-(lnBt/LnK))-Ct - t+1
PELLA & TOMLINSON (1969)
Bt+1=Bt + rBt (1-Bt/K)p - Ct - t+1
B=biomass
r= intrinsic rate of population growth
K= Virgin stock biomass ( “carrying capacity”)
CW = catch in weigth
P= shape parameter
Sustainable means the value obtained assuming f remains
unchanged for a certain number of years (equilibrium)
4
4000
MSY
3.5
3500
3
3000
Ye
Ye
2500
2.5
2000
2
1.5
1500
1
1000
0.5
500
Fishing
Fishing effort
effort
fMSY
6000
6000
5600
5600
5200
5200
4800
4800
4400
4400
4000
4000
3600
3600
3200
3200
2800
2800
2400
2400
2000
2000
1600
1600
1200
1200
800
400
0
0
The population adapt to the different levels of effort and
reach a new equilibrium under each exploitation rate. In
this case, a direct relationship between fishing effort and
biomass in equilibrium (and hence with catch) can be
defined
250
Yield
200
150
100
50
0
0
500
1000
1500 2000
Fishing effort
2500
3000
Equilibrium concept
Recruitment (annual contribute of the new
generations or cohorts) of similar entity
Survival rates unchanged along the lifespan
of the species (for all the observed cohorts)
In consequence, demographic structure of
the population remains similar along time
USE OF FISHERIES DEPENDENT DATA
DATA ON DEMOGRAPHIC STRUCTURE OF THE CATCHES
NOT AVAILABLE
ONLY CATCH AND EFFORT DATA AND STOCKS NOT
Penaeus kerathurus
IN EQUILIBRIUM
EFFORT CATCH
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
17760.00
14640.00
11760.00
10320.00
10800.00
12000.00
12560.00
12640.00
12560.00
12160.00
11760.00
11360.00
11280.00
11286.67
11260.00
11200.00
3454.465
3293.402
1956.614
1389.932
1652.774
3171.509
1699.105
2467.796
5066.293
3322.602
6577.858
5210.565
3406.528
6065.723
4915.034
6458.907
ASPIC 5.0 (Prager, 1994, 2005)
A Stock-Production model Incorporating Covariates
• non-equilibrium
• continuous-time
• observation-error estimator
• dBt/dt = (r-Ft)Bt-(r/K)Bt2
ASPIC (Prager, 1994, 2005)
MAIN OUTPUTS OF ASPIC
FITTING MODELS
FORECASTING
TARGET AND LIMIT
REFERENCE POINTS
Reference Points derived from the Threshold
Biomass approach
T is a threshold value of Biomass that is supposed to be
a lower limit below which depensation mechanisms can
be triggered
Fmax is the level of F that produces the maximum Yield
Ymax is the maximum yield potentially obtained
FT (threshold) is the value of F corresponding to BT
Multispecies Surplus production models
10
10
10
Y 999
SPECIES1
SPECIES1
SPECIES1
SPECIES2
SPECIES2
TOTAL
TOTAL
SPECIES3
TOTAL
TOTAL
888
777
666
555
444
33
33
22
22
1
111
0
000
1 4 7 10
13
16
19
22
25
28
31
34
37
40
43 46
49 52
55 58
10
13
16
19 22
22 25
25 28
28 31
31 34
34
3740
40
111 444 777 10
28
31
3437
37
404343
434646
46
49
52
55
58
10 13
13 16
16 19
4949
5252
5555
58 58
61
Fishing effort
Overall Maximum Sustainable Yield can be risky for
the less productive species