A Spatial-Dynamic Approach for the Integrated
Management of Coastal Ecosystems
Pierre-Alexandre Chateau, Yang-Chi Chang
Department of Marine Environment and Engineering
National Sun Yat-sen University
70 Lien-Hai Road, Kaohsiung 80424, Taiwan
Abstract
Coral reef is a key coastal resource to indicate the integrity and soundness of the
marine environment. Inappropriate coastal management practices are likely to
weaken coral reef ability to cope with disturbances and may therefore lead to
undesirable phase shifts in ecosystem composition. Ecosystem-Based Management
(EBM) is now recognized as being the most appropriate tool for the sustainable use
of coastal resources. To incorporate EBM in coastal management for resource
conservation, interdisciplinary modelling approaches are needed. This study
develops a spatiotemporal modelling framework based on the Ecopath with Ecosim
(EwE) software for sustainable coral reef management in Nanwan bay, Kenting,
Taiwan. The System Dynamics (SD) approach is used to integrate socioeconomic and
ecological systems and perform scenarios analysis. Preliminary results suggests that
an integrated Marine Protected Area (MPA) (no take + no waste water discharge)
might have more beneficial effects on both the ecosystem and the fishery sector
than a simple no-take MPA.
Keywords: Ecosystem-Based Management, Ecopath with Ecosim, System Dynamics
Corresponding author: Pierre-Alexandre Chateau (pachateau@staff.nsysu.edu.tw)
1 Introduction
Although coastal zones only represent 7% of the total surface of the oceans, they
contribute to 90% of the total catches (Pauly, Christensen et al. 2002). Among them,
coral reefs constitute the source of around 10% of the fish consumed by humans
(Moberg and Folke 1999). However, subject to increasing fishing pressure, ocean
acidification and/or nutrient enrichment, coral reefs are declining worldwide
(Bellwood, Hughes et al. 2004). Ecosystem-Based Management (EBM) has been
defined as: “the careful and skilful use of ecological, economic, social, and
managerial principles in managing ecosystems to produce, restore, or sustain
ecosystem integrity and desired conditions, uses, products, values, and services over
the long term” (Christensen, Bartuska et al. 1996). In order to define what these
desired conditions are, Costanza and Mageau (1999) stated that a healthy ecosystem
is one that is sustainable. They define ecosystem health as follows: “the ability to
maintain its structure (organization) and function (vigour) over time in the face of
external stress (resilience)”. Organization can be measured by the Averaged Mutual
Information index (AMI, (Ulanowicz 1986)), vigour is usually measured by the Total
System Throughput (TST = Consumption + Respiration + Flow to detritus + Exports)
and resilience is traditionally measured by the speed at which the system returns to a
1
pre-disturbance state. As a tool to describe complex trophic relations and assess the
effects of different management policies, ecosystem modelling has a very important
role to play. We present a System Dynamics (SD) based framework which allows the
integration of different modules such as an ecosystem module that replicates the
award-winning Ecopath with Ecosim (EwE), a profit-driven fishery sector and a
tourism sector. The model is spatially explicit, in a fashion quite similar to Ecospace,
which allows the simulation of Marine Protected Area related policies.
2 Method
As a decision-making support, ecosystem models are becoming an essential tool,
especially when integrated with socio-economic systems. This study presents an
integrated modelling framework that combines the strengths of the EwE approach
(mass-balance equilibrium and realistic ecosystem description) with the modular
capability of the System Dynamics approach.
2.1 Ecopath with Ecosim
Ecopath with Ecosim (EwE) is a free ecosystem modelling package developed at the
University of British Columbia’s Fishery Centre. Its foundation is an Ecopath model
which creates a static mass-balanced snapshot of the resources in an ecosystem
represented by trophically linked biomass pools. The biomass pools consist of a
single species, or species groups representing ecological guilds. Ecopath data
requirements are relatively simple, and data is often already available from stock
assessment, ecological studies, or from the fishBase website
(http://www.fishbase.org/search.php). The parameterization of an Ecopath model is
based on satisfying two master equations:
P= )'B, * PM, +OM, +FM, +X, +BA, Ca}
J
Ci =P) + Ri + UF; (2)
With P;, the production of each functional group i, PMy the predation mortality of /
caused by the biomass of predator j (Bj), OM; the baseline mortality, FM; the fishing
mortality, X; the other exports, BA; the biomass accumulation, CG; the consumption, Rj
the respiration and UF; the unassimilated food. Equation 1 ensures that the
biomasses of each functional group are kept constant, and equation 2 ensures that
energy inputs and outputs are balanced for each group. Ecopath sets up a series of
linear equations to solve for unknown values establishing mass balance during the
operation.
Ecosim is the dynamic module of EwE, which re-expresses the linear equations of
Ecopath as differential equations:
dB,
“eC tM — Cy -OM, - FM, -X, (3)
J J
With g; the gross factor of species i, G; the consumption of i by j, M;the immigration
rate, OM; the other mortality rate, FM; the fishing mortality rate and xX; the export
rate. Consumption rates are calculated upon the “foraging arena” theory, where the
biomass of / is divided into a vulnerable and a non-vulnerable fraction. The transfer
2
rate between these two fractions is what determines the flow control (bottom-up or
top-down).
Ecospace is the spatial-dynamic version of Ecopath. It employs an Ecosim model in
each cell of a raster grid, while accounting for cell connectivity and fish movements
explicitly. Fishing effort is distributed over space according to a gravity model that
seeks the optimization of the profitability of fishing. Ecospace is often used to
simulate the effects of Marine Protected Areas (MPA).
2.2 System Dynamics
System dynamics is an approach to study the behaviour of complex systems over
time. SD was created during the 1950’s by Jay Forrester of the Massachusetts
Institute of Technology (Forrester 1961). Originally developed to help corporate
managers improve their understanding of industrial processes, it is currently widely
used in the public and private sectors for policy analysis and design. SD models have
proven useful for a range of ecosystem management related issues (Costanza,
Duplisea et al. 1998) such as fisheries (Ruth 1995; Ruth and Lindholm 2002;
Wakeland, Cangur et al. 2003; Moxnes 2005; Dudley 2008). However, these fishery
models often emphasize the socioeconomic side of the fishing activity at the expense
of a realistic description of ecosystem structure and functioning. In order to prevent
this over-simplification, the Ecopath with Ecosim framework has been replicated, to
serve as our core ecological sector.
3 Model formulation
In order to develop a reliable ecosystem module, we replicated the structure of the
EwE software. We then extended its scope, to include a fishery, tourism and coral
subsectors. Furthermore, the model is developed over a grid of cells. The underlying
Ecopath model is a 18 species model built by Liu et al. (2009).
3.1 Ewe replication
The causal-loop diagram (CLD) of an Ecosim model is shown on figure 1.
Vulnerabilities
Predation mortality
Production —_, - +p: |
R Bi, B
es lee 2 Mt Other mortality
BI |
oy, ts we)
Saturating E “ Dt
function foe ><
8
Fishing mortality Detritus exports
Figure 1: CLD of the Ecosim framework
3
avy
. Ee car M =
i he
ee ee '@)
Figure 2: Stock and flow diagram of the Ecosim framework
In orange Ecopath outputs are displayed (the diet matrix, the equilibrium biomasses,
the ratio of consumption over biomass, the ratio of production over biomass, the
other mortality factors, the fishing mortality factors, the detritus export, and the
unassimilated food factors. In green, Ecosim inputs as specified by the user (ratio;, xj
and the fishing effort). Other constants are displayed in black and dynamic variables
are in blue. The biomass stock is arrayed over the number of species in the
ecosystem. It increases with production P, calculated separately for primary
producers (Pp;) and consumers (Pcj). Primary production in Ecosim is calculated using
the following saturating function:
dB r
Tp
dt 14+B*h | (4)
af BY)
With B;, the biomass of primary producer i, ~rato,+{2.) , the maximum growth
i
factor that can be attained when B; is low (ratio; is a user defined parameter) and
ae -1
h, = ——+— . B; appears two times in equation 4: once in the numerator and once
in the desominato, meaning that two feedback loops (one positive and one negative)
govern its growth rate, ensuring that the growth factor of the primary producer
varies from r; to 0 as its biomass B; increases from 0 to +e° as shown on figure 3:
Lota. Voters
| 2) =
(P/8)*
we
———e 3@)= (L8H)
Figure 3: Growth factor as a function of biomass
As indicated by Walters et al. (1997), setting ratio; very large has the effect of making
primary production rates in the system remain constant at Ecopath estimates,
independently of primary producer biomass, as shown on figure 4.
ratio=
ratio, =2
# ratio=5:
dt i ee ratio,=100
os
Bi
Figure 4: Growth rate as a function of biomass for different ratioi values
Furthermore, we can note that a setting of ratio;=1, changes the formula back to the
Lotka-Volterra model (i.e. a linear increase of dB;/dt with B;). The default value of
ratio; in Ecosim is 2.
Production for consumers is calculated using fixed g; parameters that are applied to
the consumption of predator j.
Biomasses decrease with predation mortality (PM), other mortality (OM), fishing
mortality (FM) and the export of detritus outside the area (Xger).
The consumption of prey i by predator j is calculated using the following equation:
C, =s,(B))*B,*B; (5)
With s;(B;), a modified search rate that accounts for the type of control (top-down or
bottom-up) that is meant to be modelled.
x
s, =a, *———-____ for xj€ ]1;+00
1 Sy" S,-1+B, 1B, i€ | [ (6)
aj =! (7)
ii — D*aep® 7
1 BeBe
Si iS a negative function of B;; when predator biomass increases, the resulting
diminution of sj therefore tends to hamper the resulting increase of Cj. The strength
of this donor-controlled effect is determined by the choice of xj. Figure 5 shows sj as
a function of xj for three different levels of predator biomass. When x; are low (<3), sj
is very responsive to any change in predator biomass and compensates for it so that
Cj doesn’t change much. It follows that if Cj doesn’t change much when B; does, then
it will only change with 8, i.e. the system is bottom-up controlled. When x; are high
(>10), the influence of predator biomass on sj becomes almost nonexistent. sj~= aj 5
whatever the relative importance of predator j. This is the Lotka-Volterra formulation,
where Cj is as much influenced by 8; as it is by 8. In other words, the system is
top-down controlled.
eat
x <3 > bottom-up control
3.< x) <10—> mixed control
x, > 10 > top-down control
1a" L A 1 A f A 1 L
7 20 30 a0 6 ca 70 30 3 709
Xi
Figure 5: Modified search rate sij as a function of vulnerability setting xij
The xj settings have a strong influence on overall system behaviour and define a
continuum from steady state behaviour for bottom-up (low vulnerabilities) systems
to oscillatory behaviour for top-down (high vulnerabilities) systems (Walters,
Christensen et al. 1997). Figure 6 displays ecosystem responses to the same increase
in fishing effort in both bottom-up systems (left) and top-down systems (right).
Figure 6: FM*3 during year 2 with xi .001 (a) and xij = 100 (b).
From Cj, we calculate PM and G, the total consumption of predator j. Part of this
consumption is excreted (UF rates) and flows to the detritus pool.
Figure 7 shows the agreement between our SD model and the Ecosim software, for a
scenario with high vulnerabilities and high fishing effort. Results are compared for 18
species, after 10, 50 and 100 years.
20
y =|0.9877x + 0.008
R?=0.9991
16
12
8
4
10)
0 4 8 12 16 20
Figure 7: Model results vs. Ecosim results with FM*5 & xij=100, after 10, 50 and 100 years
3.2 Model spatialization
The Nanwan model has been built as a spatially explicit model. We have replicated
the structure over a grid of cells so that we work with a 2D (Species, Cell) model. As
for the one-cell version of Ecosim, each cell of the grid has to refer to an Ecopath
model for the calculation of consumption rates. This set of reference values is
identical in each cell and is a simple fraction of the original set. The immediate
consequence of this assumption is that, when dealing with spatial heterogeneity,
these equilibrium values cannot hold anymore. If a species is absent from a cell, we
cannot expect the situation in this cell to look anything like the averaged Ecopath set
of estimates in which it is present and accounted for. The only cells in which species
may behave like the Ecopath estimate are thus the ones where all the species are
7
present together. This is a serious limitation, especially when a model contains sessile
species like algae or corals which are only found in certain specific areas. The solution
to this problem, as implemented in Ecospace (Walters, Pauly et al. 1999), is to define
preferred and non-preferred habitats for each predator that is able to move and to
modify their search rate and vulnerability accordingly. In their preferred habitat,
predators are likely to be more efficient and less vulnerable than in non-preferred
habitats. Moreover, moving rates are also affected accordingly, in order to reflect the
fact that predators will spend more time foraging in preferred cells than in
non-preferred cells. These corrections of the model are supposed to smooth out
local discrepancies so that globally, the model behaves like its one-cell counterpart.
3.2.1 Spatial movements
Spatial movements from a cell into its adjacent cells play a central role in this search
for spatial coherence and are defined as a function of:
. Species average swimming speed,
- Habitat preference (increases speed if non-preferred)
- Risk (increased with predation and fishing, reduced with consumption).
In order to model movements over the grid, we first need to add two flows to our
biomass stock: immigration (inflow) and emigration (outflow). We consider the
Moore neighbourhood (8 cells neighbourhood) shown on figure 8:
NW N NE
WwW E
SW S SE
Figure 8: The Moore neighbourhood
In its simplest form, the outflow from a cell is defined as:
out, =B; * MF, (8)
Bj is the biomass of species jin cell j and MF; is the moving fraction of species j. As
the fraction of biomass that leaves the cell each year, MF; can be assimilated to the
speed of species i.
The amount of biomass that leaves the cell is then randomly distributed in 8
directions (NW, N, NE, W, E, SW, S, SE) according to the frequency formula:
Pix
- (9)
> Pix
fa
With out; the amount of biomass i that leaves cell j to cell k, pj, is the probability
that j leaves cell j to cell k. Probabilities are re-sampled every time step.
Now than we know what is going where, we can easily write the inflow equation as
being the sum of the 8 neighbouring cells outflows into the current cell. For the
example in figure 8, the inflow into the centre cell will be the sum of what flows SE
out of the NW cell plus what flows S form the N cell and so on. A special rule is added
for border cells so that the outflow from a border cell is scaled to the number of
neighbouring cells. Overall, nothing goes in or out of the map.
out;;, = out, *
Furthermore, species are likely to leave non-preferred cells faster than preferred cells.
Same thing for cells were there is danger. A factor dj higher than unity is added to
the flow out of the cells that are defined as non-preferred and another one smaller
than one is added to the cells defined as preferred.
Following the formulation in Ecospace (Walters, Pauly et al. 1999), we define the risk
as being made up of two fractions: the risk of being killed and the risk of starving.
FM, +PM,
€
ij
risk, = (10)
Equation 10 ensures that risk increases with predation and decreases with
consumption. We calculate riskj , the average risk for i in j using Ecopath estimates of
FMi, PM; and C; and compare the risk inherent in cell j to this “acceptable” level of
risk in the following way:
risk,
mh = a (11)
risk;
The square root function has been added to the ratio in order to limit the amplitude
of rr, which, if too high may notably increase computation time. Equation 8 finally
becomes:
out, =B, * MF, *d, * rn, (12)
3.2.2 Other spatial considerations
In order to prevent species from leaving the map, border cells are defined so that the
species can only move into a direction that is still in the map. The outflow from a
border cell is scaled to the number of neighbours the cell has.
The fishing effort is distributed according to the relative availability of fished species.
We apply a term to each cell fishing mortality in order to distribute the fishing effort
over the map. The fishing mortality becomes:
Simulation Model of Diabetes and Diabetic Nephropathy-induced Dialysis in
Japan through 2022: Evaluation of Possible Strategies
Takehiro Sugiyama'”, Sayuri Goryoda*, Kaori Inoue!, Noriko Sugiyama-Ihana', Nobuo
Nishi?
1. National Center for Global Health and Medicine, Tokyo, Japan
2. The University of Tokyo, Tokyo, Japan
3. National Institute of Health and Nutrition, Tokyo, Japan
ABSTRACT
We developed an aging chain simulation model about diabetes management especially
focusing on avoiding dialysis initiation in Japan, and we used the model to predict the
numbers of people with diabetes and people on dialysis due to diabetic nephropathy up
to 2022 based on the population data between 2000 and 2012. Our model suggested that
the diabetes prevention intervention would have little impact on the number of dialysis
initiation at least in the perspective of less than 10 years after the initiation of effective
interventions. Interventions aiming for avoiding dialysis initiation such as glycemic and
blood pressure control for patients with diabetes will have a larger and faster impact on
the number of dialysis initiation at least within the scope of our prediction. The model
implied that it would take more than 10 years for an effective diabetes prevention
intervention to decrease the number of dialysis patients due to diabetic nephropathy via
the decrease in diabetes patients. Policy makers will need to have a long perspective
when they consider future interventions with regard to management of diabetes and its
complication.
FM,, = FMf, * FE * B, * smthl dre, ts
= smth, —————_—__, 13
" ‘ 4 py; relB,, /ncell (43)
With FMf; the fishing mortality factor for species i, FE the fishing effort, ncel/ the
number of cells and ts the time period necessary for the fishery to locate better
fishing grounds.
Eventually, a Marine Protected Area (MPA) within which fishing is prohibited might
be designed. The fishing pressure that would have been exerted in the protected
area has then to be reported outside the MPA and equation 13 becomes:
FM, = FMf *FE*B, *__2cel 2, rey wis] (44)
4 ‘ " neell —nMPA Day relB;, ((ncell TaMPAY’
With nMPA, the number of cells that are to be protected in the MPA.
3.2.3 Map and spatial equilibrium
Nanwan bay is a 40 km? wide area. Using a resolution of 300*300 meters per cell
(0.09 km?), our spatial grid contains 680 cells which are distributed as:
- 239 land cells,
- 75 coral reef cells,
- 3 harbour cells,
- 44 sand cells,
= 182 shallow water cells (depth<30m),
- 137 deep water cells (depth<50m)
Figure 9 shows the map of Nanwan bay, Kenting, Taiwan (21257’N, 120244’E).
Nanwan Bay
1 cell = 0.09 km?
Land
Coral
Harbour
sand
Shallow
Deep
Sewage
IPA (ecological).
MPA (landlscape}
Figure 9: Map of Nanwan Bay
Ecopath estimates biomass densities (tons per km’) so, as a first step, these
estimates have to be converted into tons before being affected to each cell. We
multiply the Ecopath estimates B, by 40 km? and divide the result by the number of
cells our habitats contains. All species are initially evenly distributed throughout the
map, except macrophytes, which are only found in shallow water cells and coral cells
and soft corals, hard corals and sea anemones which are only found in coral cells.
10
Species able to move voluntarily (all species except phytoplankton, macrophytes,
hard and soft corals, and sea anemones) have then to be assigned to their preferred
habitat, so that we can modify their search rates, vulnerabilities and dispersal rates
as a function of the kind of cells in which they are located. In Ecospace, default values
in non-preferred habitats are set to:
- Search rates * 0.5 (user can choose within [0.01;1])
- Vulnerabilities * 2 (user can choose within [1;100])
- Dispersal rates * 2 (user can choose within [1;10])
With all values unchanged (i.e. factor equal to one) in preferred habitats.
We use the PEST calibration software to estimate those parameters. We run a basic
steady state scenario over a five-year period and calibrate the total relative
biomasses of each species to unity. A top-down control is assumed (xj=8). Using
these parameters, we ensure that the resulting spatial distributions, some of them
shown in table 1, are globally consistent with original Ecopath estimates. Figure 10
displays the total biomasses, relative to their Ecopath estimates over the course of
the calibration period.
Table 1: Initial distributions and spatial equilibriums for some species
Species Initial distribution Spatial equilibrium
Hard Corals
™
7
Polyp-feeding
Fishes
z
r*
Piscivorous L
fishes
11
Tire)
ous Fin
omnvorie te
Plewenuaiel
eras ay
p15] ilenpen eding aah
toeewa
Figure 10: Total biomasses over the map, relative to their original Ecopath estimates
Figure 11 displays the equilibrium spatial distributions of the Total System
Throughput (7ST*) and Fishing Effort (FE*). Not surprisingly, ecosystem activity is
highest in reef and shallow-water cells, where most of the species are found. The
resulting fishing effort is higher in those cells.
~~
TST* FE*
Figure 11: Equilibrium spatial distributions of TST (left), and FE (right)
3.3. Additions to the model
The sectors that are to be linked with the ecological sector are meant to integrate the
influence of human populations on the ecosystem. According to previous studies in
Nanwan bay, we identified three main subsectors that had to be added to the
original ecosystem model: a fishery, tourism and a coral subsector.
Figure 12 displays the CLD of additional subsectors. The original ecosystem model is
depicted in yellow.
[Coral subsector ,
Tourism subsector
© CP ona
Unsatisfied
z Available Area
>} Demand (2) ke)
purt ot] bs ©
~™ dHousing dia
FMi.
~~
Ecospace
[EN
C
Fishery su
Figure 12: Causal-loop diagram of the additional sectors
3.3.1 Fishery subsector
The first sector we add is a simple bio-economic fishery model (de Kok and Wind
1996). Fishing mortality is defined as:
FM, =q,*B,*FE (15)
qj is the catchability coefficient, it equals the Ecopath estimate of the fishing
mortality factor. FE is the unitless fishing effort. Its Ecopath value is one.
FM,*p
PUE =).—+—-C (16)
x FE
PUE is the profit per unit of FE, p; is the selling price of species j (NT/Kg). Cis the cost
of fishing per year, per unit of fishing effort and per km?.
dFE
“dt
ris the conversion factor from profits to fishing effort and tf is the time delay over
which the PUE is smoothed out.
=r*smth(PUE,tf)* FE (17)
The fishery sector adds 3 feedback loops to the model, whose sign may change
according to the current profitability. If PUE>0, then dFE/dt will be positive and will
therefore increase FE. In this situation, the loop between dFE/dt and FE is positive, as
well as the bigger loop than links FE to FMj, PUE and dFE/dt. Because PUE is the
profit per unit of FE, FE is found on the denominator of equation 16 and this creates
a negative loop. In the situation where PUE<O, then dFE/dt will be negative as well
and will thus decrease FE. All loops then change signs and the model is then made up
of two negative feedback loops and one positive. Described in this way, the fishery
subsector is a self correcting entity. When overfishing occurs and harvests decrease,
the reduction in profitability incites some of the fishermen (the less successful ones)
to leave the fishery which reduces fishing pressure on the resource. This helps the
fish stock to rebuild and soon enough, comfortable profits are to be earned,
attracting new people to fishing.
3.3.2 Tourism subsector
The demand for holidays in Kenting is defined as a sinusoidal function that peaks up
during summer and down during winter. Furthermore, it is assumed to be a positive
function of the health of Nanwan bay’s ecosystem. Following Costanza’s definition of
ecosystem health, we made up the composite variable called Ecosystem Health with
different ecological indicators that are monitored throughout the simulation, such as
Total System Throughput (TST) that measures ecosystem vigour, the Shannon index
that measures the system’s entropy and the total living biomass that reflects
ecosystem size. Demand for holidays is constrained by housing in the area, so that
the number of tourists that visit Kenting is calculated as MAX (Demand, Housing).
Unsatisfied demand is smoothed over a time delay and positively influences housing,
thus allowing the area capacity for hosting tourists to increase with time. For
illustration purposes, figure 13 shows the behaviour of the tourism subsector, before
its linkage with the ecological sector. Demand is here arbitrary defined using two
sinusoidal waves, which allows us to check the behaviour of our variables. Between
year O and year 12, demand (in red) is always higher than housing (blue) so the
number of tourists (green) equals housing. This tends to make housing increase since
unsatisfied demand is positive. After year 12 however, demand becomes inferior to
housing so that the number of tourists now equals the demand. Housing starts to
decline when some businesses close down due to the lack of clients.
1: housing 2: demand 3: tourists
0000:
55000:
Figure 13: Housing, demand and tourists over time (for illustration only)
Tourism in Kenting is assumed to have two main effects on the ecosystem. Firstly, it
tends to increase the fishing effort and secondly, it increases sewage discharge in the
bay.
The first point is dealt with by making the prices of fished species vary with the
number of tourists in the area.
T
T,
base
Pi = Phasa * ¥ (18)
p; is the variable price of fished species i, Ppase; is its reference value, T is the number
of tourists and Those is the reference number of tourists in Kenting, x is a parameter
that reflects the sensitivity of prices to the number of tourists. The highest x is, the
14
less sensitive are the prices, and the closest prices get to Ppasei.
For sewage discharge, we assumed that nitrogen N, as released in the waters of the
bay, has a positive influence on primary producers (phytoplankton and macrophytes).
But instead of assuming a forcing function that would simply increase the
productivity of primary producers without really calculating the concentration of
nutrient, we adopted the model proposed by Huppert et al. (2002). This model
depicts nutrient uptake by phytoplankton and its consequent growth as:
dN
—*=e-Sb*N*P
7° zh P, (19)
SPL ao, N* Pp, -d,* Pp, (20)
With N the concentration of nitrogen in ppm, Pp; the concentration of primary
producer i in ppm, e the annual enrichment of N into the bay, 6 the nitrogen uptake
factor by producer i, c; the growth factor of i per ppm of N and dj the death rate of i.
We use an averaged depth to convert from ppm to ton/km?. This model is an
overshoot and collapse model: Pp uses N to grow, and as it does so, depletes N.
When N declines low enough, the production rate of Pp falls under its death rate and
Pp collapses. For illustration purposes, figure 14 shows the reaction of phytoplankton
to nitrogen enrichment with parameters taken form Huppert (2002). A negative
correlation between chlorophyll a and nitrate has been observed in Nanwan bay
(Chen, Wang et al. 2004), which validates this structure as a useful add-on to the
model.
50.00:
0.20
25.00, XN a
0.10 2
2
z }
/ iN
o.a0 A
00 250.00 500.00 750.00 1000.0
Days
Figure 14: Phytoplankton and nitrogen over time (for illustration only)
The amount of nitrogen that is discharged in the bay is calculated using a regression
by Lin et al. (Lin, Wu et al. 2007):
N,, = 0.0231*T + 555.44 (21)
Nin is the total nitrogen loading (in kg/month) and T is the number of tourists (in
thousands). N;, enters the bay via the 17 sewage cells shown on figure 9. It is equally
distributed among them. Nitrogen and phytoplankton are mixed over the map as
15
well as with the outside, in order to prevent unrealistic accumulations within the bay.
3.3.3 Coral subsector
Another important modification of the original ecological sector lies in the
implementation of competition for space between macrophytes and corals. In a
mesocosm experiment, Liu (2009) demonstrated that, under nutrient enrichment,
the competitive hierarchy between the green algae Codium Edule, the branching
hard coral Acropora Muricata and the sea anemone Mesactinia Genesis was C. Edule
> M. Genesis > A. Muricata.
In order to simulate competition between algae and coral, we introduce the
following mediation function:
TER gaye. 1
z= 22
"| reBaigac > 1 1 s{_%m 4 (22)
(Zim —1) TAB igac
: — : _ Batgae
With zj,a factor that is applied to the growth of coral species and TB gac “BO
algae
the relative biomass of macrophyte. This formulation makes z vary from 1 (no
influence) when re/Baigae <1 to a negative value depending on the parameter Zjim
when re/Baigae tends towards +e°. This means that when the abundance of
macrophyte is very high, corals are not only unable to growth but also die quicker
than usual. When re/Baigae= Zim, coral growth equals 0.
4 Policy analysis
We compare three scenarios in order to test the potential effects of a Marine
Protected Area (MPA).
- scenario 0 (SO): no MPA
The whole area is available for fishermen to fish, nutrient are discharged in the
bay via the 17 sewage points shown on figure 9.
- scenario 1 (S1): type 1 MPA
The MPA shown on figure 9 is designed. Fishing is prohibited in MPA cells.
Nutrients are still discharged in the 17 sewage points, even if 7 of them fall within the
MPA.
: scenario 2 (S2): type 2 MPA
Fishing is prohibited in MPA cells. Nutrient discharge is banned in the 7 cells that
belong to the MPA. The amount of nutrient that would have been discharged in
those cells is reported in the 10 other sewage cells.
Policies are launched in year 10. Our first results show that a type 1 MPA (S1) is not
likely to significantly alter ecosystem health (defined as a composite indicator
including TST, Shannon diversity and species abundances). Whereas a type 2 MPA (S2)
16
leads to animprovement of ecosystem health after year 20 (figure 15).
eee FHO 08 eee FH] == = © FH?
13 yates
ee
1.25
f
1.15 f
I
f
EE
Unitless
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Years
Figure 15: Ecosystem health in SO, S1 and $2
A better ecosystem health level can be reached in S2 because coral degradation is
slowed down, as shown on figure 16.
e°CORL = = COR2
<_< CORO
Unitless
°
io
0.8 T T T T T T 7 T T T T T T
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Years
Figure 16: Coral biomasses in SO, S1 and $2
Interestingly, S2 also significantly benefits the fishermen. Figure 17 shows the total
profits accumulated by the fishery sector over the time span of the simulation. Their
averages from year 10 to year 30 are 2.86E+10 NTD, 2.91E+10 NTD and 3.58E+10
NTD for SO, S1 and S2 respectively.
4.5E+10
4.0E+10
3.5E+10
3.0E+10
2.5E+10
2.0E+10
1.5E+10
1.0E+10
5.0E+09
0.0E+00
-5.0E+09
NTD
Years
Figure 17: Total accumulated profits in SO, S1 and S2
5 Conclusion
The present study develops a Spatial System Dynamics (SSD) ecosystem model that
replicates and extends the well-known Ecospace module of the Ecopath with Ecosim
suite. Fishery and tourism subsectors are added in order to integrate socioeconomic
influences to the marine environment and a coral subsector is added in order to
customize the original ecosystem model to our study site, Nanwan bay in South
Taiwan.
Model use demonstrates the ability of SD to:
: Extend model scope to any relevant factor,
- Build and monitor custom indicators, such as Ecosystem Health,
: Explore spatial policies such as the instauration of Marine Protected Areas.
Preliminary results suggest that an integrated MPA (which considers both fishing and
pollution) can be effective in ecosystem conservation terms while at the same time
allowing fishermen to get better profits. A win-win situation might therefore exist
between ocean conservation and exploitation.
We are now collecting historical data for model spatial-temporal calibration, and
exploring MPA-related policies with Monte-Carlo simulations. We are also looking
forward to provide local authorities with an estimation of a “tourist carrying capacity’
above which ecosystem health starts to be jeopardized.
We are thankful to the National Science Council of Taiwan for subsidizing this
research project under grant NSC-101-2221-E-110-023.
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