Efimas meeting Nicosia Crete 2004 April 11-12
Modelling GCFM-GSA biological production functions within the EFIMAS project.
By V. Placenti 1
Introduction
Defining biological production functions for the stocks selected in Efimas for each
case studies and each Italian regions first requires to have information on the population
parameters describing their dynamics. Concerning the Italian regions of interest in the Efimas
project, one main international organisation is in charge of stock assessment (the General
Fisheries Commission for the Mediterranean - GFCM), while the one main national
Institution is the Italian Ministry (through its various funding programme research’s). In the
Mediterranean, assessments are generally done without continuity in time and can display a
large uncertainty due to the data poor quality (Lleonart and Maynou, 2003). Generally, data
on stock assessments is generally available on-line but mainly concern the most valuable
stocks and/or stocks of political interest in Europe (e.g., ICES databank). Very few
information on population parameters for some Mediterranean stocks is sometimes available,
although they may be essential at a local scale. In a first step, the link between terrestrial
landings in a given Italian regions and the maritime nature of the stocks targeted by various
national and international fishing fleets need to be emphasised. As an illustration, a simulation
model is presented that takes account for the reactivity of other international fleets regarding
their effort allocation on a stock also fished by Italian fleet segments. We then describe the
methodology adopted to define biological production functions by estimating surplus
production models from age-structured assessments.
***
We finally present a theoretical simulation model that enables to characterize the potential
variability in production functions inherent to trophic interactions and to the main features of
the ecosystem functioning.
The regional production model
Part of the Finistère fisheries in the total fishing activity
In order to estimate the impact that fisheries from the region of Finistère have on the
different species targeted, the proportion in catch due to Finistère vessels was estimated for
each stock. In a second step, total and Finistère catches realized for the stocks limited within
the boundaries of their associated ‘Ecosystem Fishery Units’ were estimated. Total catches
were extracted from the ICES database with the Fishshstat Plus software (© FAO, 2000), by
considering the ICES subdivisions of presence of each stock. In the same way, the catches
harvested by the Finistère for all the stocks were extracted from the Finistère landings
database. Catches within the EFU generally represent the majority of the stock catches except
for the hake (Merluccius merluccius), anglerfish (Lophius spp.), cuckoo ray (Raja naevus) and
saithe (pollachius virens) that display wide areas of distribution and are therefore targeted by
numerous fisheries other than the Finistère ones. Table I displays the results when considering
the total catch on the stocks. Finistère fisheries generally represent a relatively important part
in the total catches of the different stocks considered except for the saithe (Pollachius virens)
IREPA, IstitutoRicerche Economiche per la Pesca e l’Acquacoltura, Via S. Leonardo – Trav. Migliaro, 84131
Salerno (Italy). Reference contact : Vincenzo Placenti [email protected].
1
and hake (Merluccius merluccius). Table II shows the results when restricting the estimation
of total and Finistère catches to the subdivisions composing each EFU.
Table I. Total catches (tons) and Finistère (F.) landings (tons) for the stocks considered for all the
ICES subdivisions defining their boundaries. Catches and landings represent an average on the period
1995-1997.
Stocks
Norway lobster (VIIIa, VIIIb)
European hake (IIIa, IV, VI, VII, VIIIa,b,d)
Edible crab (VIId,e)
Anglerfish (VIIb-k VIIIa,b,d)
Atlantic cod (VII e-k)
Whiting (VII e-k)
Haddock (VII b-k)
Norway lobster (M et L)
Megrim (VIIb,c,e-k VIIIa,b,d)
Cuckoo ray (no stock defined)
Saithe (IIIa, IV, VIa,b)
Roundnose grenadier (VI, VII, Vb)
Total catches
4 133
49 133
11 479
28 930
12 092
20 051
7 367
9 243
15 100
5 971
93 000
7 943
F. landings
F. part
2 064 50%
2 687
5%
1 490 13%
8 708 30%
4 229 35%
4 120 21%
2 701 37%
2 729 30%
2 687 18%
1 833 31%
2 357
3%
2 475 31%
Table II. Total catches (tons) and Finistère landings (tons) for the different stocks limited within the
boundaries of their associated Ecosystem Fishery Units (EFU). Catches and landings represent an
average on the period 1995-1997.
EFU
Bay of Biscay
Stocks
Norway lobster (VIIIa, VIIIb)
European hake (IIIa, IV, VI, VII, VIIIa, b,d)
Total catches
4 133
14 993
F. landings
F. part
2 064 50%
1 435 10%
English Channel
Edible crab (VIId,e)
11 479
1 490
13%
Anglerfish (VIIb-k VIIIa,b,d)
Atlantic cod (VIIe-k)
Whiting (VII e-k)
Haddock (VII b-k)
Norway lobster (M et L)
Megrim (VIIb,c,e-k VIIIa,b,d)
Cuckoo ray (no stock defined)
12 415
10 649
17 518
6 017
5 839
10 635
2 479
5 083
4 074
3 904
2 441
2 216
1 866
1 833
41%
38%
22%
41%
38%
18%
74%
Saithe (IIIa, IV, VIa,b)
Roundnose grenadier (VI, VII, Vb)
11 457
7 102
2 785
2 366
24%
33%
Celtic Sea
West of ScotlandIreland
In order to estimate the impact that the fishing vessels of the Finistère can have on a
given stock, a simulation model is developed. This model is relatively simple and aims to be a
didactic tool that emphasizes the importance of considering all the fleets targeting the stock
and the relative part of each fleet in the total catches. Indeed, because potential management
actions can be carried out at the regional scale, it is important to keep in mind the fact that fish
stocks are generally targeted by numerous fisheries capable of adopting different fishing
strategies in time and space.
Data and Method
No data is required in this analysis because a simulation model is used. Using such a
model enables a high flexibility about the input parameters and the assumptions drawn. A Fox
model (1970) is used to represent the dynamics of the population. The current situation is
considered in order to define the parameter  that represents the relative part of the Finistère
in the total catches for the stock. This parameter is supposed to represent the fraction between
the regional and total efforts. A distinction is made between a regional fleet (in) and an
outside fleet (out) and the model aims to account for the relationship existing between the
fleets through a parameter of reactivity (). This parameter enables to represent how the
outside fleet responds to a variation in the fishing effort of the regional fleet. A power type
function is used in order to simulate different scenarios of response when considering a large
range of  values.
Production model
The Fox model (1970) estimates the yields realized on the stock for a given fishing
mortality (F). This mortality can be expressed in function of an effort multiplier (mf)
relatively to the current situation.
(1)
Y  mf  a  exp b  mf 
Both parameters a and b only depend on the dynamics of the stock and are not linked to the
characteristics of the exploitation. In the simulations, parameters are chosen arbitrarily in
order to get a yield value of 1 for an total effort of 1.
Fishing efforts
The major point of the analysis is to define how the outside fleet is supposed to
respond to a variation in the fishing effort of the regional fleet. This also questions how the
total fishing effort affecting the entire stock will vary consequently to a modification of the
regional and outside fishing efforts. These are defined in terms of effort multipliers relatively
to the current situation (mf=1). A power type function relating the effort multiplier of the
outside fleet (mfout) to the effort multiplier of the regional fleet (mfin) is assumed:
(2)
mfout  mfin 

The total effort multiplier (mf) depends both on the regional mf and on the relationship
between the mf in the region and the mf out of the region. It is defined by taking into account
the relative part of the region in the total effort (or catches) for the current situation:
(3)
f curr, in

Y
 in
 
f curr, total Ytotal

mf
 total    mf in  1     mf out
Equation (3) implies for the current situation:
(4)
1   

 f curr, out    f curr, in

1
f
  f curr, in
curr
,
total


Because each effort multiplier (mfin, mfout, mftotal) refers to its current fishing effort
(respectively fcurr, in, fcurr,out, fcurr,total), it requires to define all the mf in reference to the current
effort of the region (fcurr, in):
(5)
1

 f mf , out mf out  f curr, out mf out    f curr, in
1


 mf out 

f curr, in
f curr, in

 f curr, in

1

mftotal   f curr, in
f
mf

f
mftotal
 mf , total  total curr, total 


 f
f curr, in
f curr, in

 curr, in

1 

mf out  mf in     


(5)  
  mfin  1     mf out 
mf

total


Total biomass and catches
Defining the outside and total mf relatively to the mf of the region enables to estimate
the total biomass of the stock and the catches harvested by each fleet. Using the equation (1)
gives :
 B  a  exp b  mf total 
Y  mf  a  exp b  mf 
 in
in
total

Yout  mf out  a  exp b  mf total 
Ytotal  mf total  a  exp b  mf total 
Simulations
Different scenarios of exploitation are simulated. First, the influence of the relative
part of the region in the total effort () applied on the stock is tested. In a second step,
different levels for the value of reactivity () are considered. Table III summaries the input
values for the parameters according to the different scenarios.
Table III. Parameter values according to the different simulations conducted in the analysis. For all the
simulations, a=3.66; b=-1.3.


Simulation 1
Simulation 2
Simulation 3
0.3
0.6
0.9
1
1
1
Simulation 4
Simulation 5
Simulation 6
0.6
0.6
0.6
0
1
2
Regional part
Reactivity
Results
Efforts multipliers
Combining different values for the parameters  and  enables to obtain a large range
of possible situations for the evolutions of the outside and total effort multipliers (mf)
according to the values of the mf in the region (Fig. 1). Notably, the presupposed power type
function (equation 2) can generate various outside effort evolutions when increasing the
regional effort. Except for =0, efforts multipliers simulated evolve in the same way but at a
different rate.
2,0
2,0
=0,3
=0
1,5
mf
1,0
1,0
0,5
1,0
0,5
0,0
0,5
0,0
0,0
0,5
1,0
1,5
2,0
0,0
0,0
0,5
1,0
mf in
2,0
0,0
2,0
0,5
0,0
0,5
1,0
mf in
1,5
2,0
2,0
1,0
0,5
0,0
1,5
=0,9
=1,5
1,5
mf
mf
2,0
1,0
0,5
1,0
mf in
=0,9
=0,5
1,5
1,0
0,0
0,5
mf in
=0,9
=0
1,5
1,5
mf
2,0
=0,3
=1,5
1,5
mf
mf
1,5
2,0
=0,3
=0,5
0,0
0,0
0,5
1,0
mf in
1,5
2,0
0,0
0,5
1,0
1,5
2,0
mf in
Fig. 1. Different evolutions for the outside (solid line) and total (dashed line) effort multipliers
according to the values taken by the effort multiplier in the region (mf in).  is the relative part of the
region in the total effort for the current situation and  is the reactivity of the outside fishing fleet.
Simulations 1-3
In this first set of simulations, the coefficient of reactivity  is equal to 1, describing a
linear and similar response between regional and outside fishing efforts. Simulations carried
out show a logical increase of the regional yields when increasing the relative part () of the
regional fishing effort in the total effort for the current situation (Fig. 2). According to the
values of the coefficient , the curve of the regional yields show very different behaviours.
For low values of , the stock seems relatively robust to an increase in the total fishing effort
because the regional effort remains relatively low (Fig. 2a). However, for high values of ,
the regional production curve gets closer to the curve of total yields, characterized by the
parameters of the Fox model defined in equation (1). In this case, the stock can display a
decrease in yields corresponding to an overexploitation for a high fishing pressure (Fig 2b, c).
0,5
0,0
0,0
0,0
0,5
1,0
1,5
2,0
0,4
0,5
0,0
0,0
0,0
0,5
1,0
1,5
2,0
2,0
1,5
0,8
1,0
0,4
0,5
0,0
0,0
0,0
0,5
1,0
f tot
f tot
f tot
(a)
(b)
(c)
1,5
2,0
Fig. 2. Production curves for the total fleet (thick solid line) in relation to the total effort applied for
different values of (see for details in text). Total fleet is composed of a regional fleet (thin solid line)
and an outside fleet (dashed line). Line with triangles represents the regional fishing effort in relation
to the total effort and line with circles is the total stock biomass. ftot=total fishing effort ; mfin=regional
effort multiplier.
Simulations 4-6
In a second set of simulations, different values for the reactivity parameter () are
tested. The values considered should display extreme cases of response of the outside effort to
the regional effort :
- constant outside fishing effort (=0)
- similar effort evolution (=1) for both fleets
- faster evolution of the outside fleet corresponding to a faster increase (or decrease )
in the outside effort following an increase (or decrease) in the regional effort
Simulation results show that production curves for both fleets (outside and regional)
can greatly vary according to the values of the parameter . For a value of 0, the fishing
effort outside the region remains constant whatever the evolution of the regional effort. The
value of the outside effort is in this case defined by the parameter  characterizing the current
situation. By construction, the total effort can not take lower values than the constant outside
fishing effort. Because the outside fishing effort is constant, an increase in the total effort is
obtained by an increase in the regional effort. Thus, the outside yields progressively decrease
as the relative part of the regional effort increases in the total effort (Fig 3a). Defining a high
mfin
1,5
0,8
1,0
=0,9
1,2
2,0
Yields and total biomass
0,4
Yields and total biomass
1,5
0,8
1,0
=0,6
1,2
mfin
Yields and total biomass
2,0
mfin
=0,3
1,2
effort reactivity implies a rapid response of the outside effort to the regional effort evolution.
Thus, for a total effort decreasing by reference to the current situation (ftot<1), the relative part
of the regional effort will increase faster and generate higher yields for a higher reactivity
because the outside effort decreases faster. By contrast, when the total effort increases (ftot>1),
the outside effort increases faster relatively to the regional effort and enables to maintain
relatively high yields in the case of a higher reactivity.
0,5
0,0
0,0
0,0
0,5
1,0
f tot
(a)
1,5
2,0
1,5
0,8
1,0
0,4
0,5
0,0
0,0
0,0
0,5
1,0
f tot
(b)
1,5
2,0
=2
1,2
2,0
1,5
0,8
1,0
mfin
2,0
Yields and total biomass
0,4
Yields and total biomass
1,5
0,8
1,0
=1
1,2
mfin
Yields and total biomass
2,0
mfin
=0
1,2
0,4
0,5
0,0
0,0
0,0
0,5
1,0
1,5
2,0
f tot
(c)
Fig. 3. Production curves for the total fleet (thick solid line) in relation to the total effort applied for
different values of (see for details in text). Total fleet is composed of a regional fleet (thin solid line)
and an outside fleet (dashed line). Line with triangles represents the regional fishing effort in relation
to the total effort and line with circles is the total stock biomass. ftot=total fishing effort ; mfin=regional
effort multiplier.
Discussion
A simple model
In the simulation model, the dynamics of the stock are modelled by the means of a Fox
model (Fox, 1970). Using generalized production models could enable to represent a larger
range of possible shapes for the production curves (Pella and Tomlinson, 1969). However,
using such models would not have changed the general conclusions of the analysis.
Simulations carried out only deal with 2 distinct fisheries although such an over-simplistic
case is rarely encountered in real situations. Within a region, various fleets can target the same
stock and the evolution of their respective efforts in time might differ greatly. Moreover, the
multispecific nature of many fisheries can generate technical interactions that either
correspond to congestion or stock externalities (Ulrich et al., 2001). Such interactions are very
difficult to quantify and predict because of the fisher’s ability to adapt their effort in a current
situation of competitive behaviour among fishing units (Ulrich et al., 2001). Yet, aggregating
all the efforts of the vessels targeting a given stock is a common task in fisheries sciences
although only a few studies deal with a regional effort. Again, the simplicity of the case study
is sufficient to emphasize the potential problems raised by a study that deals at this type of
local scale. In a real case, estimating a global effort applied on a stock requires some
standardisation analyses according to the gears used. This can be greatly complicated by the
quantification of the trends in fishing power (Laurec, 1977 ; Millisher et al., 1999 ; Marchal et
al., 2002).
Regional contribution in the total effort
Reasoning at the scale of a given region to quantify the impact it can have on a
targeted stock requires to first define the relative part of the regional effort in the total fishing
pressure. Indeed, simulating an increase in the regional fishing effort will poorly affect the
state of the stock when the regional part in the total effort is relatively low. This should be
notably true for highly migratory and widespread stocks such as mackerel (Scomber
scombrus). Moreover, considering the potential evolution of the fishing effort following a
management action for instance, implies to include in the analysis the consequences it can
have on the other fleets. Indeed, bio-economic models generally focus on the variations of the
regional effort by considering the “rest of the world” fixed. This can lead to dangerous results
showing that local fisheries will always increase yields when increasing their effort, without
any risk of overexploitation (Ulrich, 2000). Competitive behaviour leading to technical
interactions (as discussed above) can drive to high variations in the allocation of effort in
time. Indeed, many reasons such as technological innovations, variations in some species
prices, species abundance and future catch restrictions can drive fishermen to modify the
species preferentially targeted (Ulrich et al., 2001 ; Millisher et al., 1999 ; Marchal et al.,
2002). This can change the relative contribution of the effort of a given fleet in the total effort.
However, for a given stock widely targeted by the region, it seems plausible to consider the
total regional effort relatively constant from one year to another in comparison with the rest of
the effort applied on the stock.
Outside fleet reactivity
The parameter  quantifies how the outside fleet reacts to a modification in the
regional effort and is critical to estimate the implementation of a management scenario at the
regional scale. According to its values, the outside effort may display very different
evolutions relatively to the regional fishing effort. As a consequence, the stock will not
display the same dynamics and this will strongly modify the potential yields for the regional
fishery. Because both fleets can be composed of a multitude of fishing fleets targeting the
same stock, the estimation of the total regional and outside efforts requires to identify
exhaustively the fleets concerned and to have their corresponding effort data. The variability
of fishing effort in time associated with fishing strategies and tactics (discussed above) makes
very difficult any precise prediction about the values of  according to a given management
action. Although some global trends may be drawn, the prediction of the evolution in the
outside fishing effort is related to numerous factors highly difficult to quantify such as the
degree of dependence between the fleets (competition, passive or active cooperation), the
rates of transfer of information between the different segments of the fishery and the nature of
the stock targeted (degree of clustering). In this perspective, it seems pertinent to define a
possible range of  values when simulating various scenarios of management for the region.
Conclusion
Although the simulation model developed appears to be relatively simple in its
structure, it aims to point out essential parameters that are necessary to take into account when
dealing at a regional scale. Indeed, both issues of the relative contribution of the region in the
total fishing effort as well as the behaviour of other fleets will have a consequence on the
yields, and eventually the state of the stock targeted. The response of other fleets notably
relates to the classic opposition in fisheries economics between the global management of a
common resource and the individual strategy of fishermen that mostly act on a short term
perspective. In this case, the reactivity parameter should enable to understand the impact on a
stock due to regional exploitation in function of different possible fishing behaviours of the
outside fleet through various simulations.
From age-structured assessments to surplus production models
State of the stock
Table IV describes the state of the 13 stocks of interest for the Finistère. Because of
missing data and biological information for the haddock (VII b-k) and the roundnose
grenadier, the state of these stocks is unknown.
Table IV. State of the stocks and corresponding source of information.
Species
Stock
Source
State of the stock
Anglerfish
Lophius piscatorius
Lophius budegassa
Gadus morhua
Leucoraja naevus
Cancer pagurus
Coryphaenoides rupestris
Melanogrammus aeglefinus
Merluccius merluccius
Lepidorhombus whiffiagonis
Nephrops norvegicus
Management area M
Management area L
Management area N
Pollachius virens
Merlangius merlangus
ICES CM 2003/ACFM:01
ICES CM 2003/ACFM:01
Outside safe biological limits
Inside safe biological limits
Outside safe biological limits
Growth overexploitation
Situation of MSY
Unknown
Unknown
Outside safe biological limits
Outside safe biological limits
Cod
Cuckoo ray
Edible crab
Grenadier
Haddock
Hake
Megrim
Norway lobster
Saithe
Whiting
ICES CM 2003/ACFM:03
Heessen, 2003
Ulrich, 2000
ICES CM 2002/ACFM:16
ICES CM 2003/ACFM:03
ICES CM 2003/ACFM:01
ICES CM 2003/ACFM:01
ICES CM 2001/ACFM:16
ICES CM 2001/ACFM:16
ICES CM 2001/ACFM:16
ICES CM 2003/ACFM:02
ICES CM 2003/ACFM:03
Exploited at sustainable levels
Exploited at sustainable levels
Outside safe biological limits
Inside safe biological limits
Inside safe biological limits
Biological Production functions
First, a generalized production model (Pella and Tomlinson, 1969) is fitted to the
yield-per-recruit functions when available. This assumes that a surplus production model can
well represent a major part of the dynamics estimated through yield-per-recruit assessment. It
thus implies that the recruitment is considered independent on the spawners biomass for a
large range of fishing intensity and it can then be represented by a mean value, averaging its
potential variability due for instance to climatic factors. Equation of the equilibrium
production curve is obtained from the differential equation:
(6)
  B  m1 
dB
 r B 1      F B
 K 
dt


where B is the biomass of the stock, r is the intrinsic growth rate, K is the carrying capacity,
m is the shape parameter and F is the fishing mortality that can be expressed as a function of
the nominal effort (f) and the coefficient of catchability (q) : F=qf.
Setting equation (6) to zero gives biomass and yield at equilibrium:
(7)
1

m
1
F
 B  K 1  
e

r


1

 F  m 1
Ye  F Be  FK 1  
r


Fishing mortality is expressed in function of a fishing effort multiplier (mf comprised
between 0 and 2) and the current catchability estimated for the situation of reference. The
parameters r, K and m are estimated by the least squared method for all the stocks with
sufficient available data. Equation (7) is re-expressed as :
1

m 1
q
mf


 B  K 1  curr

 e
r




  q mf
Ye  qcurr mf 1   curr
r

 
(8)
1
  m1
 

The high flexibility of the generalized production model (Pella and Tomlinson, 1969)
enables to fit well the yield-per-recruit curves (Fig. 4). Figure 5 shows an example of
production curve estimated with the method for the stock of northern hake (Merluccius
merluccius). All models were fitted on yield-per-recruit curves estimated by ACFM except
the edible crab (Cancer pagurus), the cuckoo ray (Leucoraja naevus) and the roundnose
grenadier (Coryphaenoides rupestris). This latter was assessed by pseudo-cohort analysis
corrected for changes in fishing effort (Allain, 1999; Lorance et al., 2001). The method
requires relatively strong assumptions that question the conclusions (Lorance et al., 2001) but
it remains the only available assessment for this species. The stock of cuckoo ray was
assessed through the use of a yield-per-recruit model (Chavance, 2001) and the stock of edible
crab by a Fox (1970) model by Ulrich (2000). This latter model mathematically corresponds
to the generalized production model when the shape parameter tends to 1. It is expressed as:
(9)
dB
 ln B 
 r B 1 
F B
dt
 ln K 
Except the trivial null solution, the equilibrium solution for (9) is:
Be  K e

ln K
F
r
As for the generalized model, the biomass and catches can thus be expressed in function of a
fishing mortality multiplier (mF) because the catchability is unknown:
(10)
ln K

mF

r
B

K
e
 e

ln K
Y  q mF K e  r
curr
 e
mF
All exploitation and population parameters estimated are given in appendix 4 and 5.
Production models were not estimated for some stocks of Norway lobster (Nephrops
norvegicus) because required information is currently not available.
Yields at equilibrium (kg)
6,E+04
5,E+04
3,E+04
Y=Y/R * Rprev
2,E+04
Generalized model
0,E+00
0
0,5
1
1,5
2
Fishing mortality (mF)
Fig. 4. Equilibrium curve of a generalized production model fitted to a series of yields estimated
through yield-per-recruit assessment for the northern hake (Merluccius merluccius).
Biomass at equilibrium (tons)
2,E+06
1,E+06
8,E+05
4,E+05
0,E+00
0,E+00
2,E+04
4,E+04
6,E+04
Yields at equilibrium (tons)
Fig. 5. Plots of the biomass at equilibrium of the northern hake (Merluccius merluccius) in relation
with the corresponding yields at equilibrium. Biomasses and yields are estimated by fitting a
generalized production model to a series of yield-per-recruit for a range of fishing mortality.
Modelling variability in biological production functions
The following text is the abstract of a paper submitted to the journal ‘Aquatic Living
Resources’. Although the article mainly deals with theoretical ecology, the approach
presented will be used in the next steps of the PECHDEV project. Indeed, the objective is to
define alternative biological production functions for some stocks according to the biomass of
their preys and predators within the ecosystem considered. This approach should be applied in
the Celtic Sea ‘Ecosystem Fishery Unit’ for some fish species of major economic importance
for the Finistère.
Abstract
A simulation model is developed in order to analyse the variability of production
functions in a virtual exploited ecosystem. We assume that a complex food web can be
represented by a set of trophic classes interacting by predation. Each class is given a model of
recruitment, growth, survival, catch and a function of trophic preference. Preys are selected
according to their abundance in the system and the function of trophic preference of predator
classes estimated in the virgin situation. A parameter of food consumption per unit biomass
defines the magnitude of foraging of each trophic class. The fishery mainly targets high
trophic levels following a given function of selectivity. Some major features of the ecosystem
functioning are tested by simulations: the intensity of top-down and bottom-up controls and
the degree of trophic opportunism. Results show that production functions are highly
dependent on the predation parameters and vary differently according to trophic level. Fishing
activity modifies the biomass distribution and strongly affects high trophic levels which are
very sensitive to exploitation. Trophic dynamics within the system are thus altered through
the rates of predation mortality. In systems where predation mortality is high, top-down
control predominates so that fishing affects all the components of the food web. These
“fishing controlled” systems display compensatory mechanisms by release from predation
control. We also show that systems where productivity is dependent on prey abundance are
more “environment controlled” and seem more sensitive to overexploitation, particularly in
the high trophic levels. Trophic opportunism tends to dampen the propagation of top-down or
bottom-up controls through the food web and thus stabilizes the ecosystem. Trophic
relationships are thus essential factors of the ecosystems that determine their production and
reaction capacity to exploitation. A major key in ecosystem approach lies in their routine
analysis.
Application to other regions
The French fishery sector
Introduction
Within the PECHDEV project, the French fishery sector and more particularly the fish
production sub-sector is chosen as a first case of application of the Computable General
Equilibrium Model (CGEM) to real data. The French fish production is arbitrarily separated
between a gadoid group and a ‘others’ group that gathers all remaining landed species. This
enables to deal with the problem of overexploitation of most of the Gadidae species in the
Northeast Atlantic. First, parameters of surplus production models in the form of Fox models
(Fox, 1970) are estimated following an empirical approach presented and based on catch data
time-series. In a second step, a biological production function to implement in the
Computable General Equilibrium Model (CGEM) is proposed and allows to take account for
the reactivity of foreign fleets regarding a variation in the French fishing effort targeting a
given group. Three different scenarios of reactivity are considered and drive to 3 different sets
of parameters for the biological production functions of the 2 “stocks” of interest.
Estimating biological production functions
The surplus production model of Fox (Fox, 1970) is selected in the analysis and can be
expressed as:
dB
K
 g ( B)  FB  r  B  ln    FB
dt
B
(1)
where g is the growth function of the stock, F is the fishing mortality applied on the stock, r is
the intrinsic growth rate parameter and K is the carrying capacity i.e., the maximal biomass
sustained by the environment.
In order to estimate the parameters of the biological production functions for the gadoid and
‘others’ groups, the parameters of the Fox model are re-expressed in function of Maximum
Sustainable Yield (MSY) and the corresponding fishing mortality (FMSY):
MSY  e

K 
FMSY

r  F
MSY

(2)
This parameterisation enables to express the yield and biomass at equilibrium following
equation (3):
 FMSY  F 





 Be  MSY  e  FMSY 
FMSY


 F 

MSY  e  FMSY 
e
Ye  F 
FMSY

(3)
Some strong assumptions are made in order to approximate the biological production
functions of the fish groups from time-series of catch data. Considering that fishing effort has
slowly increased in Northwest Atlantic, we first assume that catch time-series data
approximately follow equilibrium catches. We thus consider that the Maximum Sustainable
Yield (MSY) corresponds to the maximum of mean catch for a few years observed in the
time-series data. It is then directly given by the data. We then assume that the mean yield for
the groups estimated on the last few years of data considered is at equilibrium (Ycurr). We
finally assume that the fishing mortality is equal to the natural mortality (M) affecting the
stock in the situation of MSY (Garcia et al., 1989). We assume a natural mortality of 0.2 for
the gadoid group and of 0.4 for the ‘others’ group. Considering equation 3 in the current
situation allows to estimate Fcurr from solving equation 4:
(4)
Ycurr
 Fcurr  e
K
 Fcu rr
r
Application to the gadoid and ‘others’ groups
Total catches
The approach assumes that the gadoid and ‘others’ stocks are unique in the Northeast
Atlantic. The set of Gadidae species landed in France is selected as gadoid group (Appendix
1). The blue whiting (Micromesistius poutassou) is excluded of the group because it
corresponds to a recent fishery that extended rapidly in the last decade. Therefore, the blue
whiting landings have increased whereas the aim of the analysis is to evaluate the impact of
the overexploitation of Gadidae species. Plotting the catch of the gadoid group versus time
shows a strong decrease that began in the middle of the 70s, following the famous ‘gadoid
outburst’ of the 60s and 70s (Hislop, 1996).
4.E+06
Catches (Tons)
Pollachius virens
3.E+06
Molva molva
Merluccius merluccius
2.E+06
Merlangius merlangus
1.E+06
Melanogrammus aeglefinus
0.E+00
1950
1960
1970
1980
1990
2000
Gadus morhua
Years
Fig. 1. Total catches of the gadoid group in the Northeast Atlantic (Source: FAO). Only main
species are given in legend.
The ‘others’ group includes all other species landed in France except all aquatic plants. This
group displays 154 species or species groups (Appendix 2). Figure 2 shows a global
increasing trend in the catches since the 50s. We assume in the analysis that the catch of the
‘others’ group are nowadays at the Maximum Sustainable Yield (MSY).
Sprattus sprattus
1.E+07
Catches (Tons)
Scomber scombrus
8.E+06
Micromesistius poutassou
5.E+06
Mallotus villosus
3.E+06
Clupea harengus
0.E+00
1950
1960
1970
1980
Years
1990
2000
Ammodytes spp
Fig. 2. Total catches on the gadoid group in the Northeast Atlantic (Source: FAO). Only main
species are given in legend.
Exploitation parameters
From the time-series of catch data provided by the FAO2, the parameters of the gadoid and
‘others’ groups can be estimated following the method presented above (Table I).
Table I. Parameters of the biological production models for the gadoid and ‘others’ groups.
r
K
MSY FMSY Y curr
B curr F curr
0.2 48547829 3571950 0.2 1725632 3157205 0.55
0.4 60293405.1 8872282 0.4 8872282 22180704
0.4
Gadidae
Others
Regional Production Model (RPM)
Model and assumptions
In the CGEM applied to the French fishery sector, the French yield (Yin) is estimated within
the economic sub-module. However, no data is provided regarding the fishing effort applied
to the same stock by foreign fleets. This requires that assumptions are made on the fishing
behaviour of these fleets. In this perspective, a power type function linking the effort
multipliers between French and foreign fleets is assumed (Equation 5). This enables to
simulate different fishing behaviours between the two fleets.
Fout  F
curr
out
(5)
 Fin 

  curr

F
 in 

where F is the fishing mortality, out indicates the foreign fleets (other than French), curr
indicates the current situation, in indicates the French fleet and  is the reactivity parameter.
In the current situation, the French catch represent a relative part () of the total catch :
 Yincurr Fincurr
 curr  curr  
Ftot
 Ytot
 curr
curr
 Yout  Fout  1  
 Y curr F curr
out
 tot
(6)
(7)
2

Fincurr


curr
1
Fout
Ytot  Yin  Yout
FAO. 2000. Fisheries Department, Fishery Information, Data and Statistics Unit. Fishstat
Plus: Universal software for fishery statistical time series Version 2.3.
Ytot  Fin  B  Fout  B

Ytot  Fin  B  F
curr
out
 Fin 
  B
  curr
 Fin 
 1 

F curr  Fin 

Ytot  Fin  B   1  out
 F curr  F curr  1 
in
in



(8)
Ytot

 1
 1 Y
B curr  
in

 Yin  1 
   curr 


 B Yin  

Equation (8) can be included in the biological equations approximated in the CGEM as:
(9)
Bt 1

 Bt  g ( Bt )  Yt 1  


with  
1


Y
  t
 Bt



 1




B curr
Yincurr
where B is the biomass of the stock, t is the time step in the model (year), g is the growth
function of the stock (equation1), Y is the yield estimated in the economic sub-module of the
CGEM,  is a constant parameter and  is the reactivity parameter. Values of  are 6.0% for
the Gadoids and 3.6% for the ‘others’ group respectively.
Simulation scenarios
We propose to simulate 3 different scenarios of reactivity to illustrate the potential range of
responses of the stock to fishing exploitation (Table II). The example of subventions from the
European Union is chosen for illustration purpose:
-
-
=1, foreign fleets exactly follow the variation in effort allocation of the French fleet.
This can represent situations in which European policy is similar for all the European
fleets: subventions for the exit of fishing vessels concerning all European countries.
=0.5, variations in foreign fleets efforts are slower than variations in French fishing
effort representing a case of difference in the magnitude of the subvention.
=0, foreign fleets do not modify their fishing effort i.e., the foreign fishing mortality
remains constant whatever the variations in French effort allocation. This can simulate
cases of subvention concerning only 1 given region or country in the EU.
Table II. Values of the  parameter of equation (9) according to the different values of .

0
0.5
1
Gadoids
0.51
2.84
15.74
Others
0.39
3.21
26.69
Conclusion
The approach presented to estimate biological production functions lies on really strong
assumptions certainly not verified for the 2 groups of interest. However, the aim of the present
study is not to conduct new stock assessments but only to give an order of magnitude for the
production functions. The application of a CGEM to the fishery sector is original from an
economic point of view because this type of modelling has never been applied to real data in
this sector. It is also in complete rupture with traditional bio-economic approaches because i)
the yield is estimated through economic equations including capital and labour explicitly and
does not require the estimation of a fishing effort ii) the biological module describing the
stock dynamics is thus separated from the economic module iii) the model can take account
for the fishing strategies of other fleets harvesting on the same stock as the fleet of interest.
Finistère and Salerno cases
The most important species in terms of tonnage and value selected for all the PECHDEV
regions are given in appendix 3. The methodology presented above allowed us to estimate
population and exploitation parameters for the cases of Finistère and Salerno (Tables VI-IX).
For the Salerno case, when no age-structured stock assessment was available, empirical
production functions following the method presented for the French fishery sector were
estimated. Appendix 4 gives the relative part of Salerno catch on the total catch harvested by
the Salerno fleets. This approach should also be conducted for the stocks of Norway lobster
(Nephrops norvegicus) in the Celtic Sea for the Finistère case.
Table VI. Exploitation parameters estimated for the stocks selected for the Finistère case.
Scientific name
ICES subdivisions
VIII a, b (MA N)
Merluccius merluccius
III a, IV, VI, VII, VIII a, b, d
Cancer pagurus
Stock France
Cancer pagurus
Stock United Kingdom
Lophius piscatorius
VII, VIII a, b
Lophius budegassa
VII, VIII a, b
Gadus morhua
VII e, f, g, h, j, k
Merlangius merlangus
VII e, f, g, h, j, k
Melanogrammus aeglefinus VII b, c, d, e, f, g, h, j, k
Nephrops norvegicus
VII, f, g, h (MA M)
Nephrops norvegicus
VII b, c, j, k (MA L)
Lepidorhombus whiffiagonis VII, VIII a, b, d, e
Leucoraja naevus
one unique stock
Pollachius virens
III a, IV, VI a, b
Coryphaenoides rupestris
V b, VI, VII
Nephrops norvegicus
q curr
0,366
0,240
N#A
N#A
0,244
0,183
0,640
0,316
0,317
N#A
N#A
0,236
0,215
0,229
0,068
F curr Ye (Tons)
0,5220
3 123
0,2849 45 360
1,443
3 844
1,443
5 259
0,2944 16 771
0,2425
6 986
1,0142
5 920
0,6251 16 806
0,4741
7 569
N#A
N#A
N#A
N#A
0,2473 16 673
0,4000
5 695
0,4495 119 130
0,1045
8 090
Table VII. Population parameters estimated for the stocks selected for the Finistère case.
Scientific name
ICES subdivisions
VIII a, b (MA N)
Merluccius merluccius
III a, IV, VI, VII, VIII a, b, d
Cancer pagurus
Stock France
Cancer pagurus
Stock United Kingdom
Lophius piscatorius
VII, VIII a, b
Lophius budegassa
VII, VIII a, b
Gadus morhua
VII e, f, g, h, j, k
Merlangius merlangus
VII e, f, g, h, j, k
Melanogrammus aeglefinus VII b, c, d, e, f, g, h, j, k
Nephrops norvegicus
VII, f, g, h (MA M)
Nephrops norvegicus
VII b, c, j, k (MA L)
Lepidorhombus whiffiagonis VII, VIII a, b, d, e
Leucoraja naevus
one unique stock
Pollachius virens
III a, IV, VI a, b
Coryphaenoides rupestris
V b, VI, VII
Nephrops norvegicus
r
-0,108
-0,159
12,822
13,274
-0,062
-0,096
-0,126
-0,072
-0,288
N#A
N#A
-0,128
-0,233
-0,053
-0,021
K (Tons)
84 786
1 284 398
7 242
9 908
1 219 609
288 029
208 575
357 662
89 125
N#A
N#A
458 632
100 000
5 896 535
578 293
m
0,349
0,519
1
1
0,444
0,471
0,421
0,115
0,436
N#A
N#A
0,442
0,508
0,314
0,085
Table VIII. Population parameters estimated for the stocks selected for the Salerno case.
Scientific name
Sub-areas
Aristaemorpha foliacea G5 operational unit
Aristeus antennatus
G5 operational unit
Engraulis encrasicolus Sardinia
Merluccius merluccius G5 operational unit
Mullus barbatus
G5 operational unit
Mullus surmuletus
Sardinia
Nephrops norvegicus
Sardinia
Octopus vulgaris
Sardinia
Others
Sardinia
Parapaeneus longirostris G5 operational unit
Sardina pilchardus
Sardinia
Sepia officinalis
Sardinia
Squilla mantis
Sardinia
Thunnus thynnus
East Atl. & Mediterranean
r
K (Tons)
-0.38
25
-0.30
10
0.84
75794
-0.70
500
-0.38
150
0.2
2433
0.18
15163
0.25
38441
0.4 338063
-0.34
50
0.22 296426
0.25
1207
1.41
1902
0.36 297271
m
0.295
0.137
1
0.555
0.201
1
1
1
1
0.329
1
1
1
1
Table VIII. Exploitation parameters estimated for the stocks selected for the Salerno case.
Scientific name
Sub-areas
F curr Ycurr B curr
Thunnus thynnus
G5 operational unit area
0.72 28959 40282
Sepia officinalis
G5 operational unit area
0.47
322
690
Octopus vulgaris
Sardinia
0.39 3158
8130
Aristaemorpha foliacea G5 operational unit area
0.48
3.5
15
Aristeus antennatus
G5 operational unit area
0.66
1.9
6
Parapaeneus longirostris Sardinia
1.02
9.2
20
Mullus barbatus
Sardinia
1.46 29.2
48
Squilla mantis
Sardinia
3.90
465
119
Engraulis encrasicolus Sardinia
3.02 6414
2127
Merluccius merluccius G5 operational unit area
0.93
57
131
Nephrops norvegicus
Sardinia
0.55
387
704
Sardina pilchardus
Sardinia
0.78 6575
8379
Mullus surmuletus
Sardinia
0.2
179
895
Others
East Atl. & Mediterranean
0.4 49747 124366
Perspectives
The estimation of biological production functions should be done for all the stocks selected by
each region of the PECHDEV project. In the case of Salerno, some uncertainty lies on the
areas of definition of the stocks targeted. Therefore, it could be interesting to test different
hypotheses defining alternative biological production functions for the stocks for which some
uncertainty exists. The effects of these alternative hypotheses on the outputs of the CGEM
would be interesting to analyse. Besides, production functions based on age-structured data
assume a recruitment fluctuating around a mean value. However, the decrease in spawning
stock biomass can generate recruitment overexploitation and sometimes imply the collapse
and eventually the extinction of a given fish stock. An approach based on the reference points
defined by the assessments working groups such as Blim (biomass limit) or Bpa (biomass of
precautionary approach) when they are available could enable to complete the functions
estimated in the case of high fishing pressure.
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Appendix
Appendix 1. List of Gadidae species selected in the gadoid group for the French fishery sector.
Scientific name
Brosme brosme
Coryphaenoides rupestris
Gadiformes
Gadus morhua
Gaidropsarus spp
Macrourus berglax
Melanogrammus aeglefinus
Merlangius merlangus
Merluccius merluccius
Molva dypterygia
Molva molva
Moridae
Phycis blennoides
Pollachius pollachius
Pollachius virens
Trisopterus luscus
English name
Tusk
Roundnose grenadier
Gadiformes
Cod
Rocklings
Roughhead grenadier
Haddock
Whiting
Hake
Blue ling
Ling
Moras
Greater forkbeard
Pollack
Saithe
Pouting
Appendix 2. List of species selected in the ‘others’ group for the French fishery sector.
Scientific names
Acipenseridae
Aequipecten opercularis
Alopias vulpinus
Alosa alosa
Alosa fallax
Alosa spp
Ammodytes spp
Anarhichas lupus
Anguilla anguilla
Aphanopus carbo
Apogonidae
Argentina spp
Argyrosomus regius
Atherinidae
Balistes carolinensis
Belone belone
Beryx spp
Bivalvia
Boops boops
Brachyura
Brama brama
Buccinum undatum
Cancer pagurus
Carcinus maenas
Centroscyllium fabricii
Cerastoderma edule
Cetorhinus maximus
Chamelea gallina
Clupea harengus
Clupeoidei
Conger conger
Crangon crangon
Crassostrea gigas
Crustacea
Dasyatis spp
Dicentrarchus labrax
Dicentrarchus punctatus
Dicologlossa cuneata
Diplodus sargus
Donax spp
Elasmobranchii
Engraulis encrasicolus
Epigonus telescopus
Epinephelus marginatus
Galatheidae
Galeorhinus galeus
Gastropoda
Glyptocephalus cynoglossus
Haliotis tuberculata
Helicolenus dactylopterus
Hippoglossoides platessoides
Scientific names
Hydrolagus spp
Illex coindetii
Labridae
Lamna nasus
Lepas spp
Lepidopus caudatus
Lepidorhombus whiffiagonis
Limanda limanda
Lithognathus mormyrus
Littorina spp
Loliginidae, Ommastrephidae
Lophius piscatorius
Maja squinado
Mallotus villosus
Microchirus spp
Micromesistius poutassou
Microstomus kitt
Mollusca
Mugilidae
Mullus surmuletus
Mustelus spp
Myliobatidae
Mytilidae
Mytilus edulis
Natantia
Nephrops norvegicus
Octopodidae
Osmerus eperlanus
Osteichthyes
Ostrea edulis
Pagellus acarne
Pagellus bogaraveo
Pagellus erythrinus
Pagrus pagrus
Palaemon serratus
Palinurus elephas
Palinurus mauritanicus
Palinurus spp
Pandalus borealis
Paracentrotus lividus
Pecten maximus
Pectinidae
Petromyzon marinus
Platichthys flesus
Pleuronectes platessa
Pleuronectiformes
Polyprion americanus
Portunus spp
Prionace glauca
Psetta maxima
Raja batis
Scientific names
Raja microocellata
Raja montagui
Raja naevus
Raja oxyrinchus
Raja spp
Reinhardtius hippoglossoides
Ruditapes decussatus
Salmo salar
Salmo trutta
Salmonoidei
Sarda sarda
Sardina pilchardus
Sarpa salpa
Scomber japonicus
Scomber scombrus
Scombridae
Scophthalmus rhombus
Scorpaenidae
Scyliorhinus canicula
Scyliorhinus spp
Scyliorhinus stellaris
Sebastes spp
Sepiidae, Sepiolidae
Solea lascaris
Solea solea
Soleidae
Sparidae
Sparus aurata
Spisula solida
Spondyliosoma cantharus
Sprattus sprattus
Squalidae
Squalus acanthias
Squatinidae
Thunnus alalunga
Thunnus obesus
Thunnus thynnus
Torpedo spp
Trachinus draco
Trachurus trachurus
Triglidae
Umbrina canariensis
Veneridae
Venerupis pullastra
Xiphias gladius
Zeus faber
Hippoglossus hippoglossus
Homarus gammarus
Hoplostethus atlanticus
Raja circularis
Raja clavata
Raja fullonica
Appendix 3. List of the species selected for each region of interest for the PECHDEV project.
Region
Salerno
Scientific name
Aristaemorpha foliacea
Aristeus antennatus
Engraulis encrasicolus
Merluccius merluccius
Mullus barbatus
Mullus surmuletus
Nephrops norvegicus
Octopus vulgaris
Parapaeneus longirostris
Sardina pilchardus
Sepia officinalis
Squilla mantis
Thunnus thynnus
Cornwall Cancer pagurus
Lepidorhombus Whiffiagonis
Lophiidae
Merlucciidae
Microstomus kitt
Pectinidae
Pollachius pollachius
Scombridae
Scophtalmus maximus
Soleidae
Finistère Cancer pagurus
Coryphaenoides rupestris
Gadus morhua
Lepidorhombus whiffiagonis
Leucoraja naevus
Lophius budegassa
Lophius piscatorius
Melanogrammus aeglefinus
Merlangius merlangus
Merluccius merluccius
Nephrops norvegicus
English name
Giant red shrimp
Blue and red shrimp
European anchovy
European hake
Striped mullet
Red mullet
Norway lobster
Common octopus
Deepwater rose shrimp
European pilchard
Common cuttlefish
Spottail mantis squillid
Northern bluefin tuna
Crabs
Megrim
Monks
Hake
Lemon sole
Scallops
Pollack
Mackerel
Turbot
Sole
Edible crab
Grenadier
Atlantic cod
Megrim
Cuckoo ray
Anglerfish
Anglerfish
Haddock
Whiting
European hake
Norway
Regional name
Gamberi rossi
Gamberi rossi
Alici
Naselli
Triglia di fango
Triglia di scoglio
Scampi
Polpi
Gamberi bianchi
Sardine
Seppie
Pannochie
Tonno rosso
Crabs
Megrim
Monks
Hake
Lemon sole
Scallops
Pollack
Mackerel
Turbot
Sole
Tourteau
Grenadier
Morue
Cardine
Raie fleurie
Baudroie rousse
Baudroie commune
Eglefin
Merlan
Merlu
Langoustine
Pollachius virens
Bornholm Gadus morhua
Pandalus borealis
Pleuronectes platessa
Salmo salar
Sprattus sprattus
Saithe
Cod
Northern prawn
Plaice
Salmon
Sprat
Lieu noir
Torsk
Rejer
Rotspatte
Laks
Brisling
Appendix 3 (end). List of the species selected for each region of interest for the PECHDEV project..
Region
Scientific name
Pontevedra Cerastoderma edule
Conger conger
Hippoglossus hippoglossus
Lepidorhombus boscii
Lophius budegassa
Merluccius merluccius
Micromesistius poutassou
Mytilus Galloprovincialis
Nephrops Norvegicus
Octopus Vulgaris
Pollicipies cornucopiae
Psetta maxima
Sardina pilchardus
Scomber scombrus
Thunnus alalunga
Todaropsis eblanae
Trachurus trachurus
Venerupis pulastra
Xiphias gladius
English name
Common edible cockle
Conger eel
Atlantic halibut
Megrim
Black bellied angler
Hake
Blue whiting
Mussel
Norway lobster
Common octopus
Barnacle
Turbot
European pilchard
Atlantic mackerel
Albacore
Lesses flying squid
Horse mackerel
Carpet shell
Swordfish
Regional name
Berbercho
Congrio
Fletan
Gallo
Rape
Merluza
Lirio
Mejillón
Cigala
Pulpo
Percebe
Rodaballo
Sardina
Caballa
Bonito
Pota costera
Jurel
Almeja
Pez espada
Appendix 4. Relative proportion of Salerno catch in the total catch for each stock targeted.
Scientific name
Aristaemorpha foliacea
Aristeus antennatus
Engraulis encrasicolus
Merluccius merluccius
Mullus barbatus
Mullus surmuletus
Nephrops norvegicus
Octopus vulgaris
Others
Parapaeneus longirotris
Sardina pilchardus
Sepia officinalis
Squilla mantis
Thunnus thynnus
Sub-areas
Salerno relative part
G5 operational unit
100%
G5 operational unit
100%
Sardinia
3%
G5 operational unit
100%
G5 operational unit
100%
Sardinia
3%
Sardinia
100%
Sardinia
6%
Sardinia
5%
G5 operational unit
100%
Sardinia
2%
Sardinia
24%
Sardinia
34%
East Atl. & Mediterranean
9%