Download Single and multispecies reference points for Baltic

ICES Journal of Marine Science, 56: 571–583. 1999
Article No. jmsc.1999.0492, available online at http://www.idealibrary.com on
Single and multispecies reference points for Baltic fish stocks
H. Gislason
Gislason, H. 1999. Single and multispecies reference points for Baltic fish stocks. –
ICES Journal of Marine Science, 56: 571–583.
Single and multispecies models are used to examine the effect of species interaction on
biological reference points for cod, herring, and sprat in the Baltic. The results
demonstrate that reference points are different in single and multispecies contexts.
Reference points for fishing mortality based on single-species yield and SSB calculations are difficult to use when natural mortality depends on the absolute abundance of
the predators and their alternative prey. Reference points based on maximizing total
yield from the system may lead to impractical results when species interact. Multispecies predictions suggest that the cod stock in the Baltic should be reduced to a very low
level of biomass in order to benefit from the higher productivity of herring and sprat,
its major prey. Such a result stresses the need for incorporating socio-economic
considerations in the definition of target reference points. Management advice based
on biomass reference points will also differ. In the single species situation the
combinations of cod and pelagic fishing effort for which the equilibrium spawningstock biomass of the three species is above the biomass reference points forms a
rectangular area. When biological interaction is taken into account the limits of this
area becomes curved. Reference limits for forage fish cannot be defined without
considering changes in the biomass of their natural predators. Likewise, reference
limits for predators cannot be defined without considering changes in the biomass of
their prey.
1999 International Council for the Exploration of the Sea
Key words: multispecies models, biological reference points, species interaction.
Received 26 October 1998; accepted 12 May 1999.
H. Gislason: University of Copenhagen, c/o Danish Institute for Fisheries Research,
Charlottenlund Castle, DK2920 Charlottenlund, Denmark. Tel: +45 33963361; fax:
+45 33963333; e-mail: [email protected]
Introduction
The call to develop a precautionary approach to fisheries
management has recently renewed the debate about the
definition and estimation of biological reference points
(e.g. Smith et al., 1993; Caddy and Mahon, 1995; FAO,
1995; Rosenberg and Restrepo, 1995; ICES, 1997c).
Biological reference points are used as benchmarks to
characterize the state of a stock or fishery. They are
commonly divided into target and limit reference points.
Target reference points represent a desired level of
fishing mortality or biomass, while limit reference points
are used to define either an upper bound to the fishing
mortality or a lower bound to the biomass.
Biological reference points are often derived from
models where the yield from the fishery and the biomass
of the exploited stock is related to fishing mortality
(Caddy and Mahon, 1995). It is common practice to use
single-species models where each species is considered in
isolation from the rest of the ecosystem. Little effort has
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so far been spent on examining how reference points
might be defined and used in a multispecies context.
However, species interactions are likely to have direct
effects on biological reference points (Brander, 1988;
ICES, 1997d). Failure to account for these may lead to
undesirable outcomes, such as overexploitation and
stock collapses, even if the probability of such outcomes
appears to be negligible in a single species analysis. Not
accounting for species interactions may be just as problematic as neglecting uncertainty in the basic assessment
data in the overall management plan (ICES, 1997d).
Previous analyses of multispecies and multifleet fisheries models have shown that the maximum overall
benefit to society cannot be estimated without considering the relative value of the different species caught and
the costs associated with their capture (May et al., 1979;
Flaaten, 1988). In fisheries where the economic benefit
to society is the overriding management concern, it has
been proposed to use the maximum of the long-term
resource rent, defined as the gross catch value minus
1999 International Council for the Exploration of the Sea
572
H. Gislason
the harvest costs, as the main economic management
objective (Flaaten, 1998).
The fish community in the Baltic Sea is relatively
simple and dominated by cod, herring, and sprat
(Elmgren, 1984). These species are the primary targets
for the commercial fishery and the interactions among
them are well studied (Sparholt, 1994). Single and
multispecies model are used to estimate and compare a
few of the commonly used reference points for cod,
herring, and sprat in the central Baltic. The models are
initially used to assess the historic stock size and fishing
mortality of the three species. Based on these assessments long-term equilibrium predictions of yield, biomass, value, and resource rent are made at various
fishing mortalities.
food available. In years with less food available growth
will be slower. Weight at age of cod is thus described by:
where Avail(a,y): is the amount of food available to cod
age group a in year y; w̄(a,y) is the average weight of cod
age group a in year y; and:
The model framework
The models consist of a single-species VPA (Gulland,
1965; Megrey, 1989), a MultiSpecies VPA (MSVPA)
(Gislason and Helgason, 1985; Sparre 1991; Magnusson,
1995), and an extended MultiSpecies VPA (MSGVPA),
in which cod growth and maturity are modelled as a
function of available food.
All three models were used in both retrospective and
predictive modes and operated with an annual timestep.
In the predictive mode an average of the fishing mortalities over a recent number of years was used to predict
long-term equilibrium yields and biomasses in the status
quo situation. Separate effort multipliers were used to
change the status quo fishing mortalities generated by the
two major fisheries: the cod fishery and the pelagic
fishery for herring and sprat. An index of total catch
value was calculated by multiplying the catch of each
species by its relative first-hand price. An index of costs
was generated by assuming that the fisheries presently
are in bionomic equilibrium where costs and catch value
balance (Clark, 1985), and that costs were directly
proportional to effort. Resource rent was estimated by
subtracting costs from the value of the catch.
Recruitment was predicted from a Ricker stock and
recruitment relationship (Ricker, 1954):
N (0,y)=R1 SSB(y)exp[R2 SSB(y)]
where w̄obs(a,y) is the average observed weight at age of
cod age group a in year y; and ny is the number of years
over which the calculations are performed.
Food consumption is calculated by assuming constant
conversion efficiency at age:
where R(a,y) is the per capita food consumption of cod
age group a in year y; and CE(a) is the conversion
efficiency; i.e. the proportion of the total food intake
that is converted to somatic growth for cod age group a.
In a model where growth and food intake depend on
the amount of available food, it is inconsistent to assume
that the biomass of other food is constant and does not
respond to changes in predation. The model was therefore extended by a simple description of the dynamics of
other food in which the biomass of other food was made
a function of the predator’s intake.
The total intake of other food of type b, is calculated
by the model from:
(1)
where R1 and R2 are species-specific constants determined from the recruitment and SSB estimated in the
retrospective part of the models.
In the MSGVPA, cod growth depends on the amount
of available food. Weight-at-age is assumed to equal
weight-at-age in the cohort during the preceding year
plus a growth term. The growth term depends on
whether the amount of available food in a particular
year is above or below the average. Growth will be faster
than average in years where there is more than average
where Suit(a,b) is the suitability of other food of type b
to predation by cod age group a; N
z (a,y) is the average
number of fish alive in age group a during year y; and
B
z (b,y) is the average biomass of other food of type b in
year y.
The average biomass of other food of type b was
assumed to decline exponentially as a function of the
amount eaten:
B
z (b,y)=exp[K(b)L(b)Cons(*,b,y)]
(7)
Baltic fish stocks
where B
z (b,y) is the average biomass of other food of
type b in year y; K(b) is a constant expressing the log of
the biomass of other food type b when predation is zero,
corresponding to the unexploited biomass in a surplus
production model; and L(b) is a constant expressing the
amount of change in log biomass of other food per unit
of predator consumption.
Finally, the forecasting part of the model was
extended to take changes in maturity at age of cod into
account by introducing a sigmoid relationship between
the proportion mature and body weight:
PM(a,y)={1exp[PM1*w̄(a,y)]}PM2
(8)
where PM1 and PM2 are constants determined by
non-linear regression of proportion mature vs. observed
weights at age.
Input data
The three models were used to analyse a single set of
assessment data from the central Baltic, which cover the
period from 1977 to 1996. Catch-at-age, terminal fishing
mortalities, proportion mature-at-age, single-species
total natural mortality, and weight-at-age for herring
and sprat were taken from ICES (1997a). For cod,
quarterly weight-at-age and stomach contents data for
1977–1991 were obtained from the revised set of input
data generated by ICES (1997b).1 The quarterly values
were averaged for each year to produce annual mean
weights-at-age and annual stomach content at age.
Residual natural mortality, M1(s), was set to 0.2 for all
three species, the same value as used in ICES (1997b).
Food conversion efficiencies for different age groups of
cod were taken from ICES (1992). An index of firsthand value was derived by assuming that cod was 10
times as valuable as herring and sprat. This estimate
reflects the relative price in Denmark and Sweden, two
of the major fishing nations (Directorate of Fisheries,
1997; OECD, 1997).
In the stomach content database, all food items except
cod, herring, and sprat are lumped together in one
category of ‘‘other food’’. However, the species composition of this category is not the same for large and
small cod. For cod >50 cm (age group 4+) it consists
almost exclusively of a large isopod, Saduria entomon,
while for smaller cod other invertebrates are also
included (Sparholt, 1994). Initial attempts to model cod
growth with only one category of other food proved
unable to describe the changes in the growth of older
cod, and it was therefore decided to split other food into
1
The database is currently being revised, but the most recent
version of the data was kindly made available by Stefan
Neuenfeldt (pers. comm.).
573
Saduria and other invertebrates. First, it was assumed
that other food of age 4+ cod contained only Saduria.
Secondly, for ages 1–3, it was assumed that Saduria
constituted the same proportion of the diet as for older
cod and that the remainder of the other food category
consisted of other invertebrates. In the MSVPA, the
biomass of Saduria was set to 4 million tons and the
total amount of ‘‘other invertebrates’’ to 10 million
tons. In the MSGVPA, these biomasses were used to
calculate K(b). Alternative biologically plausible
values for the biomass of ‘‘other invertebrates’’ and
Saduria produced virtually identical results in both the
MSVPA and MSGVPA, confirming the insensitivity of
the models to the input biomass of other food (Finn
et al., 1991). The observed weights-at-age for the
0-group and for all age groups in 1977 were used as the
starting values in the growth model incorporated in
the MSGVPA.
Parameter estimation
Annual fishing mortalities were estimated by Newton
iteration in all three models. Average suitability coefficients in the two multispecies versions were estimated
from all available stomach content data in an iterative
procedure as explained in Magnusson (1995). The parameters, L(b), used to describe the change in the biomass of invertebrates and Saduria in the MSGVPA were
estimated by minimizing the sum of squares of deviation
between observed and estimated weight-at-age in the
model.
The Ricker stock recruitment relationship was fitted
separately for each model. Because of changes in
environmental conditions, cod recruitment success has
changed considerably over the years (Sparholt, 1996).
The number of recruits produced per SSB drop in the
middle of the 1980s (Sparholt, 1995). In order not to
generate too optimistic predictions only data from the
low recruitment period from 1986 to 1995 were used.
The right hand downward sloping side of the Ricker
curve is often attributed to cannibalism (Hilborn and
Walters, 1992). In the multispecies models, cannibalism
is already dealt with, and, in accordance with Sparholt
(1995, 1996), a linear rather than a dome-shaped stock
recruitment relationship for cod was therefore assumed
by setting the parameter R2 to zero. For herring and
sprat, the data contained little information about the
shape of the stock recruitment curve. Initial parameter
estimates resulted in recruitment maxima far outside the
observations and produced unlikely predictions of virgin
stock biomass. The parameters were therefore selected
so that the maximum of the stock recruitment curve
corresponded to the point defined by the average SSB
and average recruitment over the period from 1977 to
1995.
574
H. Gislason
1.40
600
1.20
500
1.00
Av. F(4–7)
SSB, tons (×103)
(a)
700
400
300
0.80
0.60
200
0.40
100
0.20
0
1977
1982
1987
0.00
1977
1992
1982
1987
1992
3
Recruitment at age 0 (×10 )
Recruitment at age 0 (×103)
100 000
10 000
1000
100
1977
1982
1987
1000
500
0
1992
100
200
300
SSB
400
500
0.40
1600
0.35
1400
0.30
1200
Av. F(3–6)
SSB, tons (×103)
(b)
1800
1000
800
600
0.20
0.15
400
0.10
200
0.05
0
1977
1982
1987
0.00
1977
1992
Recruitment at age 0 (×103)
100 000
10 000
1000
100
1977
1982
1987
1992
140 000
1 000 000
Recruitment at age 0 (×103)
0.25
1982
1987
120 000
100 000
80 000
60 000
40 000
20 000
1992
Figure 1. (a) and (b).
0
1000
SSB
2000
Baltic fish stocks
575
(c)
2500
0.70
0.60
SSB, tons (×103)
2000
Av. F(3–7)
0.50
1500
1000
0.40
0.30
0.20
500
0
1977
0.10
1982
1987
0.00
1977
1992
1982
1987
1992
Recruitment at age 0 (×103)
Recruitment at age 0 (×103)
1 000 000
100 000
10 000
1000
100
1977
1982
VPA
1987
MSVPA
400 000
300 000
200 000
100 000
0
1992
MSGVPA
VPA
500
1000
SSB
MSVPA
1500
2000
MSGVPA
Figure 1. (c).
Figure 1. Spawning-Stock Biomass (SSB), average fishing mortality (F), recruitment, and SSB recruitment relationship estimated
by single-species VPA, MSVPA, and MSGVPA. (a) cod, (b) herring, (c) sprat.
The non-linear regression used to estimate the parameters in the equation describing the proportion
mature-at-age explained 99% of the variance in the
data.
The status quo fishing mortality used in the prediction
was calculated by rescaling the average exploitation
patterns to the fishing mortality in 1996, the last year of
the retrospective analysis.
Basic output
The spawning-stock sizes, average fishing mortalities,
recruitment estimates, and stock recruitment relationships produced by the three models are compared in
Figure 1. The models produce almost identical estimates
of spawning-stock biomass, but recruitment differs.
Prior to 1990, recruitment is generally estimated to have
been at a higher level in the multispecies models than in
the single species VPA. The estimated fishing mortalities
are similar, except for sprat, where fishing mortality is
estimated to be lower prior to 1986 in the multispecies
models.
The total predation estimated by the two multispecies
models is shown in Figure 2. The estimated consumption of cod, herring, and sprat is of the same magnitude
in both models, but is less variable in the MSGVPA than
in the MSVPA.
The predicted weight at age of cod in the MSGVPA is
compared to the observed in Figure 3 for cod age groups
1–5. For ages 1–3 the predicted weight at age is close to
the observed, but they deviate for ages 4 and 5, particularly in the most recent years. In addition, the discrepancy between the patterns for ages 4 and 5 in 1990–1992
suggests that there may be problems with the weight-atage data. Correlations between observed and predicted
weight-at-age were significant for all ages (Fig. 4). However, with the exception of age group 3, the predicted
weight-at-age in general changed less than the observed.
The status quo fishing mortality for cod, herring, and
sprat is given in Table 1 together with the corresponding
spawning-stock biomasses and virgin SSB’s estimated
from each model. Note that for herring and sprat the
status quo SSB’s are larger than the virgin SSB’s in both
multispecies models.
576
H. Gislason
2.5
2000
1800
(a)
1600
2.0
Age 5
1200
Weight (kg)
Tons (×103)
1400
1000
800
600
1.5
Age 4
1.0
Age 3
400
Age 2
200
0.5
0
1977
1982
1987
1992
Age 1
2000
1800
(b)
Cod
Herring
Sprat
1600
1982
1987
Year
1992
Figure 3. Observed weight-at-age (filled symbols) of cod ages
1–5 compared to estimated weight-at-age from MSGVPA
(open symbols).
1400
Tons (×103)
0.0
1977
1200
1000
Results
800
600
400
200
0
1977
1982
1987
Year
1992
Figure 2. Total consumption of cod, herring, and sprat estimated by (a) MSVPA and (b) MSGVPA.
Selection of reference points
ICES (1997c) contains a list of commonly used reference
points. Many of these are derived by using single-species
SSB per recruit calculations to estimate the fishing
mortality corresponding to a specific replacement line in
a plot of SSB vs. recruitment (e.g. Flow, Fmed, Fhigh,
Fcrash, and Floss). It is not straightforward to estimate
these reference points in a multispecies context, because
natural mortality, and hence also SSB per recruit,
changes as a function of the absolute abundance of the
predators and their prey (Gislason, 1991, 1993). A
particular replacement line is a function of both fishing
and predation mortality and these may vary independently. Therefore, only target reference points based on
predictions of yield (F0.1, FMSY), value, and resource
rent were considered together with limit reference points
based on predictions of virgin SSB or on precautionary
SBB, Bpa, as defined by ICES (1997c, 1998).
Figure 5a shows how FMSY for cod depends on the
relative fishing effort in the pelagic fishery. In the
single-species model, where natural mortality and
growth are constant, FMSY is constant. In the two
multispecies models, FMSY depends on the amount of
pelagic fishing effort, because cod cannibalism increases
as the pelagic fishery reduces the biomass of herring and
sprat. An increase in the fishing mortality of cod will
counteract the increase in cannibalism by reducing the
biomass of older cod. FMSY is higher in MSGVPA than
in MSVPA. In MSGVPA, a higher fishing mortality and
lower stock size will be counteracted by increases in cod
growth. The effort in the pelagic fishery that will generate the maximum catch of herring and sprat combined is
likewise a function of cod effort (Fig. 5b). If the biomass
of cod is high (low cod fishing mortality), predation
mortality is high. With a high predation mortality,
fishing mortality has to be reduced in order to avoid
recruitment overfishing. Except for herring and sprat at
low cod fishing mortality, the single-species model produces lower FMSY values than the two multispecies
models.
The F0.1 curves follow the same pattern as the FMSY
curves (Fig. 5c and d). Again the two multispecies
models generate higher F0.1 values than the singlespecies model, and both for cod and for herring and
sprat combined, F0.1 increases as a function of the
fishing effort in the alternative fishery. Therefore, if there
are strong species interactions, it is impossible to derive
a single fixed value for FMSY for any species, without
Estimated weight-at-age
Estimated weight-at-age
Estimated weight-at-age
Baltic fish stocks
0.4
1.8
R2 = 0.70
Age 1
1.6
577
R2 = 0.42
Age 4
0.3
1.4
0.2
1.2
1.0
0.1
0.8
0
1.0
0.1
0.2
0.3
2
0.4 0.6
Age 2
R = 0.79
2.4
0.8 1.0 1.2 1.4 1.6 1.8
2
Age 5
R = 0.27
0.8
2.0
0.6
1.6
0.4
1.2
0.2
0
1.2
0.2
0.4
1.0 0.8
4.5
Age 3
4.0
0.6
0.8
R2 = 0.88
1.0
1.6
0.8
2.0
R2 = 0.17
2.4
Age 6
3.5
0.8
3.0
0.6
2.5
2.0
0.4
0.2
1.5
0.4 0.6 0.8 1.0 1.2 1.0
Observed weight-at-age
1.5 2.0 2.5 3.0 3.5 4.0 4.5
Observed weight-at-age
Figure 4. Estimated vs. observed weight-at-age for cod ages 1–6.
Table 1. Estimates of status quo fishing mortality (year 1), SSB, and virgin SSB (103 tons)
produced by the three models.
Status quo F
Cod
age 4–7
VPA
MSVPA
MSGVPA

 0.67

Herring
age 3–6

 0.27

Status quo SSB
Sprat
age 3–7

 0.32

Virgin SSB
Cod
Herring
Sprat
Cod
Herring
Sprat
221
233
330
970
1610
1510
628
939
826
687
632
705
1929
1006
1096
1137
839
818
conditioning this value on the stock size of its predators
and/or prey.
An alternative would be to define FMSY as the effort
combination that generates the maximum total yield
from the system. In the single-species situation the result
is trivial: The maximum yield is generated by keeping
fishing mortality at FMSY in each of the fisheries, i.e. by
decreasing cod effort by 30% and increasing pelagic
effort by 26%. In the multispecies situation, both models
show that cod should be fished down to the lowest
biomass possible in order to benefit from the higher
productivity of its prey. Because cod is more valuable
than herring and sprat these results make little sense in a
management context.
The value surfaces are shown in Figure 6 and the
effort multipliers for which the maximum overall value is
578
H. Gislason
3
(a)
Relative pelagic effort
Relative cod effort
1.5
1.0
0.5
0
1
2
3
Relative pelagic effort
1
0.5
1.0
1.5
Relative cod effort
2.0
0.5
1.0
1.5
Relative cod effort
2.0
3
(c)
Relative pelagic effort
Relative cod effort
2
0
1.5
1.0
0.5
0
(b)
1
2
3
Relative pelagic effort
VPA
(d)
2
1
0
MSVPA
MSGVPA
Figure 5. Relative effort corresponding to FMSY (a) or F0.1 (c) in the cod fishery vs. relative effort in the fishery for pelagic species,
and relative effort corresponding to FMSY (b) or F0.1 (d) in the pelagic fishery vs. relative effort in the cod fishery.
obtained are given in Table 2a. The single-species
results are again trivial. As before, the maximum value
is generated at the single-species FMSY by reducing cod
effort by 30% and increasing pelagic effort by 26%. In
the MSVPA, cod effort should be increased by 15%
and pelagic effort by 63% to generate the maximum
value. The MSGVPA predicts that cod effort should be
increased by 86% and pelagic effort by 82% to reach
the maximum. The differences between the two latter
models is again due to compensatory changes in
weight- and maturity-at-age, making the cod stock
more resilient to exploitation in MSGVPA than in
MSVPA.
Estimating F0.1, the fishing mortality where the slope
of the value surface is a tenth of the slope at the origin,
is not straightforward. The slope at the origin is a
function of both cod and pelagic fishing mortality.
Various fixed relationships between cod and pelagic
effort factors were therefore explored. For each fixed
relationship, the slope at the origin was determined and
the point where the slope of the value surface was 10% of
the slope at the origin identified (Fig. 7). In all three
models the F0.1 contour bends backward at low cod
effort. The highest values of F0.1 are generated by the
MSGVPA, whereas the single-species model produced,
in general, the lowest. However, there is no simple
relationship between the fishing mortalities generated by
the two fisheries and the overall F0.1. Thus, in a multispecies context it appears difficult to use the overall F0.1
as a target reference point.
The effort combinations that would generate the
maximum resource rent are given in Table 2b. For cod
the three models produce similar results. Cod fishing
mortality should be approximately halved to generate
the maximum resource rent. For the pelagic fishery the
answers depend on the model. In the multispecies
models, fishing mortality should be reduced to 10% or
less of the present level, while in the single-species model
fishing mortality should be halved. The difference
between single and multispecies results is once again
caused by the indirect effect of herring and sprat
biomass on cod cannibalism.
The three models were also used to investigate limit
reference points based on total spawning-stock biomass.
The equilibrium SSB for cod, herring, and sprat were
predicted for various combinations of cod and pelagic
effort. These predictions were compared to the biomass
reference points by plotting the effort combinations that
would lead to stock sizes below or above a particular
reference point in a surface plot (Fig. 8). Two different
reference points were considered. The fishing mortality
where SSB fell below 50% of the virgin SSB (Fig. 8a–c),
and the precautionary biomass reference point, Bpa
(Fig. 8d–f) adopted by ICES (1998). The target reference
Baltic fish stocks
(a)
579
Table 2. Effort multipliers for which the highest value of the
total landings (a) and the highest resource rent (b) of the Baltic
fishery is obtained. Cod is assumed to be 10 times more
valuable than herring and sprat, and costs in (b) to be directly
proportional to effort (total value in arbitrary units).
(a)
2.1
1.9
1.7
1.5
1.1
0.9
0.7
Fishery
Cod effort
1.3
0.5
Cod
Herring and sprat
Total value
(b)
Fishery
0.3
VPA
MSVPA
MSGVPA
0.70
1.26
1720
1.15
1.63
2047
1.86
1.82
2300
VPA
MSVPA
MSGVPA
0.42
0.47
1401
0.45
0.03
1264
0.45
0.10
1371
0.1
6.0
5.0
4.0
3.0
2.0
1.0
(b)
Cod
Herring and sprat
Total value
0.0
2.1
1.9
2.0
1.7
VPA
MSVPA
MSGVPA
1.5
0.9
0.7
1.5
Cod effort
1.1
Cod effort
1.3
1.0
0.5
0.3
0.5
0.1
6.0
5.0
4.0
3.0
2.0
1.0
0.0
0
(c)
2.1
1.7
1.5
0.9
0.7
0.5
0.3
0.1
6.0
5.0
4.0
3.0
2.0
Pelagic effort
0–500
500–1000
1500–2000
2000–2500
1.0
1000–1500
0.0
Cod effort
1.1
1.0
1.5
Pelagic effort
2.0
Figure 7. Isolines of F0.1 estimated by single-species predictions,
MSVPA, and MSGVPA. F0.1 estimated as the effort combination where the slope of the relative value of the total catch is
one-tenth of the slope at the origin.
1.9
1.3
0.5
points corresponding to maximum catch value and
resource rent are also included in the figure.
In the single species case, the combination of efforts
where all three species are above 50% of their virgin SSB
is rectangular (Fig. 8a). For a cod effort above half the
present, the cod stock will be below 50% of its virgin
biomass. For herring and sprat, an increase in effort
above the present will produce a SSB below B50%. In
MSVPA, the cod effort influences the borderline where
Figure 6. Relative total value of catch for different combinations of effort in the pelagic and cod fishery. Cod assumed to be
10 times as valuable as herring and sprat. (a) Single-species
predictions, (b) MSVPA, (c) MSGVPA.
580
H. Gislason
Figure 8. Effort combinations for which the predicted SSB is above either 50% of the virgin SSB (a,b,c) or above Bpa (d,e,f) shown
together with the effort combinations corresponding to the current fishing mortality, maximum overall value of catch, and
maximum net revenue. Bpa equal to 240, 1000, and 275 thousand tons for cod, herring, and sprat, respectively (ICES 1998). (a),
(d) Single-species predictions, (b), (e) MSVPA, (c), (f) MSGVPA.
Baltic fish stocks
the pelagic species drop below 50% of their virgin level. If
cod effort is high, the cod stock and the predation
mortality it generates on herring and sprat are both
reduced. In this situation, sprat and herring can sustain
higher fishing mortalities before their biomasses fall
below the limit. If pelagic effort is high, cannibalism of
cod increases, and the stock is no longer able to sustain
high effort. The same applies to the MSGVPA, except
that cod in general is able to sustain higher effort, due to
the compensatory changes in growth and maturity at low
cod biomass caused by increases in the available food for
cod. In single species VPA and MSVPA, the cod stock is
predicted to be below 50% of its virgin biomass at the
present effort. In MSGVPA, present fishing is predicted
to lead to a spawning stock that is slightly less than 50%
of the virgin. The effort combination producing
maximum resource rent lies in the area where all three
species are above 50% of their virgin SSB.
The picture changes somewhat if the precautionary
biomass, Bpa, is used as the reference point (Fig. 8d–f).
Single-species VPA indicates that the present fishing
effort is likely to result in a SSB for cod and herring
below Bpa, while the predicted SSB for sprat is above
Bpa. In MSVPA predictions cod is below Bpa, but
herring and sprat are above. Finally, the MSGVPA
predicts that all three species would be above Bpa at
current effort. The effort combination producing
maximum value is once more outside the sustainable
area where the SSB of all three species are above Bpa.
The effort combination producing maximum resource
rent is within the sustainable area in all three models.
Discussion
The results clearly show how single-species reference
points are affected by species interaction. Instead of
being point estimates, they are turned into reference
curves or surfaces, when two or more fisheries and
species are considered. Furthermore, the single-species
estimates do not always fall on the curves generated by
the multispecies models. Compared to the single-species
predictions, both multispecies models predict that higher
efforts than the present are needed to achieve MSY in
the two fisheries. The differences between multispecies
and single-species predictions raise questions about the
utility of single-species reference points in situations
where species interactions are important.
In multispecies assessments it is potentially misleading
to consider each fishery in isolation. Even though curves
of cod FMSY vs. pelagic effort can be constructed for the
Baltic, they are of limited use because they do not
simultaneously reflect how changes in predation on
herring and sprat will affect the yield from the pelagic
fishery. In the multispecies situation maximization of
total yield by weight points to a strategy where the
581
predators are fished down to the lowest biomass possible
in order to benefit from the larger productive capacity
of their prey. In a management context this result
makes little sense. Cod is more valuable than herring
and sprat and it seems more sensible to use the total
catch value of the combined fishery rather than the yield
in the search for the optimum. However, this requires
that estimates of the relative value of the different
species are available. In this paper it was, for simplicity,
assumed that 1 kg of cod was 10 times more valuable
than 1 kg of herring and sprat, and that discount rates
were zero. Clearly a much more detailed analysis of the
socio-economics of the various fisheries is necessary.
Without such an analysis useful target reference points
cannot be derived.
When total catch value is considered, the single
species model predicts that cod effort should be reduced
by 30% and that pelagic effort should be increased by
26%, while both multispecies models suggest that effort
should be increased. In the MSGVPA the maximum is
found at a combination of cod and pelagic fishing efforts
corresponding to a 86% increase of the fishery for cod
and an 82% increase in the fishery for herring and sprat.
This suggests that FMSY could be a dangerous reference
point to use in a multispecies context. For all three
species it lies beyond the range of historical observations
where uncertainty about the stock dynamics may lead to
an unacceptable high risk of stock collapses.
Estimates of effort combinations corresponding to
F0.1 can be derived from the slope of the overall value
surface. However, it is difficult to derive a single value
that can be used as an overall reference point. For this
reason tentative estimates of costs were used to calculate
the combination of effort that would produce the maximum resource rent. Surprisingly, for cod all models
produced similar results, suggesting that cod effort
should be reduced by 50–60%. Although this reference
point for cod appears to be robust to the choice of
model, this is not the case for the pelagic fishery, where
the maximum resource rent was obtained at a much
lower level of effort in the multispecies than in the
single-species case. However, more information on the
economics of the fisheries would be required before a
maximum resource rent approach could be considered
acceptable for management.
The position of the present situation in relation to the
biomass reference limits differs between the three
models. The multispecies models allow a higher effort in
the pelagic fishery at high levels of cod effort than the
single-species model. At low levels of cod effort the
multispecies models predict that the pelagic fishery
should be reduced or even closed to keep the pelagic
species above the limits. For cod, the multispecies
models predict that fishing should be reduced at
high levels of pelagic effort, while at low levels of
pelagic effort cod effort can be higher than in the
582
H. Gislason
single-species case. This is most pronounced in the
MSGVPA where growth increases with increases in
available food. These results show that it is impossible to
define a ‘‘safe’’ level of biomass without taking changes
in species interactions into account. Reference limits for
forage fish cannot be defined without considering
changes in the biomass of their natural predators. Likewise, reference limits for predators cannot be defined
without considering changes in the biomass of their prey.
The results also point to the importance of structural
uncertainty in the model formulation. Alternative models could have been used. For instance, Rijnsdorp
(1993), suggested that maturity-at-age depends not only
on weight-at-age, but also on the age of the fish and its
previous growth history. However, insufficient data were
available to warrant a more complicated model than the
simple relationship between maturity and weight-at-age
used here. Also the recruitment model could have been
expanded. The use of a simple Ricker relationship allows
extrapolations outside the range of observed values and
does not reflect the large uncertainty about the form of
the relationship, particularly at low spawning-stock size.
Large residuals are obtained when the models are fitted
to the historic data. Sparholt (1996) incorporated sprat
and herring predation on cod eggs and larvae in the
stock recruitment relationship, effectively producing yet
another feedback loop not considered here. Additional
uncertainty about the future development of the
environment in the Baltic might be added (Kuikka et al.,
1999). Clearly all uncertainties will have to be taken
into account before the models might be considered
operational for management purposes.
Besides the need to provide a relative value to the
landings of different species and fleets, one of the main
impediments for using multispecies models is the difficulty of illustrating the present situation in relation to
the reference points in an easy comprehensible way,
when more than two species and fisheries are considered.
The Baltic is relatively easy in this respect, but in more
complicated systems, like the North Sea, the multidimensionality of biological and technical interactions
makes this a challenging task.
Acknowledgements
I would like to thank the members of the ICES
Multispecies Assessment Working Group for valuable
comments and discussions. Its chairman, Jake Rice,
provided useful comments and suggestions on an earlier
draft of this paper.
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