Chapter 13 in Top Predators in Marine Ecosystems. Their Role in Monitoring and Management..
Cambridge, UK.: Cambridge University Press 2006. ISBN 978-0-521-84773-5. s. 310-323
The Scenario Barents Sea Study, a Case of Minimal
Realistic Modelling to compare Management Strategies
for Marine Ecosystems
Tore Schweder1
Abstract
Management of a marine ecosystem is regarded as a game played by the Government Agency against
Nature. The quality of the management strategy is evaluated using models for the strategy taken by Nature.
These models should be sufficiently realistic and also practical to implement and investigate on a computer.
Whaling and sealing in the Barents Sea are of little economic interest of themselves, but might impact some
other fisheries positively. Our model to evaluate strategies for whaling and sealing includes cod, herring,
capelin, harp seals and minke whales, and emphasizes interactions between these populations caused by
predation. For proposed management strategies, the stochastic system is repeatedly simulated over 100
years, and the strategies are evaluated by the resulting cod, capelin and herring TACs that are calculated
from fixed rules. Our line of study was first pursued in the 1990s with an emphasis on management
strategies for cod, herring and minke whales. It is now extended and refined with harp seals included, and
with improved modelling of how predation mortality in the fish species is non-linearly linked to the
abundances of all the modelled species.
Introduction
Scenario modelling to evaluate management strategies was originally developed for
whaling, but is now increasingly applied in fisheries. The basic idea is to establish a
minimal but realistic model for computer simulation of the system, with removals
governed by a management strategy, predation and additional natural mortality. The
system is projected forward under competing strategies for a number of years and in
replications to capture the statistical uncertainties surrounding the system. Strategies are
compared in terms of their simulated long term performance.
The purpose of the present study is to evaluate the effect on the cod-, capelin-, and
herring fisheries of managing minke whaling and harp sealing in the Barents Sea in this
way. The study is funded by the Norwegian Ministry of Fisheries. In a recent White
Paper (Stortingsmelding nr. 27) on the management of marine mammals in Norwegian
waters, the Ministry plans “to establish a scientific basis for changing to ecosystem-based
management where marine mammal stocks are managed in conjunction with the other
living marine resources”.
To manage a marine ecosystem is to play a game with Nature, and perhaps also with
other players such as fishermen and industries which are causing the system to become
increasingly polluted. The game we consider is played by the Agency (Government
body) and Nature.
1
Norwegian Computing Center, Box 114 Blindern, 0314 Oslo, Norway; and Department of Economics,
University of Oslo, Box 1095 Blindern, 0317 Oslo, Norway; tore.schweder@econ.uio.no
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Chapter 13 in Top Predators in Marine Ecosystems. Their Role in Monitoring and Management..
Cambridge, UK.: Cambridge University Press 2006. ISBN 978-0-521-84773-5. s. 310-323
The concept of strategy is central to game theory. A management strategy is a feed-back
rule that specifies the action to be taken, given the history of the process as observed by
the player. For our purpose, the actions open to the Agency are to set total allowable
catches (TACs) for removals of harp seals and minke whales. The Agency also sets
TACs for the fisheries. TACs are assumed to be exactly filled if abundance allows.
Fishermen behave also according to economic realities, and may discard or take more
than the TAC. These economic realities are disregarded here.
The strategy of Nature is determined by the internal dynamics of the ecosystem, and its
dynamic reaction to the removals caused by the fisheries. The better the Agency knows
Nature’s strategy, the better it can assess the quality of a given management strategy for
whaling and sealing. Our study is an attempt to assemble the available knowledge and
data pertinent to the relevant dynamics of the upper trophic level of the ecosystem.
Despite more than 100 years of marine research in the area and despite the system is less
complex than many other ecosystems and comparably well known, our knowledge of the
Barents Sea ecosystem is rather limited. The quality of understanding varies considerably
depending on the topic. For features of the ecosystem about which little is known, the
model must be simple in order not to spread the available information too thinly. Other
better known features might be less relevant for the interaction between the modelled
species, and are therefore modelled in less detail than is possible. Our aim is not a
detailed description of the ecosystem representing all available knowledge, but rather a
practical and reasonably realistic model tailored to the purpose of the study. Borrowing a
term from Punt and Butterworth (1995), a model that balances realism and uncertainty,
and that is operational and practical to use, is called a minimal realistic model.
We consider the Barents Sea, including the spawning grounds for North East Arctic cod
in Lofoten, and also a residual area where Norwegian spring spawning herring and minke
whales are found when they are not present in the Barents Sea. Only young herring
migrates to the Barents Sea. The minke whales feed in the study area and breed elsewhere
during winter. With our limited and pragmatic purpose, we will include only harp seals,
minke whales, cod, capelin and herring in the model. Hamre (1994) describes the main
features of the Barents Sea- Norwegian Sea ecosystem.
A strategy should be evaluated in terms of its anticipated performance in the long run.
The system needs more than 100 years to become stationary, due the slow dynamics of
minke whales. We will therefore simulate catches and stock status over at least a
hundred-year period, and study performance by statistics summarising the simulation
results. It is beyond the scope of this study to give weights to the various objectives for
management, and to interpret results in financial terms.
The model has yearly stochastic variation, mainly in fish recruitment and in the stock
abundance estimates on the basis of which TACs are set. This last uncertainty applies
also to abundance estimates for minke whales and harp seals, and translates into
stochastic variation in TACs for these species as well.
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Chapter 13 in Top Predators in Marine Ecosystems. Their Role in Monitoring and Management..
Cambridge, UK.: Cambridge University Press 2006. ISBN 978-0-521-84773-5. s. 310-323
The Agency is faced with uncertainties with respect to the population dynamics of the
key stocks, and also to the interactions caused by predation between stocks. These
uncertainties are handled by drawing parameters from statistical distributions for each run
of the simulation model, but uncertainties with respect to functional forms are not
addressed.
Historical background
The present study (2002-2004) is a sequel to a previous Scenario Barents Sea study. The
aim of that earlier study was to compare management strategies for cod, capelin and
herring (Hagen, Hatlebakk and Schweder 1998). The model was previously extended to
study the effects on the fisheries of retuning the Revised Management Procedure of the
International Whaling Commission (the RMP of the IWC, International Whaling
Commission 1994) for minke whales (Schweder, Hagen and Hatlebakk 1998; 2000). In
addition to including harp seals in the current model, the structural forms of the predation
models are changed, and they are re-estimated.
Our study, and that of Punt and Butterworth (1995), which was developed to reflect
recommendations reported in Butterworth and Harwood (1991), has been inspired by the
simulation approach taken when the RMP of the IWC was developed for managing single
baleen whale stocks (Kirkwood, Hammond and Donovan, 1997). The resulting RMP is
robust against the type and extent of uncertainties that usually surrounds stocks of baleen
whales, as demonstrated in a scenario study focusing on uncertainties represented by
variability and bias in survey data, and in variations in the population dynamics, e.g. in
the shape and strength of density dependent recruitment, changes in carrying capacity,
episodic events etc.
In the early 1970s the Club of Rome based its gloomy predictions on scenarios simulated
on computers to illustrate environmental effects of population growth and industrial
activity. This work was inspired by Buckminster Fuller, who educated many Americans
in strategic thinking and in the use of simulation through computers and otherwise to
improve environmental and other policies. He conducted military war games to save
Spaceship Earth from destruction (http://www.bfi.org) throughout American university
campuses, and was an inspiration to the environmental movement.
The present Scenario Barents Sea model
Overview
Cod, capelin, herring, harp seals and minke whales are distributed over the seven areas
used in previous studies (Bogstad et al. 1997) plus a residual area (Figure 1), and over
age and month. Fish are also distributed over lengths. The chosen subdivision of the
study area and the time step is regarded as the coarsest possible temporal and spatial
stratification respecting gradients in seasonal overlaps between predators and prey in the
Barents Sea system (S. Tjelmeland, personal communication, 2004).
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Chapter 13 in Top Predators in Marine Ecosystems. Their Role in Monitoring and Management..
Cambridge, UK.: Cambridge University Press 2006. ISBN 978-0-521-84773-5. s. 310-323
Moving from one month to the next, surviving fish of the same length are allocated to
new length groups according to an individual growth schedule which depends on season
and species. Individual growth in cod depends on the supply of capelin, but is
independent of prey availability for capelin and herring. A fixed length-weight
relationship for each fish species is used for calculating the biomass of the species at any
time. This is needed because fish TACs and predation are calculated in biomass terms.
The population dynamics model for minke whale is taken from International Whaling
Commission (1993), and is identical to that in Schweder et al. (1998). The model for harp
seal is taken from Skaug and Øien (2003). Recruitment in cod, capelin and herring is
modelled by Beverton-Holt functions augmented with stochastic variability.
Minke whales and harp seals are top predators. Their population dynamics is modelled as
unaffected by fish stock abundance. While this is not quite realistic, it is nevertheless
considered adequate for present purposes because the modelled population dynamics
broadly reflect prey abundances similar to those expected over the simulation period. The
marine mammals prey on all three species of fish, and also on other organisms, as do cod
which is a cannibal. Herring prey on capelin larvae. Capelin is at the base of the model.
The interactions between populations are modelled solely as mortality due to predation.
These interactions are additive in the sense that they act only to cause removals.
Hjermann, Stenseth and Ottersen (2004) found the mortality factors to be additive and not
compensatory for Barents Sea capelin. Fishing is also assumed to cause removals but not
have indirect effects. In addition to mortality due to modelled removals, there is a
component of fixed residual natural mortality.
Predation is modelled in two steps. The daily biomass consumed is calculated for each
group of predators from energetic considerations and from other sources,. This
consumption is then split between the groups of prey according to prey choice
probabilities. The prey choice probabilities are estimated from stomach content data and
estimated prey availability by time and area.
Key equations of the model are discussed below, together with some comments on the
estimation of their parameters. Additional information is found at:
http://www.nr.no/files/samba/emr/scenario_document.pdf
Recruitment and yearly dynamics
Juvenile capelin are recruited as one year olds on 1 October. Juvenile cod and herring are
recruited as one year olds on 1 January. Given a spawning stock with biomass B , the
number of recruits, R , one year later is calculated from the Beverton-Holt function
R = Lµ B /( B + η ) ,
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Chapter 13 in Top Predators in Marine Ecosystems. Their Role in Monitoring and Management..
Cambridge, UK.: Cambridge University Press 2006. ISBN 978-0-521-84773-5. s. 310-323
with multiplicative log-normal stochastic variation L with median 1 and coefficient of
variation σ , maximal recruitment in median years µ , and half-value parameterη . There
are stochastically chosen abnormal years, where the recruitment parameters are switched
to more productive values. Newly recruited fish are distributed by length group.
Recruitment in minke whales follows the age- and sex-structured model used by the
International Whaling Commission. The median age at maturity is seven years, and the
fecundity drops as the number of mature females N approaches a carrying capacity K
according to the Pella Tomlinson formula
( (
R = N β 1+ α 1− ( N / K )
z
)) ,
where β is the mean number of live births per year for mature females at carrying
capacity, α is the resilience parameter, and z is the degree of compensation. The last
two parameters determine the stock level, here 60% of carrying capacity, corresponding
to maximum sustainable yield. Recruitment to the exploitable stock happens one year
after birth. The recruitment parameters are estimated using catch data, abundance data,
and a series of relative abundance indices based on catch and effort data (Schweder et al.
1998).
Recruitment in harp seals is also modelled by the Pella Tomlinson formula above, but
with z = 1 degree of compensation, making the maximum sustainable yield stock level
around 50% (Skaug and Øien, 2003).
Migration and monthly dynamics
Monthly age-dependent transition matrices between areas (migration matrices) based on
survey data were developed by Bogstad et al. (1997). The stationary distributions related
to these matrices are used to distribute the various populations over areas, by month and
age.
Mortality in fish has three components: removals due to fishing, removals due to
modelled predation, and residual natural mortality. Removals due to fishing are
calculated from the yearly TAC, and distributed according to a specified scheme over
areas and months.
TACs for cod and herring are calculated from yearly abundance estimates obtained from
a simple VPA assessment by applying fixed fishing mortalities, and based on catch data
and yearly survey data simulated with noise. Capelin is managed according to the
approach described in Gjøsæter, Bogstad and Tjelmeland (2002) which, approximately, is
to set aside the estimated amount of capelin needed to feed the cod, and also 500
thousand tons of capelin to spawn.
The removals due to predation in a given month and area are calculated from the number
of predators present and the biomass of all their prey species, as described below. From
the number of individuals in a given category at the beginning of a month, the number
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Chapter 13 in Top Predators in Marine Ecosystems. Their Role in Monitoring and Management..
Cambridge, UK.: Cambridge University Press 2006. ISBN 978-0-521-84773-5. s. 310-323
consumed by predators and the number harvested are subtracted, and the remainder are
reduced further as a result of the residual mortality rate.
Predation
Predation models are estimated anew for cod, minke whales and harp seals. They consist
of two components: total amount eaten per day, and diet choice probabilities depending
on prey abundance. The quantity consumed is estimated from energetic considerations for
harp seals and minke whales, and also from experimental and observational studies for
cod. The choice probability models have a common multiple logistic format, and are
estimated by comparing the type of prey found in sampled stomachs to estimated prey
abundance at the time and in the area of sampling.
Food takes time to digest, and sampled stomachs often have mixed contents. Each
stomach is therefore regarded as representing three feeding events, and a rule codes them
by food item. Minke whales, for example, can choose between capelin, herring, cod and
other food, indexed from 1 to 4. If only one item is found in a stomach, all three feeding
events are coded by this item. For a covariate vector x representing area-specific
abundance of cod, capelin and herring, and for parameter vectors β k related to food item
k , the model consists of the linear predictors θ k = ∑ β ki xi leading to the logistic choice
i
probabilities
pk = exp (θ k ) / ∑ exp (θ j ) .
4
j =1
Zhu (2003) estimated the following diet choice model for minke whales
θ k = −1.82 I herring − 2.52 I capelin − 3.63I cod + 0.000231Bk + 0.265log( Bk ) ,
where Bk is abundance (in thousands of tons) of fish species k in the area, and I herring
indicates whether herring is present or not, and similarly for cod and capelin. Other food
is the reference category, θ other = 0 (i.e. pother = 1/ (1 + θ cod + θ cap + θ her ) ). All coefficients,
except that for linear abundance, are highly significant.
For harp seals, stomachs are sampled mainly on the ice north in the Barents Sea in
summer (Nilssen et al. 2000). Folkow, Nordøy and Blix (2004) found from satellite
tagging that Greenland Sea harp seals regularly migrate to the Barents Sea in summer and
autumn, and spend about half their time there in open water, presumably feeding on
capelin. The stomach contents found in sampled harp seals are therefore not
representative of the diet in the important summer feeding period in the Barents Sea. The
same presumably applies to harp seals from the White Sea, which constitutes the
dominant harp seal stock in the Barents Sea.
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Chapter 13 in Top Predators in Marine Ecosystems. Their Role in Monitoring and Management..
Cambridge, UK.: Cambridge University Press 2006. ISBN 978-0-521-84773-5. s. 310-323
Management
Fisheries are modelled to be managed by fixed and simple rules. Minke whaling is
managed by the RMP of the IWC, tuned at three different levels, while harp sealing is
managed by three different rules taken from ICES (2001). There are thus nine different
combinations of management procedures for whaling and sealing to compare.
Discussion
Current management
Fish
TACs for cod are set to target a fishing mortality of F = 0.4 when spawning stock
biomass is estimated above B pa . The stock is assessed by the VPA-method XSA, see
ICES (2004). The capelin and herring fisheries are essentially managed as modelled.
Minke whaling
Currently, Norway has a fleet of some 33 fishing vessels that harvest minke whales in the
summer months in Norwegian waters. Whaling accounts for about 25% of the income for
this fleet, and is economically sustainable. Minke whaling resumed in 1993 after it was
stopped in 1987. The catch has increased from some 250 whales in 1993-1995 to some
600 whales in recent years. This is slightly below the TAC calculated from the
management strategy. Vessel quotas are given to licensed whalers. The catch is closely
controlled with skilled observers on board.
The TAC for minke whales is calculated by the RMP of the IWC. The input data to the
RMP is the catch series and the series of absolute abundance estimates obtained from
double platform line transect surveys (Skaug et al. 2004).
The RMP can be tuned to target various population levels under cautious standard
assumptions. In the early years, a target level of 72% of carrying capacity was used to set
Norwegian minke whale TACs. This target level is that which would be reached after 100
years of application of the RMP to a stock, originally at its pristine level, with the lowest
productivity rate considered plausible. In 2003 the tuning level was reduced to 66%, and
for 2004 to 62%, resulting in higher TACs.
Harp sealing
Norwegian sealing is currently a small heavily subsidized industry carried out with old
specialized sealing vessels. In the 1990s the yearly average number of harp seals taken in
the Barents Sea by Norway was 6200, and has declined in recent years.
Norway manages harp sealing in the Barents Sea together with Russia, and according to
advice from ICES, which calculates TACs to keep the stock at its current level. The
White Sea – Barents Sea stock is now estimated to comprise nearly two million adults,
and the TAC was 53000 adult equivalents (one adult equals 2.5 pups) in 2001-2003, well
above the catch. Pups become adult at age 1.
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Chapter 13 in Top Predators in Marine Ecosystems. Their Role in Monitoring and Management..
Cambridge, UK.: Cambridge University Press 2006. ISBN 978-0-521-84773-5. s. 310-323
The economics of sealing has improved somewhat recently, but sealing will probably
need substantial subsidies to raise the catch to what is currently regarded as sound from
an economic perspective for the fishery as a whole (Stortingsmelding nr. 27).
Management issues
The Norwegian Government wants to develop a management strategy for sealing and
whaling as part of a management regime for the ecosystem containing fish and marine
mammals. For this to have scientific support, substantial research is needed, as
acknowledged in the White Paper. Since harp seals, cod and capelin are managed jointly
by Norway and Russia, while herring is managed by five parties: Norway, Russia, the
Faroes, Iceland and the EU, management of this ecosystem is far from being a national
issue for Norway alone.
The model described above is an improvement of the model used by Schweder et al.
(1998), who studied the effect on the fisheries of re-tuning the RMP of the IWC for
minke whaling. The revision is not yet complete, and no results are available. To
illustrate the type of results anticipated, our earlier tentative conclusion was that on
retuning the RMP from targeting 72% of carrying capacity down to 60%, annual catches
increase by some 300 minke whales, and 0.1 million ton cod on average. The effect on
the herring fishery was unclear. The effect on the long term minke whale abundance was
a reduction from about 96000 to 87000 whales.
Whether the previously estimated effects on fisheries from increased minke whaling will
be maintained in our current study remains to be seen. It also remains to be seen whether
increased sealing will influence the fisheries positively to the degree currently expected
by the Government and fishermen.
Modelling considerations
The various parts of the model were first estimated on relevant data, but in isolation from
the rest of the model and from other data. The model as a whole is however more than the
sum of its parts, and this piecewise estimation has turned out to be unsatisfactory. To
balance the model it has been necessary fit the model simultaneously to historical data.
This is work in progress.
The approach is the following. Assume abundance estimates with associated uncertainty
measures to be available for years 1,",T . From estimated stock status in year t , the
model predicts the stock status in year t + 1 when all parameters have given values.
Comparing the abundance estimates and the one-year predicted stock status in year t + 1 ,
accounting for observed catches, leads to a likelihood component. In addition to these
likelihood components, each piecewise fitting results in a likelihood component. The
total likelihood is then obtained by combining all the likelihood components, and
parameters are estimated by maximizing this combined likelihood.
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Chapter 13 in Top Predators in Marine Ecosystems. Their Role in Monitoring and Management..
Cambridge, UK.: Cambridge University Press 2006. ISBN 978-0-521-84773-5. s. 310-323
The log-likelihood function is expected to be approximately quadratic in the parameter
vector, perhaps after a parametric transformation. The (transformed) parameter vector
then has a multivariate normal confidence distribution representing the uncertainty in
estimated model parameters (Schweder and Hjort, 2002).
Conclusion
Our model rests on a number of assumptions of varying degrees of realism. Feedback
from fish to marine mammals is disregarded. Little is actually known of this feedback,
which presumably is of importance at least for harp seals (Haug and Nilssen, 1995). The
modelled populations interact only by removals due to predation. Other interactions are
indeed conceivable. The residual mortality rate is assumed constant, but is presumably
variable. The category “other food” has been modelled as always available in sufficient
supply. There are also a number of assumptions regarding structure and data that are open
to criticism. The predation model for harp seals is, for example, based on selective and
weak data. Making the model more realistic will on most counts entail more complexity.
The uncertainties surrounding the model are indeed substantial. They are handled by
drawing parameter values from statistical distributions in each simulation run. These
distributions will also rest on assumptions, and will broadly represent sampling
variability in the data used to estimate coefficients. There are additional uncertainties not
taken into account, particularly regarding the structure of the model and functional forms.
To establish a minimal realistic model for the upper trophic levels of the ecosystem in the
Barents Sea, also as regards the handling of uncertainty, is quite a challenge to address
adequately. The alternative to scenario modelling is however not to model, and thus to
leave the choice of management strategy to qualitative judgment. This will probably lead
to a bad strategy, perhaps based on political compromises without much consideration for
ecosystem dynamics. From this point of view, our model might in fact be criticized for
being too complex relative to the available knowledge and data, and relative to the
purpose of the exercise.
Our model, programmed in 25000 lines of C-code, might actually be too complex.
Having struggled to estimate recruitment- and mortality parameters by fitting the model
to historical data, we have not yet managed to balance the model to our satisfaction.
When simulating the model, stock trajectories in some of the runs are implausible, and
they vary too much between runs compared to historical data. Our small project is thus
unsuccessful in that no comparative simulation experiments useful for management could
be performed.
As mentioned, the Norwegian Government wants to move towards ecosystem
management of marine mammals based on science. This commitment to science is
encouraging. Our project might have been useful as a learning exercise, but more
research is needed to establish a sufficiently credible model needed for ecosystem
management. In addition to the research needs created by the Norwegian commitment to
ecosystem management, we think this research aiming at a scenario model for the Barents
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Chapter 13 in Top Predators in Marine Ecosystems. Their Role in Monitoring and Management..
Cambridge, UK.: Cambridge University Press 2006. ISBN 978-0-521-84773-5. s. 310-323
Sea should be carried forward also for general reasons. The Barents Sea system is in fact
less complex than other marine systems of comparable size in terms of biomass in the the
upper trophic level, and if marine ecosystem management at all is possible, it should
indeed be so in the Barents Sea
Acknowledgements
Thanks to Gro Hagen of Norwegian Computing Center for keeping the computer program under control,
and to Bjarte Bogstad, Ulf Lindström and Sigurd Tjelmeland of the Marine Institute, for providing data and
biological insight.
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Cambridge, UK.: Cambridge University Press 2006. ISBN 978-0-521-84773-5. s. 310-323
Figure 1. Spatial division of the Barents Sea, adapted for MULTISPEC (Bogstad et al.
1997).
12