DEEPFISHMAN
Using bioeconomic modeling
for evaluation of management
measures – an example
Institute of Economic Studies
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Construct a general bio-economic model
applicable to each case study for which
there exist appropriate data. Data
requirements
1. Stocks
2. Harvest
3. Costs
4. Revenue
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The model should be
1. Dynamic
2. Stochastic
3. Capable of incorporating various
management regimes
The model should be as simple as possible
(one cohort) to facilitate computations.
Probably Matlab-based.
Case study: Application of a stochastic, multispecies model for comparative evaluation of
fisheries policies in Denmark, Iceland and Norway
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Sustainable utilisation of marine resources in the
presence of volatile environment, both in the
ecological, physical and economic sense.
Based on a feedback model developed by Sandal
and Steinshamn (1997a, 1997b, 2001a).
Main characteristics:
• Feedback; optimal control (harvest) is a direct
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function of the state variable (stock)
Deterministic and stochastic version
Non-linear input functions
Multi-species; cod and capelin, herring and cod
Aggregate model
Goal: Find the time path of harvest that
maximises the present value of profits
Functions
• Logistic growth functions
• Linear profit functions
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Linear inverse demand function
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Non-linear cost function
• Interaction between species (cod
and herring/capelin)
Functions (cont.)
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Revenue functions
Cost functions
Development of fishable stock (4-14 years old)
1.600
1.400
1.200
´000 tons
1.000
800
600
400
200
0
1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
Year
Recruitment of three year old individuals. Millions.
400
350
Recruitment, millions
300
250
200
150
100
50
0
1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
Year
Harvest control rule
Introduced in 1995
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25% of fishable stock (average of estimate at
beginning of year and prediction for next year)
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155 thousand ton minimum
Change in 2000
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minimum abolished
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30 thousand ton limit on TAC-changes from year to year
Change in 2006
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Average of 25% of estimated stocks at the beginning of the
year and last year catches
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30 thousand ton limit abolished
Harvest control rule
Change in 2006
 Average of 25% of estimated stocks at the beginning
of the year and last year catches
 30 thousand ton limit abolished
Change in 2007
 TAC set at 130 thousand tons for the fishing year
2007/2008
 Average of 20% of estimated stocks, but a 130
thousand ton minimum
Harvest control rule and catch share.
Ht = 0.5*(0.25*Xt + Ht-1)
Catchshare
25%
12.5%
Catcht-1
Stockt
Harvest control rule
A harvest control rule can only be effective if
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Stocks are correctly estimated
Actual and projected (TAC) catches are the
same
Catches and TAC
300
250
´000 tons
200
150
100
Catch
TAC
TAC based on 2007 stock estimates
50
0
1995/96 1996/97 1997/98 1998/99 1999/00 2000/01 2001/02 2002/03 2003/04 2004/05 2005/06
Fishing year
Catches above TAC each fishing year.
Percentages of TAC.
16
14
12
%
10
8
6
4
2
0
1995/96 1996/97 1997/98 1998/99 1999/00 2000/01 2001/02 2002/03 2003/04 2004/05 2005/06
Fishing year
Feedback models
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Developed by Sandal and Steinshamn (1997,
2001), see also Arnason et al. (2004).
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Single species and two-species models, with or
without stochasticity
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Biological growth function
Allow for interaction between species in twospecies models. Aggregated biomass model.
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Profit function
Demand and cost functions estimated separately
Results
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Steady state cod stock (thousand tons) with harvesting
Single-species
1.230
Multi-species
1.445
Current estimates
650
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Evaluations of fishery policies
Stock evaluation; a value smaller than unity represents overexploitation
Single-species
0.53
Multi-species
0.43
Harvest evaluation; a value greater than unity represents overexploitation
Single-species
11.8
Multi-species
16.2
Actual and optimal harvest. Single-species
deterministic (σ=0) and stochastic models (σ>0).
σ=0
Surplus growth
σ=0,1x
Actual harvest
σ=0,5x
25% rule
Static optimal
130+20%
1000
900
800
Harvest
700
600
500
400
300
200
100
0
0
200
400
600
800
1000
Stock
1200
1400
1600
1800
2000
Two-species conclusions
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No harvesting of cod until cod stock is in excess of 500
thousand tons
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Size of capelin has little effect on this conclusion
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Minimum biomass before harvesting increases slightly
with the biomass of capelin, possibly because the intrinsic
growth rate of cod increases as the biomass of capelin
increases, making it more beneficial to conserve cod.
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Higher cod stocks; harvest is generally slightly lower the
bigger the stock of capelin. However, this effect is
reversed at low levels of capelin, probably to save the
capelin.
Comparison between actual and optimal harvest.
Actual harvest
Static optimal
1-d feedback
2-d feedback
1400
1200
Harvest
1000
800
600
400
200
0
1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
Conclusions
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Linear harvest control rules are not desirable; over-fishing when
stocks are low, under-exploitation when stocks are high
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Single-species models not very sensitive to introduction of
stochasticity when stocks are low. Larger role when stocks are
large.
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Single-species and multi-species model yield similar harvest
results.
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Multi-species models yield more conservative harvest policies
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The Icelandic cod stock has been overexploited