System Dynamics as a methodology for sustainable
coastal-zone management
J.L. de Kok and H.G. Wind
Twente University, Department of Civil Engineering Technology & Management
P.O. Box 217, 7500 AE Enschede, The Netherlands
1 Introduction
The central aim of the multidisciplinary WOTRO! research program is to develop the
scientific knowledge required for the sustainable utilization of the coastal resources in
tropical countries. The study area consists of the coastal zone of South-West Sulawesi,
Indonesia. Most coastal-zone policies are implicitly based on the expected interaction
between natural and social processes, many of which have been the subject of detailed
scientific research in the past. However, a methodology suitable to apply this knowledge
to support the integrated management of coastal resources is still lacking. A quantita-
tive system approach is followed for the management component of the project to deal
with the dynamic nature of the coastal-zone processes and cross-sectoral linkages. The
integration of the theoretical concepts developed by the social scientists of the project in
a quantitative system network is less obvious than for the natural sciences. The fisheries
sector is one of the key elements of the coastal-zone system in which human behavior
plays a role. The increasing fishing effort and introduction of destructive fishing practices
have lead to severe overfishing of near coast fish resources. A number of policy options
are available to deal with the problem including mesh size and effort restrictions. catch
quotas and the installation of marine parks. The effectiveness of these regulations de-
pends largely on the cooperation of local fishermen. Fishermen may decide to increase
the number of fishing trips above the sustainable level unless the imposed sanctions ex-
ceed the surplus profit and are effectively enforced. The perception and fishing effort
of individual fishermen can be considered as the net result of the expected social and
economic costs and benefits [1]. A simple bioeconomic model for the exploitation of a
fish stock will be used to show how human behavior can be included in a quantitative
system model in order to analyze an effort restriction policy.
2 The Model
The basic bioeconomic model [2]used consists of a logistic growth equation for the biomass
B of the fish stock and a profit-driven model for the fishing effort E:
aB B
5 = 9B (2 - Ee) —9EB a)
0E
GE oe - 2
a r (pgB —c) E, (2)
1Netherlands Foundation for the Advancement of Tropical Research
WS
where Bro, denotes the maximum biomass, g is the logistic growth constant, q is the
catchability per unit effort, and the parameters p and c represent the price per unit catch
and costs per unit fishing effort. The parameter r reflects the flexibility of fishermen to
respond to changes in profit as a result_of declining catches. The biomass, fishing effort,
and catch C are expressed per unit surface area. A key variable in fisheries management
is the catch per unit effort (CPUE) given by C/E = qB. To describe the influence
of differences in fishing behavior on the total fishing effort the community of fishermen
is divided into two groups. The effort of the first group, denoted by E,, corresponds
to a constant sustainable level of exploitation in accordance with the existing fishing
regulations. The second group of fishermen consists of rule breakers fishing at profit-
driven effort E, as in Eq. [2]. The total fishing effort is given by
Erot = (1 — @) Ey + aE, (3)
where a is the fraction of fishermen belonging to group of rule breakers. The effort of the
individual fishermen within each group is assumed to be identical. A probable situation is
that more members of the first group will decide to break the regulations if the proportion
of fishermen belonging to the second group increases [1]. Furthermore, the fraction of
rule breakers can be expected to increase with the gain expected from the surplus effort.
Mathematically this can be expressed by
ba _
ot
kan a<l-kar
, (4)
l-a@ a>1—kar
where the coefficient k represents the rate of group conformation, and 7 is the profit
surplus as a result of the rule breaking:
m= (pq B-c)(E&,-4). (5)
If the proportion of rule breakers increases the total fishing effort may exceed the sus-
tainable level of exploitation. A policy of graduated sanctions [3] may be introduced
to reduce the fishing effort to the sustainable level. This can be described by rewriting
Eqs. [2] and [5]:
= = r((pqB-c) j-<s>)
(6)
nm = (pqB-c) (;-&) - <s>
The expectation value < s > of the sanction has now been subtracted from the profit
and is obtained from:
fB(E, - F,) E,> Ey
<8 >=
0 Ex < Ey
(7)
where f is the fine imposed per unit effort surplus and f represents the fraction of rule
breaking fishermen getting caught. The model parameters and corresponding dimensional
units are shown in Table 1.
3 Results
The model results are particularly sensitive for changes in the value of the parameters r [4]
and k. Therefore, the influence of these = on the time-dependent behavior of the
I
initial biomass Bo mton/ha/yr] | 0.2 | growth rate g [I/yr] 0.50
maximum biomass Bmaz |mton/ha/yr] | 1.0 || catchability 1/(trip/ha)] 0.05
sustainable effort Fy trips/ha/yr 5 || price p USS /kg] 2.0
initial free effort E2 trips/ha/yr, 5 |] costs ¢ [US$/trip} 25.0
fine f 1000 US$} 10.0 || 6 0.10
adaptability k 1/(US$/ha)] flexibility r__[trips/yr/US $]
Table 1: Parameters and dimensions used for the bioeconomic model. Numerical values
are given for fixed parameters only.
CPUE was determined first using the Powersim simulation program [5]. The behavior
of the catch per unit effort for different values of r and k is shown in Figure 1 for a
time horizon of fifty years, using a Runge-Kutta integration routine and an integration
step of one month. The CPUE corresponding to the sustainable level of exploitation
4qBmaz is 25 kg/trip. The values r = 0.001 and k = 0.001 are selected in order to
avoid undesirable oscillations of the effort while still allowing for the situation of non-
sustainable exploitation. To illustrate how a policy of graduated sanctioning restores the
sustainability of the exploitation the CPUE and fraction of rule breaking fishermen in
the absence and presence of graduated sanctions are shown in Figure 2.
4 Discussion
The method discussed here shows how the behavior of fishermen can be incorporated in
a quantitative system model. Other types of fisheries management can be analyzed as
well by changing the model parameters. For example, an open-access policy is simulated
by omitting the sanction and setting the rule-breaking fraction equal to one. The next
step is to include the socio-cultural factors in the model which may be relevant in a
policy analysis context, such as local leadership and traditional resource-management
institutions. This requires the translation into mathematical terms of the corresponding
anthropologic concepts. If necessary, a game-theoretic approach could be followed to
predict the consequences of social organization and the choices made at the individual
level for the effectiveness of fishing regulations.
References
{1] Elinor Ostrom, Governing the Commons, The Evolution of Institutions for Collective
Action. Cambridge University Press, Cambridge, 1994.
[2] C.W. Clark, Bioeconomics, in: Theoretical Ecology, Principles and Applications,
Robert May ed., Blackwell Scientific Publications, 1981.
[3] C. Dustin Becker and Elinor Ostrom, Human ecology and resource sustainability,
Annu. Rev. Ecol. Syst. 26:113-133, 1995.
[4] Matthias Ruth, A system dynamics approach to modeling fisheries management is-
sues: Implications for spatial dynamics and resolution, System Dynamics Review,
Vol. 11, 233-243, 1995.
[5] Powersim version 2.0, The Complete Software Tool for Dynamic Simulation, Modell-
Data AS, P.O. Box 642. Bergen, Norway, 1993-1994.
nus)
CPUE [kg/trip
5}
0 10 20 30 40 50
time [years] time [years]
CPUE [kg/trip
0 10 20 30 40 50
Figure 1. Left-hand side: catch per unit effort for k = 0.001 and r= 0.0001 (solid line),
0.001 (dashed line), and 0.01 (dotted line); right-hand-side: catch per unit effort for r =
0.001 and & = 0.0001 (solid line), 0.001 (dashed line), and 0.01 (dotted line). No sanctions
are imposed.
| i 0,6 |
, ost |
| i 0,4 4
e —€ oost ?
| = 2 024 -
(2 bo} Son a |
, 1 H o vt 4 q
5 / 3 0 : Lo
ms) 0 10 20 30 40 50 | & 0 10 20 30 40 50 |
i | 3
&
time [years] time [years]
Figure 2. Catch per unit effort and fraction of rule breakers in the presence (solid line) and
absence (dashed line) of a sanction with fine f= US$ 1,000 and caught fraction B = 0.10.
The initial fraction of rule breakers is set at @ = 0.10.
Mw
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