-
ICES Journal of Marine Science, 56: 571–583. 1999Article 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 onbiological reference points for cod, herring,
and sprat in the Baltic. The resultsdemonstrate that reference
points are different in single and multispecies contexts.Reference
points for fishing mortality based on single-species yield and SSB
calcula-tions are difficult to use when natural mortality depends
on the absolute abundance ofthe predators and their alternative
prey. Reference points based on maximizing totalyield from the
system may lead to impractical results when species interact.
Multispe-cies predictions suggest that the cod stock in the Baltic
should be reduced to a very lowlevel 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-economicconsiderations in the definition of target reference
points. Management advice basedon biomass reference points will
also differ. In the single species situation thecombinations of cod
and pelagic fishing effort for which the equilibrium spawning-stock
biomass of the three species is above the biomass reference points
forms arectangular area. When biological interaction is taken into
account the limits of thisarea becomes curved. Reference limits for
forage fish cannot be defined withoutconsidering changes in the
biomass of their natural predators. Likewise, referencelimits for
predators cannot be defined without considering changes in the
biomass oftheir 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
fisheriesmanagement has recently renewed the debate about
thedefinition 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 tocharacterize the state of a stock or fishery. They
arecommonly divided into target and limit reference points.Target
reference points represent a desired level offishing mortality or
biomass, while limit reference pointsare used to define either an
upper bound to the fishingmortality or a lower bound to the
biomass.
Biological reference points are often derived frommodels where
the yield from the fishery and the biomassof the exploited stock is
related to fishing mortality(Caddy and Mahon, 1995). It is common
practice to usesingle-species models where each species is
considered inisolation from the rest of the ecosystem. Little
effort has
1054–3139/99/050571+13 $30.00/0
so far been spent on examining how reference pointsmight be
defined and used in a multispecies context.However, species
interactions are likely to have directeffects on biological
reference points (Brander, 1988;ICES, 1997d). Failure to account
for these may lead toundesirable outcomes, such as overexploitation
andstock collapses, even if the probability of such outcomesappears
to be negligible in a single species analysis. Notaccounting for
species interactions may be just as prob-lematic as neglecting
uncertainty in the basic assessmentdata in the overall management
plan (ICES, 1997d).
Previous analyses of multispecies and multifleet fish-eries
models have shown that the maximum overallbenefit to society cannot
be estimated without consider-ing the relative value of the
different species caught andthe costs associated with their capture
(May et al., 1979;Flaaten, 1988). In fisheries where the economic
benefitto society is the overriding management concern, it hasbeen
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 managementobjective
(Flaaten, 1998).
The fish community in the Baltic Sea is relativelysimple and
dominated by cod, herring, and sprat(Elmgren, 1984). These species
are the primary targetsfor the commercial fishery and the
interactions amongthem are well studied (Sparholt, 1994). Single
andmultispecies model are used to estimate and compare afew of the
commonly used reference points for cod,herring, and sprat in the
central Baltic. The models areinitially used to assess the historic
stock size and fishingmortality of the three species. Based on
these assess-ments long-term equilibrium predictions of yield,
bio-mass, value, and resource rent are made at variousfishing
mortalities.
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
afunction of available food.
All three models were used in both retrospective andpredictive
modes and operated with an annual timestep.In the predictive mode
an average of the fishing mortali-ties over a recent number of
years was used to predictlong-term equilibrium yields and biomasses
in the statusquo situation. Separate effort multipliers were used
tochange the status quo fishing mortalities generated by thetwo
major fisheries: the cod fishery and the pelagicfishery for herring
and sprat. An index of total catchvalue was calculated by
multiplying the catch of eachspecies by its relative first-hand
price. An index of costswas generated by assuming that the
fisheries presentlyare in bionomic equilibrium where costs and
catch valuebalance (Clark, 1985), and that costs were
directlyproportional to effort. Resource rent was estimated
bysubtracting costs from the value of the catch.
Recruitment was predicted from a Ricker stock andrecruitment
relationship (Ricker, 1954):
N (0,y)=R1 SSB(y)exp[�R2 SSB(y)] (1)
where R1 and R2 are species-specific constants deter-mined from
the recruitment and SSB estimated in theretrospective part of the
models.
In the MSGVPA, cod growth depends on the amountof available
food. Weight-at-age is assumed to equalweight-at-age in the cohort
during the preceding yearplus a growth term. The growth term
depends onwhether the amount of available food in a particularyear
is above or below the average. Growth will be fasterthan average in
years where there is more than average
food available. In years with less food available growthwill be
slower. Weight at age of cod is thus described by:
where Avail(a,y): is the amount of food available to codage
group a in year y; w̄(a,y) is the average weight of codage group a
in year y; and:
where w̄obs(a,y) is the average observed weight at age ofcod age
group a in year y; and ny is the number of yearsover which the
calculations are performed.
Food consumption is calculated by assuming constantconversion
efficiency at age:
where R(a,y) is the per capita food consumption of codage group
a in year y; and CE(a) is the conversionefficiency; i.e. the
proportion of the total food intakethat is converted to somatic
growth for cod age group a.
In a model where growth and food intake depend onthe amount of
available food, it is inconsistent to assumethat the biomass of
other food is constant and does notrespond to changes in predation.
The model was there-fore extended by a simple description of the
dynamics ofother food in which the biomass of other food was madea
function of the predator’s intake.
The total intake of other food of type b, is calculatedby the
model from:
where Suit(a,b) is the suitability of other food of type bto
predation by cod age group a; Nz (a,y) is the averagenumber of fish
alive in age group a during year y; andBz(b,y) is the average
biomass of other food of type b inyear y.
The average biomass of other food of type b wasassumed to
decline exponentially as a function of theamount eaten:
Bz(b,y)=exp[K(b)�L(b)Cons(*,b,y)] (7)
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573Baltic fish stocks
where Bz(b,y) is the average biomass of other food oftype b in
year y; K(b) is a constant expressing the log ofthe biomass of
other food type b when predation is zero,corresponding to the
unexploited biomass in a surplusproduction model; and L(b) is a
constant expressing theamount of change in log biomass of other
food per unitof predator consumption.
Finally, the forecasting part of the model wasextended to take
changes in maturity at age of cod intoaccount by introducing a
sigmoid relationship betweenthe proportion mature and body
weight:
PM(a,y)={1�exp[�PM1*w̄(a,y)]}PM2 (8)
where PM1 and PM2 are constants determined bynon-linear
regression of proportion mature vs. observedweights at age.
Input data
The three models were used to analyse a single set ofassessment
data from the central Baltic, which cover theperiod from 1977 to
1996. Catch-at-age, terminal fishingmortalities, proportion
mature-at-age, single-speciestotal natural mortality, and
weight-at-age for herringand sprat were taken from ICES (1997a).
For cod,quarterly weight-at-age and stomach contents data
for1977–1991 were obtained from the revised set of inputdata
generated by ICES (1997b).1 The quarterly valueswere averaged for
each year to produce annual meanweights-at-age and annual stomach
content at age.Residual natural mortality, M1(s), was set to 0.2
for allthree species, the same value as used in ICES (1997b).Food
conversion efficiencies for different age groups ofcod were taken
from ICES (1992). An index of first-hand value was derived by
assuming that cod was 10times as valuable as herring and sprat.
This estimatereflects the relative price in Denmark and Sweden,
twoof the major fishing nations (Directorate of Fisheries,1997;
OECD, 1997).
In the stomach content database, all food items exceptcod,
herring, and sprat are lumped together in onecategory of ‘‘other
food’’. However, the species com-position of this category is not
the same for large andsmall cod. For cod >50 cm (age group 4+)
it consistsalmost exclusively of a large isopod, Saduria
entomon,while for smaller cod other invertebrates are alsoincluded
(Sparholt, 1994). Initial attempts to model codgrowth with only one
category of other food provedunable to describe the changes in the
growth of oldercod, and it was therefore decided to split other
food into
Saduria and other invertebrates. First, it was assumedthat other
food of age 4+ cod contained only Saduria.Secondly, for ages 1–3,
it was assumed that Saduriaconstituted the same proportion of the
diet as for oldercod and that the remainder of the other food
categoryconsisted of other invertebrates. In the MSVPA, thebiomass
of Saduria was set to 4 million tons and thetotal amount of ‘‘other
invertebrates’’ to 10 milliontons. In the MSGVPA, these biomasses
were used tocalculate K(b). Alternative biologically
plausiblevalues for the biomass of ‘‘other invertebrates’’
andSaduria produced virtually identical results in both theMSVPA
and MSGVPA, confirming the insensitivity ofthe models to the input
biomass of other food (Finnet al., 1991). The observed
weights-at-age for the0-group and for all age groups in 1977 were
used as thestarting values in the growth model incorporated inthe
MSGVPA.
1The database is currently being revised, but the most
recentversion of the data was kindly made available by
StefanNeuenfeldt (pers. comm.).
Parameter estimation
Annual fishing mortalities were estimated by Newtoniteration in
all three models. Average suitability coeffi-cients in the two
multispecies versions were estimatedfrom all available stomach
content data in an iterativeprocedure as explained in Magnusson
(1995). The par-ameters, L(b), used to describe the change in the
bio-mass of invertebrates and Saduria in the MSGVPA wereestimated
by minimizing the sum of squares of deviationbetween observed and
estimated weight-at-age in themodel.
The Ricker stock recruitment relationship was fittedseparately
for each model. Because of changes inenvironmental conditions, cod
recruitment success haschanged considerably over the years
(Sparholt, 1996).The number of recruits produced per SSB drop in
themiddle of the 1980s (Sparholt, 1995). In order not togenerate
too optimistic predictions only data from thelow recruitment period
from 1986 to 1995 were used.The right hand downward sloping side of
the Rickercurve is often attributed to cannibalism (Hilborn
andWalters, 1992). In the multispecies models, cannibalismis
already dealt with, and, in accordance with Sparholt(1995, 1996), a
linear rather than a dome-shaped stockrecruitment relationship for
cod was therefore assumedby setting the parameter R2 to zero. For
herring andsprat, the data contained little information about
theshape of the stock recruitment curve. Initial parameterestimates
resulted in recruitment maxima far outside theobservations and
produced unlikely predictions of virginstock biomass. The
parameters were therefore selectedso that the maximum of the stock
recruitment curvecorresponded to the point defined by the average
SSBand average recruitment over the period from 1977 to1995.
-
574 H. Gislason
1001982
100 000
Rec
ruit
men
t at
age
0 (
×103
)
1977
10 000
1987 1992
1000
01982
700
(a)
SS
B, t
ons
(×10
3 )
1977
200
1987 1992
100
0 100
1000
SSB200 500
500
0.001982
1.40
1977
0.40
1987 1992
0.20
300
400
500
600
0.60
0.80
1.00
1.20
300 400
Rec
ruit
men
t at
age
0 (
×103
)A
v. F
(4–7
)
1001982
1 000 000
Rec
ruit
men
t at
age
0 (
×103
)
1977
100 000
1987 1992
1000
01982
1800
(b)
SS
B, t
ons
(×10
3 )
1977
400
1987 1992
200
0 1000SSB
2000
20 000
0.001982
0.40
1977
0.10
1987 1992
0.05
600
800
1000
1200
0.15
0.20
0.25
0.35
Rec
ruit
men
t at
age
0 (
×103
)A
v. F
(3–6
)
10 000
1400
1600
0.30
40 000
60 000
80 000
100 000
120 000
140 000
Figure 1. (a) and (b).
-
575Baltic fish stocks
The non-linear regression used to estimate the par-ameters in
the equation describing the proportionmature-at-age explained 99%
of the variance in thedata.
The status quo fishing mortality used in the predictionwas
calculated by rescaling the average exploitationpatterns to the
fishing mortality in 1996, the last year ofthe retrospective
analysis.
VPA MSVPA MSGVPA VPA MSVPA MSGVPA
1001982
1 000 000
Rec
ruit
men
t at
age
0 (
×103
)
1977
100 000
1987 1992
1000
01982
2500
(c)S
SB
, ton
s (×
103 )
1977
1000
1987 1992
500
0 1000SSB
2000
100 000
0.001982
0.70
1977
0.20
1987 1992
0.10
1500
2000
0.30
0.40
0.50
Rec
ruit
men
t at
age
0 (
×103
)A
v. F
(3–7
)
10 000
0.60
200 000
300 000
400 000
500 1500
Figure 1. (c).
Figure 1. Spawning-Stock Biomass (SSB), average fishing
mortality (F), recruitment, and SSB recruitment relationship
estimatedby single-species VPA, MSVPA, and MSGVPA. (a) cod, (b)
herring, (c) sprat.
Basic output
The spawning-stock sizes, average fishing
mortalities,recruitment estimates, and stock recruitment
relation-ships produced by the three models are compared inFigure
1. The models produce almost identical estimatesof spawning-stock
biomass, but recruitment differs.Prior to 1990, recruitment is
generally estimated to havebeen at a higher level in the
multispecies models than inthe single species VPA. The estimated
fishing mortalitiesare similar, except for sprat, where fishing
mortality isestimated to be lower prior to 1986 in the
multispeciesmodels.
The total predation estimated by the two multispeciesmodels is
shown in Figure 2. The estimated consump-tion of cod, herring, and
sprat is of the same magnitudein both models, but is less variable
in the MSGVPA thanin the MSVPA.
The predicted weight at age of cod in the MSGVPA iscompared to
the observed in Figure 3 for cod age groups1–5. For ages 1–3 the
predicted weight at age is close tothe observed, but they deviate
for ages 4 and 5, particu-larly in the most recent years. In
addition, the discrep-ancy between the patterns for ages 4 and 5 in
1990–1992suggests that there may be problems with the weight-at-age
data. Correlations between observed and predictedweight-at-age were
significant for all ages (Fig. 4). How-ever, with the exception of
age group 3, the predictedweight-at-age in general changed less
than the observed.
The status quo fishing mortality for cod, herring, andsprat is
given in Table 1 together with the correspondingspawning-stock
biomasses and virgin SSB’s estimatedfrom each model. Note that for
herring and sprat thestatus quo SSB’s are larger than the virgin
SSB’s in bothmultispecies models.
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576 H. Gislason
Selection of reference points
ICES (1997c) contains a list of commonly used referencepoints.
Many of these are derived by using single-speciesSSB per recruit
calculations to estimate the fishingmortality corresponding to a
specific replacement line ina plot of SSB vs. recruitment (e.g.
Flow, Fmed, Fhigh,Fcrash, and Floss). It is not straightforward to
estimatethese reference points in a multispecies context,
becausenatural mortality, and hence also SSB per recruit,changes as
a function of the absolute abundance of thepredators and their prey
(Gislason, 1991, 1993). Aparticular replacement line is a function
of both fishingand predation mortality and these may vary
indepen-dently. Therefore, only target reference points based
onpredictions of yield (F0.1, FMSY), value, and resourcerent were
considered together with limit reference pointsbased on predictions
of virgin SSB or on precautionarySBB, B , as defined by ICES
(1997c, 1998).
(b)
01982
200
Year
Ton
s (×
103 )
1977
400
600
800
1000
1200
1400
1600
1800
2000
1987 1992
01982
200
Ton
s (×
103 )
1977
400
600
800
1000
1200
1400
1600
1800
2000
1987 1992
CodHerringSprat
(a)
Figure 2. Total consumption of cod, herring, and sprat
esti-mated by (a) MSVPA and (b) MSGVPA.
pa
0.01992
2.5
YearW
eigh
t (k
g)
1977
Age 5
Age 4
Age 2
Age 1
Age 3
2.0
1.5
1.0
0.5
1982 1987
Figure 3. Observed weight-at-age (filled symbols) of cod ages1–5
compared to estimated weight-at-age from MSGVPA(open symbols).
Results
Figure 5a shows how FMSY for cod depends on therelative fishing
effort in the pelagic fishery. In thesingle-species model, where
natural mortality andgrowth are constant, FMSY is constant. In the
twomultispecies models, FMSY depends on the amount ofpelagic
fishing effort, because cod cannibalism increasesas the pelagic
fishery reduces the biomass of herring andsprat. An increase in the
fishing mortality of cod willcounteract the increase in cannibalism
by reducing thebiomass of older cod. FMSY is higher in MSGVPA
thanin MSVPA. In MSGVPA, a higher fishing mortality andlower stock
size will be counteracted by increases in codgrowth. The effort in
the pelagic fishery that will gener-ate the maximum catch of
herring and sprat combined islikewise a function of cod effort
(Fig. 5b). If the biomassof cod is high (low cod fishing
mortality), predationmortality is high. With a high predation
mortality,fishing mortality has to be reduced in order to
avoidrecruitment overfishing. Except for herring and sprat atlow
cod fishing mortality, the single-species model pro-duces lower
FMSY values than the two multispeciesmodels.
The F0.1 curves follow the same pattern as the FMSYcurves (Fig.
5c and d). Again the two multispeciesmodels generate higher F0.1
values than the single-species model, and both for cod and for
herring andsprat combined, F0.1 increases as a function of
thefishing effort in the alternative fishery. Therefore, if
thereare strong species interactions, it is impossible to derivea
single fixed value for F for any species, without
MSY
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577Baltic fish stocks
0.1 0.2 0.40.3
0.4
0.4
Observed weight-at-age
R2 = 0.88
Est
imat
ed w
eigh
t-at
-age
0.6 1.2
1.0
1.2
0.8 1.0
Age 3
0.6
0.8
0.2 1.5
1.5
Observed weight-at-age
R2 = 0.17
2.0 4.5
3.0
4.5
2.5 3.0
Age 6
2.0
2.5
1.0
0.4
0.4
R2 = 0.79
Est
imat
ed w
eigh
t-at
-age
0.6 1.0
1.0
0.8
Age 2
0.6
0.8
0
0.2
R2 = 0.27
0.8 2.4
2.0
2.4
1.6 2.0
Age 5
1.2
1.6
0.8
0.1
R2 = 0.70
Est
imat
ed w
eigh
t-at
-age
0.4Age 1
0.2
0.3
0 0.8
0.8
R2 = 0.42
1.0 1.8
1.4
1.8
1.2 1.4
Age 4
1.0
1.2
0.6
0.2
1.6
1.6
3.5 4.0
3.5
4.0
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 Status quo SSB Virgin SSB
Codage 4–7
Herringage 3–6
Spratage 3–7 Cod Herring Sprat Cod Herring Sprat
VPA 221 970 628 687 1929 1137MSVPA 0.67 0.27 0.32 233 1610 939
632 1006 839MSGVPA 330 1510 826 705 1096 818
conditioning this value on the stock size of its predatorsand/or
prey.
An alternative would be to define FMSY as the effortcombination
that generates the maximum total yieldfrom the system. In the
single-species situation the resultis trivial: The maximum yield is
generated by keepingfishing mortality at FMSY in each of the
fisheries, i.e. bydecreasing cod effort by 30% and increasing
pelagic
effort by 26%. In the multispecies situation, both modelsshow
that cod should be fished down to the lowestbiomass possible in
order to benefit from the higherproductivity of its prey. Because
cod is more valuablethan herring and sprat these results make
little sense in amanagement context.
The value surfaces are shown in Figure 6 and theeffort
multipliers for which the maximum overall value is
-
578 H. Gislason
0 1
0.5
Relative pelagic effort
(c)
Rel
ativ
e co
d ef
fort
2 3
1.0
1.5
0 1.0
1
Relative cod effort
(d)
Rel
ativ
e pe
lagi
c ef
fort
1.5 2.0
2
3
0.5
0 1
0.5
Relative pelagic effort
(a)
Rel
ativ
e co
d ef
fort
2 3
1.0
1.5
0 1.0
1
Relative cod effort
(b)
Rel
ativ
e pe
lagi
c ef
fort
1.5 2.0
2
3
0.5
VPA 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-speciesresults are
again trivial. As before, the maximum valueis generated at the
single-species FMSY by reducing codeffort by 30% and increasing
pelagic effort by 26%. Inthe MSVPA, cod effort should be increased
by 15%and pelagic effort by 63% to generate the maximumvalue. The
MSGVPA predicts that cod effort should beincreased by 86% and
pelagic effort by 82% to reachthe maximum. The differences between
the two lattermodels is again due to compensatory changes inweight-
and maturity-at-age, making the cod stockmore resilient to
exploitation in MSGVPA than inMSVPA.
Estimating F0.1, the fishing mortality where the slopeof the
value surface is a tenth of the slope at the origin,is not
straightforward. The slope at the origin is afunction of both cod
and pelagic fishing mortality.Various fixed relationships between
cod and pelagiceffort factors were therefore explored. For each
fixedrelationship, the slope at the origin was determined andthe
point where the slope of the value surface was 10% ofthe slope at
the origin identified (Fig. 7). In all threemodels the F0.1 contour
bends backward at low codeffort. The highest values of F0.1 are
generated by theMSGVPA, whereas the single-species model
produced,in general, the lowest. However, there is no
simplerelationship between the fishing mortalities generated by
the two fisheries and the overall F0.1. Thus, in a multi-species
context it appears difficult to use the overall F0.1as a target
reference point.
The effort combinations that would generate themaximum resource
rent are given in Table 2b. For codthe three models produce similar
results. Cod fishingmortality should be approximately halved to
generatethe maximum resource rent. For the pelagic fishery
theanswers depend on the model. In the multispeciesmodels, fishing
mortality should be reduced to 10% orless of the present level,
while in the single-species modelfishing mortality should be
halved. The differencebetween single and multispecies results is
once againcaused by the indirect effect of herring and spratbiomass
on cod cannibalism.
The three models were also used to investigate limitreference
points based on total spawning-stock biomass.The equilibrium SSB
for cod, herring, and sprat werepredicted for various combinations
of cod and pelagiceffort. These predictions were compared to the
biomassreference points by plotting the effort combinations
thatwould lead to stock sizes below or above a particularreference
point in a surface plot (Fig. 8). Two differentreference points
were considered. The fishing mortalitywhere 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
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579Baltic fish stocks
0.0
2.1
Pelagic effort
(c)
Cod effort
6.0
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
5.0 4.0 3.0 2.0 1.0
0–500 1000–1500500–1000
1500–2000 2000–2500
0.0
2.1(b)
Cod effort
6.0
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
5.0 4.0 3.0 2.0 1.0
0.0
2.1(a)
Cod effort
6.0
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
5.0 4.0 3.0 2.0 1.0
Table 2. Effort multipliers for which the highest value of
thetotal landings (a) and the highest resource rent (b) of the
Balticfishery is obtained. Cod is assumed to be 10 times
morevaluable than herring and sprat, and costs in (b) to be
directly
proportional to effort (total value in arbitrary units).(a)
Fishery VPA MSVPA MSGVPA
Cod 0.70 1.15 1.86Herring and sprat 1.26 1.63 1.82Total value
1720 2047 2300
(b)Fishery VPA MSVPA MSGVPA
Cod 0.42 0.45 0.45Herring and sprat 0.47 0.03 0.10Total value
1401 1264 1371
0 0.5
0.5
Pelagic effort
Cod
eff
ort
1.0 1.5 2.0
1.0
1.5
2.0 VPAMSVPAMSGVPA
Figure 7. Isolines of F0.1 estimated by single-species
predictions,MSVPA, and MSGVPA. F0.1 estimated as the effort
combina-tion where the slope of the relative value of the total
catch isone-tenth of the slope at the origin.
Figure 6. Relative total value of catch for different
combina-tions of effort in the pelagic and cod fishery. Cod assumed
to be10 times as valuable as herring and sprat. (a)
Single-speciespredictions, (b) MSVPA, (c) MSGVPA.
points corresponding to maximum catch value andresource rent are
also included in the figure.
In the single species case, the combination of effortswhere all
three species are above 50% of their virgin SSBis rectangular (Fig.
8a). For a cod effort above half thepresent, the cod stock will be
below 50% of its virginbiomass. For herring and sprat, an increase
in effortabove the present will produce a SSB below B50%. InMSVPA,
the cod effort influences the borderline where
-
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)
showntogether with the effort combinations corresponding to the
current fishing mortality, maximum overall value of catch,
andmaximum 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.
-
581Baltic fish stocks
the pelagic species drop below 50% of their virgin level. Ifcod
effort is high, the cod stock and the predationmortality it
generates on herring and sprat are bothreduced. In this situation,
sprat and herring can sustainhigher fishing mortalities before
their biomasses fallbelow the limit. If pelagic effort is high,
cannibalism ofcod increases, and the stock is no longer able to
sustainhigh effort. The same applies to the MSGVPA, exceptthat cod
in general is able to sustain higher effort, due tothe compensatory
changes in growth and maturity at lowcod biomass caused by
increases in the available food forcod. In single species VPA and
MSVPA, the cod stock ispredicted to be below 50% of its virgin
biomass at thepresent effort. In MSGVPA, present fishing is
predictedto lead to a spawning stock that is slightly less than
50%of the virgin. The effort combination producingmaximum resource
rent lies in the area where all threespecies are above 50% of their
virgin SSB.
The picture changes somewhat if the precautionarybiomass, Bpa,
is used as the reference point (Fig. 8d–f).Single-species VPA
indicates that the present fishingeffort is likely to result in a
SSB for cod and herringbelow Bpa, while the predicted SSB for sprat
is aboveBpa. In MSVPA predictions cod is below Bpa, butherring and
sprat are above. Finally, the MSGVPApredicts that all three species
would be above Bpa atcurrent effort. The effort combination
producingmaximum value is once more outside the sustainablearea
where the SSB of all three species are above Bpa.The effort
combination producing maximum resourcerent is within the
sustainable area in all three models.
Discussion
The results clearly show how single-species referencepoints are
affected by species interaction. Instead ofbeing point estimates,
they are turned into referencecurves or surfaces, when two or more
fisheries andspecies are considered. Furthermore, the
single-speciesestimates do not always fall on the curves generated
bythe multispecies models. Compared to the
single-speciespredictions, both multispecies models predict that
higherefforts than the present are needed to achieve MSY inthe two
fisheries. The differences between multispeciesand single-species
predictions raise questions about theutility of single-species
reference points in situationswhere species interactions are
important.
In multispecies assessments it is potentially misleadingto
consider each fishery in isolation. Even though curvesof cod FMSY
vs. pelagic effort can be constructed for theBaltic, they are of
limited use because they do notsimultaneously reflect how changes
in predation onherring and sprat will affect the yield from the
pelagicfishery. In the multispecies situation maximization oftotal
yield by weight points to a strategy where the
predators are fished down to the lowest biomass possiblein order
to benefit from the larger productive capacityof their prey. In a
management context this resultmakes little sense. Cod is more
valuable than herringand sprat and it seems more sensible to use
the totalcatch value of the combined fishery rather than the
yieldin the search for the optimum. However, this requiresthat
estimates of the relative value of the differentspecies are
available. In this paper it was, for simplicity,assumed that 1 kg
of cod was 10 times more valuablethan 1 kg of herring and sprat,
and that discount rateswere zero. Clearly a much more detailed
analysis of thesocio-economics of the various fisheries is
necessary.Without such an analysis useful target reference
pointscannot be derived.
When total catch value is considered, the singlespecies model
predicts that cod effort should be reducedby 30% and that pelagic
effort should be increased by26%, while both multispecies models
suggest that effortshould be increased. In the MSGVPA the maximum
isfound at a combination of cod and pelagic fishing
effortscorresponding to a 86% increase of the fishery for codand an
82% increase in the fishery for herring and sprat.This suggests
that FMSY could be a dangerous referencepoint to use in a
multispecies context. For all threespecies it lies beyond the range
of historical observationswhere uncertainty about the stock
dynamics may lead toan unacceptable high risk of stock
collapses.
Estimates of effort combinations corresponding toF0.1 can be
derived from the slope of the overall valuesurface. However, it is
difficult to derive a single valuethat can be used as an overall
reference point. For thisreason tentative estimates of costs were
used to calculatethe combination of effort that would produce the
maxi-mum resource rent. Surprisingly, for cod all modelsproduced
similar results, suggesting that cod effortshould be reduced by
50–60%. Although this referencepoint for cod appears to be robust
to the choice ofmodel, this is not the case for the pelagic
fishery, wherethe maximum resource rent was obtained at a muchlower
level of effort in the multispecies than in thesingle-species case.
However, more information on theeconomics of the fisheries would be
required before amaximum resource rent approach could be
consideredacceptable for management.
The position of the present situation in relation to thebiomass
reference limits differs between the threemodels. The multispecies
models allow a higher effort inthe pelagic fishery at high levels
of cod effort than thesingle-species model. At low levels of cod
effort themultispecies models predict that the pelagic
fisheryshould be reduced or even closed to keep the pelagicspecies
above the limits. For cod, the multispeciesmodels predict that
fishing should be reduced athigh levels of pelagic effort, while at
low levels ofpelagic effort cod effort can be higher than in
the
-
582 H. Gislason
single-species case. This is most pronounced in theMSGVPA where
growth increases with increases inavailable food. These results
show that it is impossible todefine a ‘‘safe’’ level of biomass
without taking changesin species interactions into account.
Reference limits forforage fish cannot be defined without
consideringchanges in the biomass of their natural predators.
Like-wise, reference limits for predators cannot be definedwithout
considering changes in the biomass of their prey.
The results also point to the importance of
structuraluncertainty in the model formulation. Alternative mod-els
could have been used. For instance, Rijnsdorp(1993), suggested that
maturity-at-age depends not onlyon weight-at-age, but also on the
age of the fish and itsprevious growth history. However,
insufficient data wereavailable to warrant a more complicated model
than thesimple relationship between maturity and weight-at-ageused
here. Also the recruitment model could have beenexpanded. The use
of a simple Ricker relationship allowsextrapolations outside the
range of observed values anddoes not reflect the large uncertainty
about the form ofthe relationship, particularly at low
spawning-stock size.Large residuals are obtained when the models
are fittedto the historic data. Sparholt (1996) incorporated
spratand herring predation on cod eggs and larvae in thestock
recruitment relationship, effectively producing yetanother feedback
loop not considered here. Additionaluncertainty about the future
development of theenvironment in the Baltic might be added (Kuikka
et al.,1999). Clearly all uncertainties will have to be takeninto
account before the models might be consideredoperational for
management purposes.
Besides the need to provide a relative value to thelandings of
different species and fleets, one of the mainimpediments for using
multispecies models is the diffi-culty of illustrating the present
situation in relation tothe 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
morecomplicated systems, like the North Sea, the
multi-dimensionality of biological and technical interactionsmakes
this a challenging task.
Acknowledgements
I would like to thank the members of the ICESMultispecies
Assessment Working Group for valuablecomments and discussions. Its
chairman, Jake Rice,provided useful comments and suggestions on an
earlierdraft of this paper.
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Single and multispecies reference points for Baltic fish
stocksIntroductionThe model frameworkInput dataParameter
estimationFigure 1. (a) and (b) Figure 1. (c)Basic outputFigure
2Selection of reference pointsFigure 3
ResultsFigure 4Table 1Figure 5Figure 6Table 2Figure 7Figure 6
(caption)Figure 8
DiscussionAcknowledgementsReferences
