Journal of Environmental Protection, 2010, 1, 117-120
doi:10.4236/jep.2010.12015 Published Online June 2010 (http://www.SciRP.org/journal/jep)
1
Quantitative Analysis of the Fishing Activity in the Gulf of
Manfredonia (Gargano, South-Italy)
Luca Grilli1, Pasquale Marcello Falcone2
1Dipartimento di Scienze Economiche, Matematiche e Statistiche Università degli Studi di Foggia, Foggia, Italy; 2Post-Graduate at
Faculty of Economics, Università degli Studi di Foggia, Foggia, Italy.
Received March 18th, 2010; revised April 1st, 2010; accepted April 18th, 2010.
ABSTRACT
The Manfredonia City Marine is the third in Italy both for its size and for its nation-wide importance, in the last decade
a considerable crisis has been registered in this economic sector as shown by the always decreasing number of fishing
boats registered in the Harbour-Office. As a result of such a reduction in the number of fishing boats, a remarkable
fall-off in the production occurs. The fishing activity registers a deep legislative, organizational and operational trans-
formation. The European Community, in order to face the indiscriminate impoverishment of the ichthyic inheritance,
has provided incentives for the fishing boats’ casting off, by mean of an adequate reward. This paper aims to quantita-
tively analyze the fishing activity in the Gulf of Manfredonia in order to present a significant picture of the forthcoming
situation on the basis of real data. To this end, we adopt a Prey-Predator model in discrete time that is suitable to de-
scribe properly the dynamics of an ecosystem in which just two species interact: predator and prey. The results show
worrying forecasts. The fishing boats’ number presents a decreasing dynamic and, above all, we record a remarkable
reduction in the stock of fishes in the Gulf of Manfredonia. The quantity of fishes, in twenty years, will be reduced of
28%. The Gulf sea, once rich in codfishes, mullets, cuttlefishes, octopus etc., runs the risk (on the basis of the results
obtained in this paper) of making such species rare. The situation should be much more critical if the fishing activity in
the Gulf runs at the rhythms of one decade ago. We apply the model at data from 1995, and we obtain catastrophical
results; the number of fishing boats in the sector in 2015 should be 107 units (77% less) and the ichthyic inheritance
about 16345 tons (45% less).
Keywords: Renewable Resources, Dynamical Systems, Sustainable Development
1. Introduction
Manfredonia (Gargano, South-Italy), a fishing and
sailing city, possesses one of the most representative
marine of Italian coasts (third in Italy).
In the last decade the situation of marine activity has
been changing and still now it is in the middle of a cri-
sis. In the year 1995, the number of fishing boats reg-
istered in the Manfredonia Harbour-Office was 450,
and in 2007 we count only 195 boats, and, on average,
the fishing boats are about 26 years old (data from
Manfredonia Harbour-Office).
The last explicative data show a strong dropping
trend of this important economic sector. In the year
1995, the registered production was 7072 tons corre-
sponding to a value of 17071134 Euro; in the year 2007
we register a production of 1014 tons equivalent to
5393154 Euro.
The reasons for such a situation, that is undoubtedly
hard and worrying, are quite complex. It should be
simplistic to blame the high cost of oil weighing upon
the management costs of a fishing boat (from 40 up to
60 percent according to the boat). The high cost of oil
has only increased the speed of a problem which was
latent and was under-estimated; this problem leads di-
rectly to a dangerous crisis which is representative of a
very bad situation. A proof for it is given by the recent
strikes and positions adopted by the professional fish-
ing category in order to reveal the increasing state of
difficulty of the fishing activity. It is worth considering
also that the fishing activity is undergoing a deep trans-
formation from the legislative, managerial and opera-
tional viewpoint.
The European Community, which is the Member
States, has impressed a vigorous legislative veer in
order to face the indiscriminate impoverishment of the
ichthyic inheritance, which was subjected to an uncon-
trolled and irrational harvesting activity. The European

Quantitative Analysis of the Fishing Activity in the Gulf of Manfredonia (Gargano, South-Italy) 118
Community, followed by the Italian Government, has
recently provided incentives, by mean of an adequate
reward, for the fishing boats’ casting off. As a conse-
quence, many fishers-ship-owners, close to the pension,
has taken this opportunity that was, for many reasons, a
providential help. This incentive has been suspended
by the Minister of Agriculture in august 2005. It is re-
alistic to suppose that the normative for the fishing
boats’ casting off will be reactivated with rewards
more attractive compared with the past. For the mo-
ment the incentives have not been restored, although it
is worth noting that the “Fondo Europeo sulla Pesca”1
(F.S.P.) has been brought into force for the period
2007-2013. The F.S.P. will provide funds to fishers and
ship-owners in the case of a temporary stop of the
fishing activity due to public safety or natural emer-
gency but also for professional training and early-re-
tirement.
The problem of resource extraction activity is of
great interest and it is studied by mean of many differ-
ent approaches. In Grilli [1,2], the author studies a dif-
ferential game in which players are overlapping gen-
erations of extractors of a renewable good, the author
considers the case in which players are not perfectly
symmetric.
In this paper we apply a discrete time model in order
to analyze and understand the evolutionary dynamic of
the ecosystem. We focus our attention on the problem
of the ichthyic inheritance’s impoverishment in the
Adriatic Sea and in particular in the Gulf of Manfredo-
nia. In order to have a picture of the future situation
that is based on real data we adopt a prey-predator
model in discrete time. Such mathematical model is
able to describe the dynamic of an ecosystem in which
only two species interact: the predator (in the case in
point we consider the fishing boats active in the Gulf of
Manfredonia) and the prey (the ichthyic inheritance in
the zone).
2. The Model
In order to construct the model it is necessary to know, a
priori, the number of preys (fishes) and predators (fishing
boats). The number of fishing boats registered in the
Manfredonia Harbour-Office for the year 2007 (the most
recent official data available for catch and fishing boats)
is 195 units. The computation of the number of fishes,
exactly the catch measured in tons, it is not trivial at all.
In this paper, in order to estimate the number of fishes in
the Gulf of Manfredonia, we consider the mean harvest-
ing rate in the Adriatic Sea, which is about 2%. The last
information together with the average quantity of catch
in the last years (we consider the last five years in the
period 2003-2007), allows us to estimate the stock of
fishes in the zone. In fact, the ichthyic stock is computed
using the ratio between the average catch and the average
harvesting rate:
The data about the catch in the zone referred to the pe-
riod considered are:
 Year 2003 = 1014 tons;
 Year 2004 = 1530 tons;
 Year 2005 = 1990 tons;
 Year 2006 = 2370 tons;
 Year 2007 = 1895 tons;
So the average catch results equal to 1760 tons.
The ichthyic stock is:
RateHarvesting
Catch
ckIchtyicSto _ 
that is:
tonsckIchtyicSto 87983
02,0
1760 
It is necessary to underline that this data refers to the
entire Adriatic Sea. Knowing that the marine of Manfre-
donia, for its position and size, is not able to reach the
entire area we have established, comparing the produc-
tion of Manfredonia to the production of other competing
cities in the Adriatic Sea (Ancona, San Benedetto del
Tronto), that the Marine of Manfredonia can influence
only one third of the ichthyic stock in the zone. As a
consequence the data interesting for our analysis is
29327 tons.
In the model, let us consider that at time t = 0 the ich-
thyic inheritance of the Gulf is 29327 tons, and the num-
ber of fishing boats is 195 units. Let us suppose that, if it
is known the quantity of predators and preys at time t, at
time t + 1 the evolutionary dynamics is the following:
1
1
Pr0, 2 Pr0,002 Pr
Pr0,39 Pr1, 022 Pr
tt
tt
edators edatorseys
eysedators eys




 

t
t
In order to understand the coefficients’ choice it is nec-
essary to present criteria adopted for their computation.
The coefficient a1,1 (0,2) must undoubtedly be < 1
since it represents the way in which the predators evolve
in absence of preys, at time t + 1 the absence of fishes
pushes the fishers out from the market even if a little part
of them decides to continue the activity in the short run.
The coefficient a1,2 (0,002) represents the variation
rate of fishing boats as a function of the ichthyic stock.
The coefficient a2,1 (–0,39) indicates the harvesting
ability, more precisely, how the number of fishes is af-
fected by the harvesting activity.
The coefficient a2,2 (1,022) describes how fishes
evolve in absence of predators. In the model, for sake of
simplicity, we suppose that the only cause of death for
fishes derives from predators. This coefficient is com-
puted as follows:
2007Stock Ichthyic
2007Catch 2007Stock Ichthyic
1European Fishery Fund

Quantitative Analysis of the Fishing Activity in the Gulf of Manfredonia (Gargano, South-Italy)119
Once the evolutionary dynamic is established it is pos-
sible, by mean of simple elements of linear algebra (ma-
trix diagonalization), to provide a picture of the fishing
activity in Manfredonia for the future in the next years.
The model, of course, provides answers that are more
accurate if we look at the short term. We are interested in
the evolution of predators (fishing boats) and preys
(fishes) in 20 years.
Let A the coefficient matrix derived by the evolution-
ary dynamic described above, if we suppose that such
dynamic does not change, it is clear that the solution of
our problem is:

















0
0 20
20
20
Pr
Pr
Pr
Pr
eys
edators
A
eys
edators
If the matrix A is diagonalizable, let S be the matrix of
eigentvectors associated to the eigenvalues of A and let D
be the diagonal matrix of its eigenvalues, it holds:
.
20120 SDSA 

The matrix A is diagonalizable in the field of real num-
bers since it presents two eigenvalues 1

and 2

, that
are real and distinct numbers:
02,1
1

and .22,0
2

The space of eigenvector associated to the eigenvalue
1

is ():

0\t









t
t
x952,410
1
The space of eigenvector associated to the eigenvalue
2

is ():

0\t









t
t
x04748,0
2
The matrix S which diagonalizes A is obtained using
the previous eigenvectors as its columns.
The last information we need in order to apply the
model is the following:

















29327
195
Pr
Pr
0
0
eys
edators
We have all the information we need in order to com-
plete our analysis.
3. Results
The solution of the model, as indicated in the previous
section, is the following:




























0
0
201
0
0 20
20
20
Pr
Pr
Pr
Pr
Pr
Pr
eys
edators
SDS
eys
edators
A
eys
edators
The last equation leads to the following result:

















23,18453
110
Pr
Pr
20
20
eys
edators
This analysis shows a very critical situation. Not only
for the number of fishing-boats, which is in a worthy
decrease, but above all for the important ichthyic inheri-
tance’s impoverishment in the area of Manfredonia.
Data show an alarming situation, in 2038 the stock of
fishes will decrease of 28% (from 29327 tons up to only
18453,23), as a consequence about 85 fishing-boats will
exit the market and as a result 435 workers (considering
an average of 5 workers per ship) will be dismissed.
Some years ago the Gulf was rich in codfishes, mullets,
cuttlefishes, octopus etc, and all such species risk to be-
come rare.
It is worth noting that the situation could be even
worst if the present fishing activity should follow the
extraction rate of one decade ago. If we apply this model
to data of the year 1995, when the fishing boats regis-
tered in the Manfredonia Harbour-Office were 450 with
more than 2000 workers and a catch of about 7702,5 tons,
we should comment a dramatic situation: the number of
fishing boats in the year 2015 should be 107 units only
(–77%) and the ichthyic stock should be only 16345 ton
(–45%).
Often data and numbers are more eloquent than many
words, such numbers show a dramatic situation. Dealing
with the problem of resource extraction of a natural re-
source it is necessary to consider the problem of inter-
generational equity. In fact actions of present generations
(in terms of extraction rates) influence the choices of
future generation in an obvious way. It is well known
among economists that if extractors do not care about the
effects of their extraction policies on future levels of
stock of resource this can result in the so called “tragedy
of commons” [3-5]. It is necessary to define in more de-
tails the concept of “intergenerational equity”. Rawls [6]
claims: “...consider the question of justice between gen-
erations. There is no need to stress the difficulties that
this problem raises. It subjects any ethical theory to se-
vere if not impossible lest”
Solow [7] considers the problem of a natural resource:
“the current generation is always entitled to take as
much resource out of the common intertemporal pool as
it can, provided only that it leaves behind the possibility
to each succeeding generation can be as well off as this
one”
It seems that, in an environmental context, with “int-
ergenerational equity” we can mean that the extraction
strategies of present generations can satisfy their own
needs and in the same time guarantee to future genera-
tions to do the same. This paper wants to be a contribu-
tion in such direction.

Quantitative Analysis of the Fishing Activity in the Gulf of Manfredonia (Gargano, South-Italy) 120
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