Download Using AMOEBAs to display multispecies

ICES Journal of Marine Science, 60: 709–720. 2003
doi:10.1016/S1054–3139(03)00042-0
Using AMOEBAs to display multispecies, multifleet
fisheries advice
Jeremy S. Collie, Henrik Gislason, and Morten Vinther
Collie, J. S., Gislason, H., and Vinther, M. 2003. Using AMOEBAs to display multispecies,
multifleet fisheries advice. – ICES Journal of Marine Science, 60: 709–720.
In multispecies fish communities, predation levels change dynamically in response to
changes in the abundance of predator and prey species, as influenced by the fisheries that
exploit them. In addition to community-level metrics, it remains necessary to track the
abundance of each species relative to its biological reference point. In situations with many
interacting species, exploited by multiple fishing fleets, it can be complicated to illustrate
how the effort of each fleet will affect the abundance of each species. We have adapted the
AMOEBA approach to graph the reference levels of multiple interacting species exploited
by multiple fleets. This method is illustrated with 10 species and eight fishing fleets in the
North Sea. We fit a relatively simple response-surface model to the predictions of a fully
age-structured multispecies model. The response-surface model links the AMOEBA for
fishing effort to separate AMOEBAs for spawning stock biomass, fishing mortality, and
yield. Ordination is used to give the shape of the AMOEBAs functional meaning by relating
fish species to the fleets that catch them. The aim is to present the results of dynamic
multispecies models in a format that can be readily understood by decision makers.
Interactive versions of the AMOEBAs can be used to identify desirable combinations of
effort levels and to test the compatibility of the set of single-species biological reference
points.
Ó 2003 International Council for the Exploration of the Sea. Published by Elsevier Ltd. All rights reserved.
Keywords: ecological indicators, fisheries management, multispecies models, North Sea.
Received 14 March 2002; accepted 5 March 2003.
J. S. Collie: University of Rhode Island, Graduate School of Oceanography, Narragansett,
RI 02882, USA. H. Gislason: University of Copenhagen, c/o Danish Institute for Fisheries
Research, Charlottenlund Castle, 2920 Charlottenlund, Denmark; tel.: þ45 3396 3361;
fax: þ45 3396 3333; e-mail: [email protected]. M. Vinther: Danish Institute for Fisheries
Research, Charlottenlund Castle, 2920 Charlottenlund, Denmark; tel.: þ45 3396 3353;
fax: þ45 3396 3333; e-mail: [email protected]. Correspondence to J. S. Collie; tel.: þ1 401
874 6859; fax: þ1 401 874 6240; e-mail: [email protected].
Introduction
There is widespread acceptance that an ecosystem perspective is needed to manage marine fisheries but much less
practical experience on how to do so. It is now recognized
that ecosystems themselves cannot be managed; it is the
human users of ecosystems that must be regulated (Bax
et al., 1999). In marine fisheries, two approaches have
emerged for incorporating ecosystem considerations into
management decisions (Murawski, 2000). One is to use the
metrics of community ecology, such as species diversity and size spectra, as indicators of ecosystem status,
ecosystem health, and ecosystem services (Rice, 2000).
The other approach is to incorporate additional ecosystem
constraints into traditional management decisions.
With respect to the first approach, criteria to aid in the
selection of ecosystem objectives and their associated metrics
1054–3139/03/080709þ12 $30.00
have been put forward by the ICES Working Group on
Ecosystem Effects of Fishing Activities (ICES, 2001, 2002a).
Although rapid progress is being made, there is presently little
theoretical understanding of how many of the proposed
metrics respond to changes in harvesting, and what the
desirable level of the metrics should be. For many important
ecosystem properties, scientific understanding of the link
between human impacts and ecosystem response is insufficient, and considerable effort is therefore needed before the
approach can be fully implemented (ICES, 2002a). Although
the concept of ecosystem health seems an intuitive analogy
with the human body, it breaks down on closer examination
because ecosystems can exist in multiple states, in all of
which basic ecological functions are maintained (Hall, 1999).
The second approach is to define reference levels for taxa
other than the targets of the directed fishery. These ecosystem
constraints have been considered as additional levers to
Ó 2003 International Council for the Exploration of the Sea. Published by Elsevier Ltd. All rights reserved.
710
J. S. Collie et al.
nudge the management process toward meeting ecosystem,
or at least community-level objectives (Bax et al., 1999).
Another way to view these constraints is as additional
dimensions or objectives to be satisfied in fishery management plans. Examples of ecosystem constraints are limits on
the take of marine mammals in fisheries, catch limits on
forage fish to preserve their predators, and area closures to
protect structural epifauna. Progress can be expected with
both approaches, but in the short-term it is more pragmatic to
incorporate ecosystem considerations as additional constraints to existing fishery management plans (Murawski,
2000). Adding ecosystem constraints is likely to increase the
complexity of the advice and may therefore increase the
difficulties of reaching consensus if trade-offs cannot be presented to stakeholders and managers in an easily comprehensible way.
Among the most important ecosystem processes in marine
fish communities are trophic interactions among the fish
species. There is empirical evidence that the mortality rate
of prey species depends on predator abundance and, conversely, that predator growth rates depend on prey abundance (Collie, 2001). Competition is implied by many
ecological models but is certainly more difficult to demonstrate than predation, and is also less likely to be structuring highly interconnected marine food webs.
There is a strong parallel between the two approaches to
incorporating ecosystem considerations and the types of
multispecies models used for each approach. Models of the
entire ecosystem (e.g. network models, dynamic ecosystem
models) should lend themselves to the derivation of ecosystem metrics (Hollowed et al., 2000). On the other hand,
community-level models of interacting species are more
useful for adding ecosystem constraints to the single-species models that are widely used in fisheries management. A
second dichotomy is whether the multispecies model is age
structured or just tracks the total abundance or biomass of
each species (Hollowed et al., 2000); age-structured models
are most widely used in the management of temperate marine
fish.
When does multispecies advice matter in fisheries management? In the short term, the feeding requirements of
predators must be considered when setting annual harvest
quotas for forage fish species (e.g. capelin off Norway). In the
medium term, biological reference points may need to be
adjusted to account for variable predation rates on prey species and variable growth rates of predators (Collie and
Gislason, 2001). Long-term management strategies need to
account for the implicit trade-offs in prey and predator yields
(May et al., 1979). In boreal ecosystems with a small number
of interacting species, it may be straightforward to condition
the reference levels of a target species on the abundances of
interacting species (Livingston and Tjelmeland, 2000). In
temperate ecosystems with a large number of fish species, the
increased dimensionality necessitates different approaches.
The North Sea is a good example of such an ecosystem. It
harbours an intensive multispecies and multifleet fishery
using a variety of gears. Demersal fisheries for human
consumption catch a mixture of roundfish species, such as
cod, haddock, whiting, and saithe, that are piscivorous to
some extent, or target flatfish species such as sole and plaice,
often with a bycatch of roundfish species. Pelagic fisheries
for human consumption are directed at species such as
herring and mackerel, while the industrial fishery targets
forage species, such as sandeel, Norway pout, and sprat, and
uses them for production of fishmeal and fish oil. Due to
excessive levels of fishing mortality many of the demersal
stocks are at present considered to be outside safe biological
limits (ICES, 2002b).
The European Common Fisheries Policy has multiple
objectives (Halliday and Pinhorn, 1996). In the short term
these are: (a) to ensure the continuity of each stock as a
commercially viable resource; (b) to decrease the fishing
effort on overexploited stocks in order to ensure yields that
are stable from year to year; and (c) to ensure the highest
possible catch from stocks, consistent with (a) and (b) and
taking into account the relationships among stocks. ICES
has established precautionary biomass (Bpa) and fishing
mortality (Fpa) levels for each stock to meet objectives (a)
and (b). These precautionary targets are intended to maintain each stock at a productive level and to provide a high
probability of avoiding stock collapse. Objective (c) implies
that fishery yields should be maximized, subject to the
biological constraints and multispecies interactions.
The North Sea fisheries have for many years been managed with a system of quotas or total allowable catches
(TACs). Particularly for the species caught in the mixed
demersal fisheries, this system has failed to produce the
intended reductions in fishing mortality. There are several
reasons for this failure, one of which is that the TACs often
have been set independently for each species. This has
contributed to extensive discarding and to little or no reduction in overall fishing mortality despite reductions in
landings. As concluded by Holden (1994), the TAC system
is a fundamentally flawed system for managing the mixed
demersal fisheries in the North Sea. Due to technical
interactions, fishing mortality cannot be regulated independently for each species. In addition there are important
biological interactions taking place and these interactions need to be taken into account in the medium and longterm projections used for formulating rebuilding strategies
(ICES, 1997).
Age-structured multispecies and multifleet models (e.g.
MSFOR) have thus been developed. Such models can be
used to investigate the consequences of different fishing
mortalities while accounting for interactions among fishing
fleets and between the predators and prey (Pope, 1991).
Although the models have now been available for more
than a decade they have not been used routinely in fisheries
management, partly because of their intensive data and
computing requirements, but mainly because the increased
complexity of multispecies models is thought to hinder
decision making (Brugge and Holden, 1991). In an attempt to
Using AMOEBAs to display multispecies, multifleet fisheries advice
construct a simpler multispecies model, Pope (1989) proposed fitting a simpler response-surface model to the results
of the more complicated multispecies model, and then using
the response-surface model to investigate alternative levels
of fishing effort. The ICES Multispecies Assessment Working Group (MSAWG) used a multispecies Schaefer or Fox
model fit to the projections of the MSFOR model (ICES,
1992). This approach greatly simplifies the multispecies
model, but leaves the problem of visualizing the results in as
many dimensions as there are interacting species and fishing
fleets. Joint levels of F0.1 and Fmsy for interacting fishing
fleets can be calculated (Pope, 1989) but such communitywide indices do not ensure that reference levels for individual
species will be met.
Pope (1997) emphasized that ‘‘whatever model of complex, multispecies, multifleet, multiarea fisheries is adopted,
it will be of little use in the real world unless its results
can be presented to the managers in as clear and as unambiguous fashion as possible’’. The results of multispecies
models can be presented with decision tables or radar plots.
AMOEBAs are extensions of radar plots that can be useful
for visualizing multidimensional situations in which several
constraints must be met simultaneously (Laane and Peters,
1993). Pioneered in the Netherlands in the context of water
quality objectives, AMOEBA is the Dutch acronym for ‘‘a
general method of ecosystem description and assessment’’
(Ten Brink et al., 1991). The AMOEBA approach has been
applied to shellfish restoration in North Carolina (Wefering
et al., 2000) and has also been proposed for displaying
ecological quality objectives in the North Sea (Lanters
et al., 1999).
In this paper we show how AMOEBAs can be used to
visualize the results of multispecies models applied to the
North Sea fish community. We extend the AMOEBA concept by giving the shape of the AMOEBAs functional meaning and by making them change dynamically in response to
changing effort levels. In creating the AMOEBA plots we
followed Tufte’s (1983) principles of graphic excellence.
According to Tufte, graphic displays should:
show the data in a way that makes large data sets coherent;
induce the viewer to think about the substance rather than
about the methodology;
present many numbers in a small space;
encourage the eye to compare the different pieces of data;
and
serve a reasonably clear purpose.
The ultimate objective of this work is to present the
results of multispecies fishery models in a format that can
be readily understood and used by decision makers.
Methods
In this paper we analyzed the multispecies, multifleet fishery of the North Sea. Multispecies VPA and projections
711
were made using the 4M program (Vinther et al., 2001).
The 4M (Multi-species, Multi-Fleet and Multi-Area Model)
package is a newer and extended implementation of the
MSVPA/MSFOR programs previously used by the ICES
MSAWG.
The forecasts were based on an MSVPA run similar to
the so-called ‘‘key-run’’ made at the last MSAWG Meeting
(ICES, 1997). This MSVPA included data for 10 VPA
species (Table 1) for the period 1974–1995 such that 1996
became the first projection year. Recruitment in the projections was assumed to follow a Ricker stock-recruitment
relation fitted to the MSVPA output for all VPA species
except North Sea mackerel. An arithmetic mean of the
estimated recruits in 1986–1995 was used for mackerel
because the stock-recruitment relation was indeterminate.
Abundance of species without analytical assessment (‘‘other
predators’’) was kept constant at the 1995 level in the
projections.
Fishing mortalities (F) estimated for 1995 by the MSVPA
were used as base line or status-quo levels in the projections.
These F values were partitioned to partial F by fleet according to catch numbers given by the STCF database
(Anon., 1991; Lewy et al., 1992), which includes detailed
catch information for 56 national fleets fishing in the North
Sea in 1991. These 56 fleets were aggregated into eight new
fleets defined by the gear used or target species; ‘‘other
gears’’ include national fleets that did not fit the grouping.
Average partial Fs over the age range used by ICES in the
calculation of reference F values are presented in Table 2.
The exploitation patterns of the fishing fleets and the stock
sizes of each species have changed considerably since 1991,
Table 1. Species included in multispecies assessment.
Size or age
groups
VPA species
Cod
Haddock
Whiting
Saithe
Mackerel (North
Sea stock)
Herring
Norway pout
Sandeel
Plaice
Sole
Other predators (abundance
Grey gurnards
Western stock mackerel
Raja radiata
Grey seals
Sea birds
Other species
Predator/
prey
Abbreviation
for figures
0–11þ
0–11þ
0–10þ
0–15þ
0–15þ
Yes/Yes
Yes/Yes
Yes/Yes
Yes/(Yes)
Yes/(Yes)
COD
HAD
WHG
POK
MAC
0–9þ
0–3þ
0–6þ
0–15þ
0–15þ
No/Yes
No/Yes
No/Yes
No/(Yes)
No/(Yes)
HER
NOP
SAN
PLE
SOL
given as input)
0–3
Yes/No
0–1
Yes/No
0–3
Yes/No
1
Yes/No
1
Yes/No
1
Yes/No
Prey (Yes) indicates very low predation mortality.
712
J. S. Collie et al.
Table 2. Average fishing mortality by fleet and species as used in the status-quo projection. Also listed are the precautionary reference
levels for fishing mortality (Fpa) and SSB (Bpa) from ICES (2002b). For herring and mackerel only, the status-quo SSB levels were used as
proxies for Bpa because these two stocks have components that are not resident in the North Sea. A plus sign (þ) indicates fishing mortality
<0.01 and a minus sign () indicates a species not caught by that gear.
Species
Fleet
Cod
Haddock
Whiting
Saithe
Plaice
Sole
Herring
Mackerel
Sandeel
Norway pout
Beam trawl
Fixed gear
Industrial (small meshed
trawl)
Pelagic (purse seine
and trawl)
Saithe (trawl)
Seine net
Trawl
Other gears
All fleets
Precautionary F level
Precautionary biomass
level (kt)
0.03
0.10
0.02
þ
þ
0.01
0.01
þ
0.04
þ
þ
0.05
0.35
0.02
þ
0.35
0.02
þ
þ
þ
0.05
þ
þ
0.02
0.36
0.36
þ
þ
þ
þ
þ
0.47
0.10
þ
þ
0.01
0.21
0.28
0.16
0.81
0.65
150
0.01
0.30
0.35
0.05
0.73
0.70
140
þ
0.16
0.27
0.01
0.49
0.65
315
0.09
0.01
0.16
0.11
0.42
0.40
200
þ
0.05
0.05
0.07
0.55
0.30
300
þ
0.03
0.11
0.51
0.40
35
þ
þ
0.11
0.20
0.83
0.25
311a
þ
þ
0.01
þ
0.12
0.17
86a
þ
0.01
0.36
0.59
600
þ
þ
0.36
0.84
150
a
Status-quo SSB used as a proxy for Bpa.
such that each fleet probably accounts for a different percentage of the total catch of each species than in 1991.
Therefore the status-quo exploitation patterns would need to
be updated before the results of projecting different management options could be used for actual management decisions.
Fishing mortality was assumed to be proportional to fishing effort. Different fishing efforts could then be modelled
as multiples of the status-quo levels. Projections of yield and
spawning stock biomass (SSB) were made for the statusquo F, and with changes in F of 10, 25, and 50% both
for all fleets combined, and by individual fleet. Each projection was run for 50 years to a (near) equilibrium state.
The 4M model explicitly differentiates between retained
and discarded catch. The multispecies production model
was fit to the retained catch (yield) only. In this manner
discarding is accounted for implicitly but is not tracked
separately with the production model. Response-surface
models were fit to the projections in which fishing effort for
each fleet was increased by 10% in turn. The projections
with other levels of fishing effort were used to compare the
predictions of the simple response-surface model with those
of the age-structured 4M model.
The response-surface model is a generalization of the
system of equations examined by Larkin (1966). Specifically, it is a multispecies production model of the Schaefer
form:
X
dSSBs
SSBs
qg eg SSBs
¼ rs SSBs 1 dt
as
g
ð1Þ
where SSBs is the SSB of species s, q is a catchability coefficient, and eg is fishing effort in fleet g. The equilibrium
SSB is:
SSBs ¼ as X
bgs eg
ð2Þ
g
where as is the SSB of species s in the absence of fishing
and parameter bgs ¼ qg as =rs measures the reduction of
SSBs per unit of fishing effort in fleet g. For convenience,
fishing effort (eg) was scaled to equal one in a reference
year (1995). For each species, SSB was predicted with the
4M model for the status-quo effort level and a 10% increase
in the effort of each fleet in turn. With m fishing fleets and
n species, these calculations can be expressed in matrix
notation as:
S¼EA
ð3Þ
where S is an (m þ 1) n matrix of SSB values, E is
an (m þ 1) (m þ 1) effort-change matrix, and A is the
(m þ 1) n matrix of parameter estimates, with one column
for each species. Matrix E represents the changes in effort
levels, with 1.1 on the diagonal, except for the first element
which is 1.0, corresponding to the a parameters. This system
of equations was solved by inverting the effort-change
matrix, E.
Separate equations were used to predict equilibrium SSB
or yield in weight. Equilibrium yield is the product of
equilibrium biomass and fishing mortality. Equations analogous to Equations (2) and (3) can be written to predict
the equilibrium yield of a given fleet, f:
Yfs ¼ afs ef X
bfgs ef eg
g
Dividing by ef, yield per unit effort, YPUE is:
ð4Þ
Using AMOEBAs to display multispecies, multifleet fisheries advice
YPUEfs ¼ afs X
ð5Þ
bfgs eg
g
Here afs is the unfished YPUE of species s in fleet f and
bfgs measures the reduction in YPUE per unit of fishing
effort. In matrix notation,
Uf ¼ E Pf
ð6Þ
where Uf is an (m þ 1) n matrix of YPUE values and E is
the same effort-change matrix. The (m þ 1) n matrix of
parameter estimates, Pf, can be estimated from the inverse
of E, and once obtained it can be used to predict yield for
different levels of fishing effort. A separate yield model was
estimated for each fishing fleet. Fishing mortality rates
corresponding to different combinations of fishing effort
were calculated as:
Fs ¼
X
eg F1995
gs
ð7Þ
g
where the partial fishing mortalities in 1995 were taken
from Table 2.
AMOEBA plots were used to display changes in SSB,
yield, and fishing mortality resulting from changes in fishing effort and the resultant changes in species interactions.
Angles for plotting the AMOEBAs were calculated with
principal components analysis (PCA) of the table of yields
by species and fleets, projected with status-quo effort levels.
The PCA was calculated from the correlation matrix so that
species and fleets with high yields would not dominate the
principal components (PCs). We plotted the first two PCs
using polar coordinates. The PCA loadings gave the angles
for the fishing fleets and the PCA scores gave the corresponding angles for the fish species. The AMOEBAs were
then used to investigate the consequences of different combinations of fishing effort.
Effort levels corresponding to the multispecies maximum
sustainable yield (MSY) can be found by maximizing the
yield of each fleet as defined in Equation (4). Let
Yf ¼
X
af ¼
Yfs
g
X
afs
s
bfg ¼
X
bfgs
ð8Þ
s
be the aggregate values for fleet f summed over species. Then
aggregate yield can be expressed as
Yf ¼ af ef X
bfg ef eg
ð9Þ
g
The partial derivative of yield with respect to effort in fleet
f is:
X
qYf
¼ af bfg eg 2bff ef
qef
g6¼f
ð10Þ
The multispecies MSY is obtained when these partial
derivatives are set to zero for all fleets simultaneously
(Pope, 1989). Let B be the m m matrix with 2bff on the
713
main diagonal and bfg in the remainder. In vector notation,
MSY is obtained when
a ¼ B Emsy
ð11Þ
and the vector Emsy can be obtained from the inverse of B.
Though easy to calculate, Emsy, is not a very useful reference point because it ignores the costs inherent in increasing fishing effort. Fishing costs are unknown, but their
effect can be approximated by assuming that at status-quo
effort levels, fishing costs equal the revenue or yield (Pope,
1997; Gislason, 1999). Most of the commercially important
fish stocks in the North Sea suffer from overfishing and the
majority of stocks are currently below the precautionary
spawning biomass limits defined by ICES (ICES, 2002b).
The North Sea fisheries are operating at a level exceeding
that necessary to produce the maximum return both in tons
caught and economic value. Although the situation differs
from fleet to fleet and good economic data are lacking,
the financial returns from fisheries are in many cases modest despite considerable subsidies. Financial returns fluctuate from year to year and in some cases costs and capital
depreciation exceed revenues (European Commission,
2001). It is therefore not unreasonable to assume that the
North Sea fisheries by and large are close to the level of
effort corresponding to the bionomic equilibrium of the
Gordon–Schaefer bio-economic fisheries model. This level
is defined as the level of effort where opportunity costs
would equal revenues in an equilibrium situation (Clark,
1985). Opportunity costs include costs due to fuel, gear and
supplies, interest and depreciation on capital, as well as
wages of skipper and crew. Assuming that each fleet is at
the bionomic equilibrium, fishing costs equals revenue and
the effort levels for maximum economic yield (Emey) can be
calculated from:
a Ysq ¼ B Emey
ð12Þ
where Ysq is the vector of status-quo yields for each fleet.
Further constraints on the effort levels may be required to
ensure that the SSBs of all species are above the precautionary levels (Bpa) and that the fishing mortality rates
are below Fpa. Bounded nonlinear optimization was used to
identify a set of effort levels to maximize yield while
ensuring SSB Bpa and F Fpa for all species.
Results
The predictions of equilibrium SSB and yield made with the
multispecies production model agree well with those of the
4M model for either a 50% increase or decrease in effort for
all fleets (Figure 1). The differences between models are
insubstantial (the points are largely superimposed) compared
with the differences between the effort scenarios. With 50%
effort the SSB of most species would be higher except for
haddock, mackerel, Norway pout, and whiting (Figure 1a).
For these species, an increase in predation mortality appears
to compensate for the decrease in fishing mortality. With
714
J. S. Collie et al.
Figure 1. Predictions of the 4M model and the multispecies production model with 50% reduction or 50% increase in effort in all fishing
fleets. The species abbreviations are defined in Table 1 and the fleet abbreviations are defined in Table 4.
þ50% fishing effort, the multispecies production model
predicts the elimination of cod and herring, whereas the 4M
model predicts small, but positive, SSB. With decreased
fishing effort, yields of cod and herring were higher due to an
increase in abundance (Figure 1b). Yields of haddock,
Norway pout, sandeel, and whiting were lower, due to
increased predation and lower fishing effort. With increased
fishing effort, yield in the industrial fleet was lower, due to
less sandeel while yield in the pelagic fleet was higher,
reflecting the increase in herring (Figure 1c). In these
validation runs, the multispecies production model was used
to predict conditions other than the data that were used to
estimate the model parameters (þ10% effort). This close
agreement indicates that the simpler response-surface model
captures the main dynamics of the fishery and can be used to
investigate different effort combinations, within a range of
50% around the status-quo levels.
The multispecies projections incorporate both technical
and biological interactions (Table 3). Technical interactions
occur because most fishing gears catch more than one
species. Beam trawls catch sole and plaice and thus the SSB
of both species would increase with a decrease in effort in
the beam trawl fleet. Biological interactions occur because
of predation among the modelled species. For example a
decrease in seine effort would lead to an increase in the SSB
of the predator cod but would decrease herring SSB
because of increased predation. These species interactions
can be plotted in three dimensions for a single species and
pairs of fleets. Haddock SSB would increase with decreased
effort in the trawl fishery and decrease with decreased effort
in the industrial fishery due to increased abundance of
the predators cod, whiting, and saithe (Figure 2). In this
example, there was also close agreement between projections made with the multispecies production model and
with the 4M model; the maximum difference between the
two response surfaces was 6% (Figure 2).
Ordination was used to project the entire table of fleetby-species interactions in two dimensions. The first two
Using AMOEBAs to display multispecies, multifleet fisheries advice
715
Table 3. Percent change in SSB of each species resulting from a 25% decrease in fishing effort of each fleet in turn, as estimated with the
4M model. Negative values result from increases in predator populations. Listed at the bottom are the scores of the first two PCs of the
PCA of yields by species and fleet projected with status-quo effort levels.
Species
Fleet
Cod
Haddock
Whiting
Beam trawl
Fixed gear
Industrial (small meshed
trawl)
Pelagic (purse seine
and trawl)
Saithe (trawl)
Seine net
Trawl
Other gears
2.89
5.81
4.47
0.77
0.62
2.12
0.71
Principal component 1 scores
Principal component 2 scores
Saithe
Plaice
Sole
Herring
0.14
0.74
3.48
0.05
0.13
4.15
19.80
0.61
0.05
25.41
1.30
0.04
0.39
0.10
17.85
0.12
0.23
0.01
0.01
0.00
0.97
13.24
20.93
13.82
0.25
5.36
3.57
0.01
0.10
0.20
0.23
1.39
6.45
1.34
12.03
8.17
0.08
2.46
3.02
4.12
1.81
1.34
2.00
1.45
0.12
0.73
1.71
0.23
1.00
0.85
PCs accounted for 28 and 26% of the variance; the third
and forth components explained only 15 and 13%. The
species and fleets are well separated in two dimensions,
expect whiting, which had low scores for PC1 and PC2
(Table 3), possibly because of its important role as both
predator and prey species. Cod and haddock had similar
scores for the first two PCs (Table 3), but different scores
for PC3. Likewise sole, mackerel, and Norway pout
clustered on the first two PCs and separated on the third,
as they are caught by different fleets. With respect to fleets,
some pairs had similar loadings for the first two PCs (Table
4) and different loadings for PC3 (fixed and seine) or PC4
(trawl and saithe; pelagic and other). Thus the PCA
provides a useful ordination of species and fleets but there
is additional variation not explained by the first two PCs.
Mackerel
Sandeel
Norway pout
0.00
0.00
1.91
0.14
0.22
12.90
0.03
0.40
7.84
14.99
12.73
0.37
0.13
0.01
0.06
1.86
8.48
0.12
3.34
0.30
15.83
0.03
0.00
1.47
0.02
0.02
0.21
0.02
0.64
0.21
2.30
2.18
0.90
1.21
0.33
1.36
3.87
1.17
0.11
2.18
0.80
1.42
0.08
In the AMOEBA plots, the directions of the fleet vectors
correspond to the directions of the species caught by that
fishing gear (Figure 3). It can easily be seen that sandeel is
caught by the industrial fishery and that sole and plaice are
caught with beam trawls. The orientation of these arrows
makes it easier to see which species will be affected by
changes in fishing effort of particular fishing fleets. The
flatfish vectors are in the upper left quadrant, the roundfish
in the upper right, and the pelagic species are scattered
in the other quadrants. It should be stressed that the PCA
was used only to aid in displaying the results of the multispecies model and in no way influences the multispecies projections. The angles derived from the PCA provide a
more informative grouping of fleets and species in two
dimensions than could be achieved in a one-dimensional
Table 4. Reference levels of fishing effort identified with the
multispecies Schaefer model. Also listed are the loadings for the
first two PCs of the PCA of yields by species and fleet projected
with status-quo effort levels.
Fleet
Figure 2. Response-surface model for haddock SSB as a function
of fishing effort in the trawl and industrial fleets. Fishing effort is
expressed relative to 1 for the status quo and effort in the remaining
six fishing fleets was fixed at 1. The flat plane corresponds to SSB
predicted with the multispecies production model; the broken lines
indicate the curved surface predicted by 4M model for effort levels
at the edges of the plane.
Beam trawl
Fixed gear
Industrial (small
meshed trawl)
Pelagic (purse
seine
and trawl)
Saithe (trawl)
Seine net
Trawl
Other gears
a
Effort relative
to status quo Abbreviations
for
plotting
Emsy Emey Epa
PCA
loadings
PC1
PC2
0.98 0.53 0.55
0.2a 2.08 0.73
1.77 0.51 0.22
btr
fix
ind
0.176 0.159
0.255 0.254
0.320 0.235
0.81 0.82 0.21
pel
0.187 0.619
3.02
2.39
1.42
1.11
sth
sei
trl
oth
0.287 0.008
0.407 0.376
0.642 0.063
0.327 0.572
0.96
0.71
0.86
0.86
0.54
0.56
0.24
0.54
Constrained to prevent a negative estimate.
716
J. S. Collie et al.
Figure 3. AMOEBA plots with status-quo effort levels. In each AMOEBA the circle represents the reference level and the arrows are the
levels predicted with the multispecies model. Effort and landings are plotted relative to the status quo. Fishing mortality is plotted relative
to Fpa and SSB is plotted relative to Bpa. Species abbreviations are given in Table 1 and fleet abbreviations in Table 4.
plot or table, or by regular spacing of the vectors around the
circle. Beyond their utility as a plotting device, the angles
derived from PCA are not important to the projection; in
fact some of the angles were jittered slightly to avoid
overlapping the vectors.
The vector lengths indicate the magnitude of each
quantity relative to its status-quo or reference level. These
quantities were calculated with the multispecies production
model, independently of the PCA. With status-quo effort
levels, plaice, whiting, and cod SSB would all be below
their precautionary biomass (Bpa) levels, and plaice, sole,
cod, saithe, and herring fishing mortality would exceed the
precautionary (Fpa) levels (Figure 3). The MSY effort levels
were much higher than status quo for several of the fleets
(Table 4), but yields in the industrial, seine, and saithe fleets
would increase only slightly. At Emsy, SSB would be below
Bpa for all species except sole, mackerel, Norway pout, and
sandeel, and fishing mortality would exceed Fpa for all
species except mackerel and Norway pout.
Effort levels for maximum economic yield (Emey) were
all less than the status quo except for the fixed gear (Table
4). Fixed gear has a very different exploitation pattern than
trawl and seine nets. The mean age of cod, plaice, and sole
in fixed gear is at least 1 year older than the other gear
types. Effort reduction in the other fleets would increase the
fixed gear yield because fixed gear targets older fish. For
the remaining fleets Emey was less than one because fishing
costs would exceed revenues at higher effort levels. At Emey
cod SSB would be below Bpa and fishing mortality would
exceed Fpa for plaice, cod, and herring (Figure 4), but all
the other biological constraints would be met. With
bounded nonlinear optimization, a combination of effort
levels was identified that would satisfy all the biological
constraints while maximizing yield (Epa, Table 4). This
combination required substantial reduction in the industrial,
pelagic, and trawl fleets in order to raise cod SSB above
Bpa and to decrease fishing mortality on cod and herring
(Figure 5). At these precautionary effort levels, the
Using AMOEBAs to display multispecies, multifleet fisheries advice
717
Figure 4. AMOEBA plots with effort levels for MEY. The features of the AMOEBAs are explained in the caption to Figure 3.
roundfish would be at or near their Bpa levels, while the
other species would be well above Bpa.
The shapes of the AMOEBAs represent the composition
of the fishery and the fish community. Compared with the
status quo (Figure 3), the precautionary effort levels would
reduce the industrial and pelagic fleets and shift the fish
community toward the prey species, especially sandeel and
herring (Figure 5). The area of the AMOEBA, relative to its
area at the reference levels, could be considered for use
as a community-level index. Likewise, the volume of the
AMOEBA could be calculated to capture more of the variance in species catch by fleet. However, such a summary
index is much less informative than looking at the actual
AMOEBA.
Discussion
We have shown how AMOEBAs can be constructed and
used to display the main interactions in a multispecies,
multifleet fishery on a single page. These plots sufficiently
capture the trade-offs in multiple fishery objectives. The
biological objectives require satisfying the Bpa and Fpa
constraints for each species. Our results indicate that these
constraints can be jointly met even when predator–prey
interactions are included. For the prey species, the benefits
of decreased fishing mortality appear to outweigh the
increased predation mortality that occurs with increased
predator abundance. At the precautionary effort levels
(Table 4) the SSB of all species would be higher than the
status-quo levels. This result differs from earlier MSFOR
projections in which the result of increased mesh size in the
roundfish fleet was to decrease the yields of the prey species
because of increased predation (Pope, 1991). The earlier
MSFOR projections did not include stock-recruitment
relationships, but assumed constant recruitment, and thus
decoupled recruitment from fishing mortality. In the 4M
model, recruitment of the prey species increases with
lower fishing mortality and higher SSB. However, the
stock-recruitment relationships remain uncertain because
they were fit to short time series of variable data. The
718
J. S. Collie et al.
Figure 5. AMOEBA plots with precautionary effort levels. The features of the AMOEBAs are explained in the caption to Figure 3.
incorporation of the stock-recruitment relationships also
tends to cause oscillations in the projected abundances.
Economic objectives operate at the fleet level. We used
the yield in weight of each fleet as a surrogate for economic
performance. It would be preferable to express yield in
monetary units to account for price differences among species. However, we lacked price data that were appropriately averaged over time, subfleets, and size of fish.
Therefore, in our estimate of MEY we implicitly assumed
that the value per weight of each fleet’s catch would remain
constant with different effort levels. Pope (1997) also found
that attaining MEY would require reducing effort in the
roundfish and industrial fleets, with the other fleets kept
near their status-quo levels.
Social objectives are usually expressed at a finer level of
geographic detail (e.g. fishing ports) than the main fleets in
our model. One approach would be to include an AMOEBA
for social objectives (e.g. employment) and to assume that
ports with similar gears would be similarly affected by effort changes (Pope, 1997). However, if there are substantial national differences, even within the main gear groups,
a two-tiered approach may be required. A coarser management model with aggregated fishing fleets would operate
at the international level. The output from this model
would then be made available to national groups to make
second-stage models at further levels of disaggregation
(Pope, 1997).
In this study, we used a multispecies Schaefer model to
describe the North Sea multispecies fishery. It was at first
surprising that a simple production model could match the
4M model predictions so closely. However, the multispecies Schaefer model was fit to the 4M projections, and
the simpler model appears to capture the main interactions.
In this manner, simplified management advice can be given
without further need for a more detailed biological model.
The multispecies Schaefer model was very convenient for
this application because the projections can be made almost
instantly, which facilitates an interactive computer model.
The model projections should be most reliable close to the
status-quo effort levels; the MSAWG cautioned against
extrapolating beyond a range of one half or twice the
status-quo effort (ICES, 1992). We found very close agreement between the model predictions within a range of
50% of status-quo effort levels for all fleets. At þ50%
effort the model projections began to diverge because the
multispecies production model predicted extinction of cod
Using AMOEBAs to display multispecies, multifleet fisheries advice
and herring, whereas the 4M model predicted that both
species would persist at low levels.
The essential features of this display are that the
AMOEBAs are linked with a multispecies model and that
projections can be made simply by altering effort levels.
Alternative model formulations could be used and/or
extensions made to the present model. One approach would
be to use the 4M model to make all the projections, without
fitting the simpler production model. However, detailed
accounting of age structure may be unnecessary unless
changes in mesh size are investigated or there is a large
price differential with size of fish. In this study the biological interactions appeared to be secondary to the direct
fishery effects on each species. However, we may have
down-played the biological interactions by ignoring variations in the predation mortality inflicted by the ‘‘other predators’’ in Table 1. Also, we did not consider the potential
bottom-up effects of the prey species on the growth rates of
their predators. Prey-dependent growth has been incorporated in other multispecies models (e.g. Gislason, 1999) but
is thought to be less important in the North Sea because of
a large variety of alternative prey species.
An alternative approach is to fit the multispecies
production model directly to catch and abundance data
without accounting for age structure (e.g. Collie and DeLong,
1999). Preliminary attempts to fit a multispecies production
model to North Sea data have not been successful even
though the species were grouped into three larger functional
units and MSVPA derived biomasses and catches were used
as input. As concluded by Sullivan (1991) the number of
parameters in multispecies production models is so large that
very long data series often are needed to fit even the simplest
multispecies system. Parameter estimation may be facilitated
by introducing auxiliary data on fishing effort, recruitment
indices, mean weight of fish in the stock, growth parameters,
residual natural mortality, and food composition. Such an
approach was followed by Horbowy (1996), who derived a
multispecies production model for Baltic cod, herring,
and sprat from the age-structured multispecies model of
Andersen and Ursin (1977) and obtained biomass estimates
consistent with results from age-structured models.
The multispecies Schaefer model was fit to equilibrium
conditions and therefore did not consider the time dynamics
of moving from the status quo to the desired situation. These
equilibrium solutions give useful targets relative to present
conditions, but in practice it would be useful to have
AMOEBAs for 1–5 year projections as well. It would also
be useful to incorporate stochasticity, especially to account
for uncertainty in the stock-recruitment relationships. If
a stochastic multispecies model was used, the arrowheads
in each AMOEBA could be replaced with error bars.
Uncertainty in the ordination could be represented with
wedges in place of the arrows. The bio-economic objectives
could also be extended, for example by including effort–cost
relationships and price elasticity; such extensions would
give a higher value to reducing fishing effort. Social
719
objectives could also be represented with AMOEBAs but
the challenge is that, to be included, they must be quantified
(Pope, 1997). While all these extensions are technically
feasible, additions to the AMOEBA plots should only be
made if they serve a reasonably clear purpose.
The combinations of effort levels in Table 4 were meant
more for illustration than for prognostication. The partial
fishing mortalities were based on 1991 values (Table 2);
fishing patterns have almost certainly changed since then.
Before making actual projections, the status-quo effort levels
would need to be updated from 1995 to present. Nevertheless, several general conclusions can be made regarding
multispecies biological reference points. Joint levels of F0.1
and Fmsy can be calculated with the methods of linear
algebra, but they are of limited usefulness because of the
tendency for extremely high or low values for some fleets.
Reference levels based on MEY appear to be more useful
because they prevent extreme effort levels and because of the
explicit link to bioeconomics. In the Baltic Sea, multispecies
reference points based on MEY were also more sensible than
the joint F0.1 and Fmsy levels (Gislason, 1999). A priority
should be to incorporate more realistic cost functions.
Our results suggest that it is possible to satisfy the Bpa
and Fpa levels of all species but that substantial reductions
in fishing effort of some fleets would be necessary. Relative
to the status quo, there would also be foregone yield,
although this loss would at least be partially compensated
by increased catch per unit effort. In reality, we should not
rely on projections with effort levels less than one half the
status quo because they imply levels of stock abundance far
different than those used to fit the models. Fishing effort
is more likely to be reduced in a step-wise fashion, with
multispecies models refit at each step.
The AMOEBA plots are very useful for displaying the
trade-offs among biological, economic, and social objectives.
It is unlikely that any ‘‘optimal’’ effort combination will be
chosen. More realistically, solutions will be sought that
maximize the objectives while violating as few constraints as
possible (Pope, 1997). The advantage of the AMOEBA
approach is that these trade-offs can be viewed explicitly. We
have also developed an interactive version of the program in
which the effort levels can be changed in the graphical
interface. In summary, we have demonstrated a method
for the clear and concise presentation of advice for a
multispecies, multifleet fishery. Incorporation of biological
interactions does require a multispecies model, but the
presentation of advice is no more complex than that required
for the technological interactions among fishing fleets.
Acknowledgements
We thank Allison DeLong, Terry Quinn, Marie-Joëlle
Rochet, and Stephen Hall for helpful comments on earlier
drafts of this paper. The research was funded by the
European Commission (Project QLK5-CT1999-01609) and
the Danish Ministry of Food, Agriculture and Fisheries.
720
J. S. Collie et al.
J.S.C. thanks the Danish Institute for Fisheries Research for
hosting his sabbatical leave and Anders Nielsen for help
with the AMOEBA plots.
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