e c o l o g i c a l m o d e l l i n g 2 1 6 ( 2 0 0 8 ) 134–144

avai lab le at www.sc iencedi rec t .com

journa l homepage: www.e lsev ier .com/ locate /eco lmodel

Analysis of annual fluctuations of C. nodosa in the Venicelagoon: Modeling approach

Nadezhda Zharova ∗, Adriano Sfriso, Bruno Pavoni, Alexey VoinovDepartment of Environmental Sciences, University of Venice, Calle Larga S. Marta 2137, 30123 Venice, Italy

a r t i c l e i n f o

Article history:

Published on line 12 April 2008

Keywords:

Cymodocea nodosa

Simulation model

Annual cycle

Limitation factors

a b s t r a c t

A simple simulation model was developed to describe the growth trends of Cymodocea nodosa

(Ucria) Ascherson based on data sets from the Venice lagoon. The model reproduces the

seasonal fluctuations in the above and belowground biomass and in shoot density. The

modeling results are in good agreement with data on net production, growth rates and

chemical–physical parameters of water. It was assumed that light and temperature are the

most important factors controlling C. nodosa development, and that the growth was not

limited by nutrient availability. The aim was to simulate biomass production as a function

of external forcing variables (light, water temperature) and internal control (plant density). A

series of simulation experiments were performed with the basic model showing that among

the most important phenomena affecting C. nodosa growth are: (1) inhibition of production

and recruitment of new shoots by high temperature and (2) light attenuation due to seasonal

fluctuation.

di Bo and later from July 2001 till June 2002 in the

1. Introduction

Seasonal biomass variability is a major determinant of thetrophic and structural role on seagrass beds in shallow coastalecosystems. Seagrasses play a key role in the coastal macro-phyte assemblages of the World and the Mediterranean Sea(Wood et al., 1969; Den Hartog, 1970, 1977; Larkum et al.,1989; Phillips and McRoy, 1990; Buia et al., 2000; Gambi etal., 2006) and at present constitute the main primary pro-ducers of the Venice lagoon (Rismondo et al., 2003; Sfrisoand Facca, 2007). The most abundant are Zostera marina L.,and Cymodocea nodosa (Ucria) Ascher. Two decades beforethose species occupied a small part of the lagoon becauseof the Ulva overgrowth. Now they are distributed all over thelagoon. Although these species are abundant in the Mediter-

ranean Sea, studies on the seasonal cycle of seagrass biomassand main factors governing the process are scarce. Tropi-cal seagrasses as C. nodosa (Larkum et al., 1989) can show

∗ Corresponding author.E-mail address: zharova@helios.unive.it (N. Zharova).

0304-3800/$ – see front matter © 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.ecolmodel.2008.03.001

© 2008 Elsevier B.V. All rights reserved.

large temporal changes. Biomass can vary up to a factor offour during the year. Recently some works on simulation ofZ. marina dynamics have appeared (Bach, 1993; Bocci et al.,1997; Zharova et al., 2001; Plus et al., 2003), however it ishardly possible to find similar studies on Cymodocea species,as far as we know, no model for C. nodosa has been pub-lished up till now. Most of the studies on Cymodocea arerelated to its morphology and some growth parameters. Lit-tle attention has been paid to the belowground compartmentand to assessing its functional role in the seagrass sys-tem.

The growth and net production of C. nodosa was studiedover one year February 1994–January 1995 in the south-ern basin of the Venice lagoon at the station called Petta

central lagoon at the station San Nicolo. These stationsare slightly different by a mean depth: 55 cm for Pettadi Bo and 75 cm for S. Nicolo. In relation to the main

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hysical–chemical parameters and nutrient concentrations inhe water column and surface sediments, C. nodosa biomassshoots, roots–rhizomes and dead parts taken separately)as sampled by collecting above and belowground partsithin a permanently established sampling area in accor-ance with the methodology set up by Sfriso and Ghetti

1998).The model was initially developed based on data acquired

y Sfriso and considers the seagrass biomass dynamics in994–1995. The model was further tested on data series relatedo 2001–2002. This study is an attempt to put together thenformation about the C. nodosa development within theramework of a simulation model.

. The model

he model has four state variables:

L – aboveground seagrass biomass, g C m−2,N – shoot density, namely number of seagrass shoots perm2,R – belowground seagrass biomass, g C m−2,D – dead seagrass biomass, g C m−2.

Two main forcing functions were T – water temperature and– photosynthetically active radiation (PAR: 400–700 nm). Dailyveraged and weekly temperature measurements from theampling stations and as well hourly measurements of irradi-nce at the station situated in the lagoon near Porto Margheraere available.

The processes that the model considers are asollows.

.1. Production

he biomass produced by shoots is limited mainly by tem-erature and irradiance. We excluded the nutrient-limitationince it is very rarely reported for our species. Accord-ng to literature nutrients can be expected to be limitingor C. nodosa if the internal shoots quota concentration isess than medium level 18 mg g−1 for N and 2 mg g−1 for PDuarte, 1990). In addition Perez et al. (1991) reported mid-ummer growth to be strongly P-limited when N:P ratio isbove 35. As it is seen from Fig. 1 in our case nitrogenoncentration in shoots were never below the critical con-entrations listed by Duarte (1990) and the highest ratio:P is 26 that is much less than the critical one. Besides,everal authors insist that factors other than nutrient sup-ly, such as light or temperature, are more likely to limithe growth of seagrass due to the fact that in seagrassesrganic carbon and nutrients can be quickly translocated over

ong distances via rhizomes and roots (Ceccherelli and Sechi,002; Duarte and Sand-Jensen, 1996; Nielsen and Pedersen,000). The results of Duarte and Sand-Jensen (1996) indi-

ate that resource limitation probably plays a more importantole in constraining the initiation of patches from seedlingsn nutrient-poor areas than in the expansion of existingatches.

6 ( 2 0 0 8 ) 134–144 135

So in our model the biomass produced by the shoot is lim-ited by temperature and irradiance and could be describedby:

PB = PL × FTprod(T) × FIL(I) × L

where PL is the maximum biomass productionrate.

The relative production is a function of temperature andirradiance. A bell-shaped function was used to describe thetemperature dependency (Zharova et al., 2001):

FTprod(T) ={

K((Topt−T)/Topt)stt

0 if T ≤ Topt

K((T−Topt)/(Tmax−Topt)stt

m if T > Topt

Topt – optimal temperature; Tmax – maximal temperature; K0,Km – function value at T = 0 and T = Tm; stt – controls the shapeof the function.

In the water column, light is attenuated by water turbid-ity and leaf biomass. Epiphyte factor is irrelevant for bothstations as it was mainly present on the old leaves (Sfriso,personal communications). According to yearly averaged fieldmeasurements only about 37% of it reaches the bottom. Perezand Romero (1992) reported that only a seagrass model takinginto account the self-shading effect could properly estimatethe leaf production. To calculate the light conditions of thewater column it is divided in 10 layers. Then the average valuefor all layers was taken.

The light limitation function for each layer was calculatedusing the following function:

FIL =

⎧⎪⎪⎨⎪⎪⎩

0 if I ≤ IC

(I − IC)(IK − IC)

if IC ≤ I < IK

1 if IK ≤ I

where H – water depth; H10 = H/10; I = I0 × exp(−Kshad

× H10) − illumination at the bottom of the layer; I0 – illu-mination at the surface of the later; IC – compensationlight intensity; IK – saturation light intensity; Kshad –light attenuation factor; Kshad = Kw + KL × L/H; Kw, KL –extinction coefficient of water and leaf biomass, respect-ively.

A part of this new produced biomass is translocated tobelowground compartment the rest remains in abovegroundpart.

2.2. Recruitment

In the model only vegetative reproduction is considered. Weignore the possibility of C. nodosa, like other seagrasses tospread and colonize new areas by means of seeds and byhorizontal elongation by lateral rhizomes from establishedpatches (Nielsen and Pedersen, 2000). In our case the seedlingsare quite unusual. Flowering of C. nodosa is very rare in theVenice lagoon (Curiel et al., 1994; Sfriso et al., 2004). It mightbe because of temperature and light conditions that do notcoincide in the right way and do not permit the flowering

and then the complete seed maturation. In addition duringrather cold winters only a small amount of seeds can sur-vive. Caye and Meinesz (1986) report that seedlings show goodgrowth only at warm temperatures between 17 and 25 ◦C and

136 e c o l o g i c a l m o d e l l i n g 2 1 6 ( 2 0 0 8 ) 134–144

con

Fig. 1 – Internal nutrient

when salinity is reduced to 20–27‰ for a long period. Our datashow that mean value of salinity during the year is 30.8‰

with a minimum 26.9‰ registered only once in April whereasthe temperature rounds between 16 and 18 ◦C. These are theprobable reasons why seedlings have been seldom in our casestudy.

tents in seagrass tissue.

The new shoots recruitment were related to the limitingfactors by the equation:

RS = REC × FTrec(T) × FNL lim(L).

It is assumed that the appearance of new shoots dependson the water temperature in the same way as for the above-

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round biomass and: FTrec – has the same shape as FTphot butts parameters are different. In addition, we have taken intoccount the space or self-shading limitation depending onensity of the aboveground biomass.

NL lim ={

1 − (L/�)2 if L ≤ �

0 if L > �;

– aboveground biomass above which no new shoots are pro-uced.

.3. Biomass losses and shoot density decrease

atural loss of seagrass leaf biomass occurred with senes-ence mortality that is temperature dependent. Measure-ents from Venice lagoon studies showed the mortality rate

o vary from 0.4% to 10% per day with maxima in July–August.tepwise function that accounts for an increase of the relative

oss rate with temperature is used:

LTloss =

⎧⎪⎪⎪⎨⎪⎪⎪⎩

dmin if T ≤ Tmin

dmin + (dmax − dmin)

×(T − Tmin)/(Tmax − Tmin) if Tmin < T < Tmax

dmax if T ≥ Tmax

here dmin, dmax – minimal and maximal loss rate; Tmin, Tmax

switch temperature values.Decreases in shoot density are explained by mechanical

osses due to wave motion that is considered constant in thisodel (LossN) and natural mortality FNTloss that is temperature

ependent in the same way as FLTloss.

N = LossN + FNTloss(T)

The belowground biomass reduction includes partial deathf roots–rhizome and energy transfer from rhizomes whenew shoots are produced. Mortality is assumed to be the step-ise function of temperature FRTloss. When new shoots are

ormed the rhizome biomass decrease is equal to the numberf new produced shoots multiplied by the biomass of one newhoot (Pnew), which is fixed.

Dead parts in the belowground biomass of C. nodosaccounted for a negligible proportion of this compartmentiomass in all seasons. In the warm season it mainly con-isted of old leaves that were still attached to the leaf bundle.nce the leaves fell into water they were transported away by

ides and water motions. Leaf detachment and fragmentationas facilitated by high temperature while transportation was

mpeded when the available free space was reduced due to thebundance of aboveground biomass.

L = FDTloss(T) + LossD × FDL lim(L)

here LossD – coefficient of loss due to water motion;FDTloss (T) – function of biomass degradation and fragmen-

ation has the same shape as FLTloss;FDLlim (L) – function of the free space limitation has the

ame shape as FNLlim.

.4. Translocation

aking into account that the organic carbon fixed by the leavess translocated in part to the roots–rhizomes system (Sfriso

6 ( 2 0 0 8 ) 134–144 137

et al., 2004) so the increase in the underground biomass hasbeen assumed to be proportional to the aboveground produc-tion biomass (KR:S). In addition our data show a rapid increasein the rhizome biomass during October when the productionand aboveground biomass go down while the intercellularconcentration of the carbon decreases significantly in deadleaves in comparison to new ones. This makes us hypothe-size that there is more translocation of fixed carbon to theroots–rhizomes system from the old parts of leaves. Thus, thecoefficient of additional translocation was introduced in themodel KTL.

2.5. System of equations

Thus, the following differential equation described the behav-ior of the state variables:

dL

dt= PB × (1 − KL:R) + RS × Pnew × N − FLTloss(T) × L

dR

dt= PB × KL:R + KTL × FLTloss(T) × L

−FRTloss(T) × R − RS × Pnew × N

dN

dt= (RS − MN) × N

dD

dt= FLTloss(T) × (1 − KTL) × L + FRTloss(T) × R − DL × D.

3. Results and discussion

The model is firstly calibrated for Peta di Bo data set and thenrun for S. Nicolo data without changing any parameter exceptthe mean water depth. Time step was 1 h.

Fig. 2 presents the simulation results showing the fourmodel variables in comparison to field measurements for bothstations. Reasonably good agreement was obtained betweenmeasured and calculated values for aboveground biomass andshoot density. Correlation coefficients for them are 0.98 and0.97, respectively. Parameter values that we found by calibra-tion are listed in Table 1.

The model can predict a marked seasonality in growth ofC. nodosa with rapid growth during May–June and very muchslower growth from October to March. The period of the high-est aboveground biomass was in August and the lowest valuesoccurred in January–February. The shoot density had a peak inmid July for Petta di Bo and in late June for S. Nicolo, a monthbefore the maximum of the aboveground biomass. The modelwas also able to reproduce the autumn biomass decline dueto lower water temperatures and light limitation.

The correlations between field data and model results forthe belowground biomass and dead parts were 0.75 and 0.78,respectively. A slight difference was observed for the below-ground biomass corresponding to the peak in late fall andbeginning of winter more pronounced for Petta di Bo station,

which could be due to the seasonal changes of translocationpercentage, which is considered constant in our model. At thesame time the amount of dead parts was a little higher duringspring and summer and, in spite of the late autumn peak, the

138 e c o l o g i c a l m o d e l l i n g 2 1 6 ( 2 0 0 8 ) 134–144

lts an

Fig. 2 – Simulation resu

model value was lower than in situ, and the following decline

was not as rapid as in the field measurements.

Altogether, the model reproduced the seasonal variationsof biomasses and shoot density for C. nodosa well showing howthe variations in temperature, light and plant density contin-

d field measurements.

uously change the growth conditions for the seagrass over the

year.

A literature review of several studies of C. nodosa presentedin literature shows that the range of variations of Cymodoceaspecies behavior is rather wide.

e c o l o g i c a l m o d e l l i n g 2 1 6 ( 2 0 0 8 ) 134–144 139

Table 1 – Values of model parameters

Parameter Unit Model value

PL day−1 0.18FTprod

K0 day−1 0.003Topt

◦C 29Tmax

◦C 35stt – 1.8FIL

IK �mol m−2 day−1 496.8IC �mol m−2 day−1 m−1 49.7Kw g C−1 m2 1.2KL 0.009H m 0.55 (Petta di Bo)

0.75 (San Nicolo)REC day−1 0.085FTrec

K0 day−1 0.002Topt

◦C 27Tmax

◦C 40stt – 1.6FNLlim

� g C m−2 500FLTlloss

dmin day−1 0.014dmax day−1 0.026Tmin

◦C 9Tmax

◦C 18KL:R – 0.2LossN day−1 0.002FNTlloss

dmin day−1 0.001dmax day−1 0.013Tmin

◦C 9Tmax

◦C 25Pnew mg C 1FDTlloss

dmin day−1 0.03dmax day−1 0.3Tmin

◦C 5Tmax

◦C 20LossD day−1 0.2FDLlim

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In general authors confirm a close coupling between shootrowth and shoot density, as we have observed in our caseTable 2). There was also a good match with biomass develop-

ent of C. nodosa during the year. Its biomass varied accordingo the season. During spring roots–rhizomes showed mini-

al growth rate while leaves were at the maximum (Agostinit al., 2003). Leaf decay began in August, as reported byuia and Mazzella (1991). Aboveground biomass was theighest in summer and the lowest in winter; the oppositeeasonal patterns in the belowground biomass were observed.he same dynamics for leaves was found by Guidetti et al.

2002), but with no clear pattern for belowground compart-ent. The data about the relationship between the abundance

f belowground and aboveground biomasses over the year areifferent. While Agostini et al. (2003) mention that below-round biomass was higher than the aboveground biomasshrough the year, Guidetti et al. (2002) report that C. nodosa

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140 e c o l o g i c a l m o d e l l i n g 2 1 6 ( 2 0 0 8 ) 134–144

oduc

Fig. 3 – Growth rate and net pr

showed a high proportion of the belowground stock in com-parison to aboveground biomass (up to 90%), with distinctseasonality. Our case does not show accordance with anyof these authors as we demonstrated pronounced seasonalfluctuations with significant change in the ratio: from 26%during summer and up to 499% during autumn. This couldbe explained by various reasons, first of all by the tempera-ture regimes. While in the northern Mediterranean Sea nearCorsica the winter is rather short and warm, thus watertemperature is never below 8 ◦C, in the Venice lagoon thewinter temperatures are rather low sometimes close to 0 ◦C,

so it is more difficult for shoots to survive. As a rule dur-ing January–February no leaves are usually observed, and thebiomass consists of leaf bundles and is very low. So the sea-grass starts to grow with low values of biomass, but the shoot

Fig. 4 – Comparison of different approximations of tem

tion of aboveground biomass.

density is always as much as twice higher than in the otherMediterranean sites. Probably, this situation, when the livingspace is in abundance and the water column is transparentis favorable for growth, and the seagrass develops the sameaboveground biomass at the peak of the vegetative period.The water depth may also play a role, since it is half the onereported in the cited study. So there is more light available forphotosynthesis. The belowground biomass is less developedall over the year probably because of the sediments texturethat contain little sand, which may prevent root and rhizomegrowth.

Data regarding the net growth rate and net productionof shoots are presented in Fig. 3. The aboveground growthis rather fast, the maximum values observed in May–Junewere up to 0.04 day−1 when the major number of shoots are

perature conditions implemented in the model.

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oung, which corresponds to the values reported by Nielsennd Pedersen (2000) i.e. 0.047 day−1 for youngest leaves in lab-

◦

ratory at 25 C.During the summer period the mean growth rate was

.024 day−1 that is close to the one reported by Van Lent et al.,991 and Munoz (1995) and three times higher than the one

Fig. 5 – Comparison of simulation results obtained by introdu

6 ( 2 0 0 8 ) 134–144 141

found by Mazzella and Buia (1996). The net production duringthe period of rapid growth could reach up to 5.6 g C m−2 day−1,

−2 −1

almost double the mean values (3.6 g C m day ) measuredby Drew (1978) for shallow waters. Rates for roots–rhizomesgrowth were 0.005–0.015 day−1 and are similar to the onesobserved by Mazzella and Buia (1996).

cing different approximation of temperature conditions.

i n g 2 1 6 ( 2 0 0 8 ) 134–144

Fig. 6 – Limiting factors for. (a) Seagrass production(dimensionless). FIL – limitation function by light; FtP –limitation function by temperature; total – combinedlimitation by both factors: total = FIL × FtP. (b) New shootrecruitment of seagrass (dimensionless). FIL – limitationfunction by light; FtN – limitation function by temperature;LimL – limitation function by aboveground biomass; total –

142 e c o l o g i c a l m o d e l l

The following experiments were conducted to test modelsensitivity to external factors. We have tested some hypothe-ses about the temperature dependencies and the lightcontrolling factors. The shape of the temperature limitingfunction for biomass growth and new shoot production waschosen in accordance with the work about the Z. marina basedon the data from the same case study (Zharova et al., 2001).Several authors stated that C. nodosa as a tropical speciesshows the greatest response to temperature (Marba et al.,1996) fluctuations.

First we analyzed the importance of temperature. We com-pared the values of water temperature acquired during weeklyfield measurements and data for air temperature produced bymeteorological station in Marghera close to our site.

The average daily air temperature was used to approxi-mate the water temperature by linear formula. Different typeof non-linear approximation was also tried but the accuracywas lower than in the linear approximation. The correlationbetween these series showed R2 of 0.94. The temperature trendbased on weekly water temperature and mean daily air tem-perature measurements is shown on Fig. 4. When introducedin the model the simulated water temperature leads to asimilar behavior (Fig. 5). This could help when the field datafor water temperature are scarce, as the model variables arerather sensitive to the temperature forcing function.

According to Marba et al. (1996) variability in water tem-perature explains most (R2 > 50%) of the annual variability ofseagrass shoot weight for all species – in our case more than70%. The life cycle of these species seems to be related to theannual temperature range rather than to other environmentalparameters (Buia and Mazzella, 1991).

Another component controlling C. nodosa growth is light.There are only a few data sets reported both for the quantityof light available for light compensation (IC) and for light sat-uration point (IK). We found that 3 mW cm−2 PAR can be usedas saturation point (IK), while compensation irradiance for C.nodosa is between 0.3 and 0.5 mW cm−2 PAR (Drew, 1978) andfor C. rotundata it is IC = 24.1 mmol photons m−2 s−1 (Agawin etal., 2001).

Experiments we made manipulating the values for IC andIK showed that the model was rather insensitive to thoseparameters. Thus, there is no need to hypothesize that thesevalues can depend on temperature (Bach, 1993) as it wasdone for Zostera (Zharova et al., 2001). Next we investigatedwhat happens if we use the empirical formulas (Bras, 1990;Vollenweider, 1974) for seasonal fluctuations of light irra-diance instead of the real measurements. Since the lightlimitation function presented in the empirical formulas is agood approximation of the one observed in field (R2 = 0.65), andfor the light limiting function the correlation is even higher(R2 = 0.77) no significant differences in the behavior of the statevariables appear. The fluctuations of the variables were withinthe deviations of the field measurements. So the seasonalchanges in light availability seem to be essential, while fur-ther improvement of definitions for light conditions are notrelevant for this model as it does not change significantly the

general trend of annual C. nodosa dynamics.

All experiments described above show that the currentsimple model is sufficient enough to simulate annual C. nodosafluctuation and there is no need for a more accurate descrip-

combined limitation by all factors: total = FIL × FtN × LimL.

tion of external conditions. This may be because of a ratherslow growth rate and, as a consequence, – a delayed responseof seagrass to acute environmental changes.

Fig. 6a summarizes the effect of different limiting factorsfor C. nodosa development. It should be noted that these arethe results of our particular case study and may not be thesame elsewhere.

Temperature seems to be the major limiting factor for C.nodosa production during the whole year. It triggers growthin spring and causes rapid biomass drop in mid summer.Reduced light in fall also contributes to the biomass decline.Temperature and light were also found important for newshoot production (Fig. 6b), fall temperature limitation beingmore significant. This limitation factors analysis suggests thatmeasurements of temperature trends are most important andneed to be performed most accurately in case someone wantsto improve simulations over certain short periods for C. nodosa.Aboveground biomass growth and shoot recruitment werestrongly associated with seasonal variation in temperatureand irradiance for C. nodosa as also reported by Marba et al.(1996).

Finally we analyzed the function that describes the fluc-tuation of the belowground and dead material in the model.It seems that the autumn fast growth of the belowgroundbiomass could not be explained only by a change in nutrient

translocation coefficient but also probably by some mecha-nisms that store nutrients in belowground parts before theleaves falling.

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Further research for this phenomenon is needed. Weave experimented with making the translocation coeffi-ient dependent upon the day length and the senescenceffect, also affected by the day length, but these modi-cations did not bring much improvement to the modelutput, even when coupled with the effect of temperature.o, further on more accurate studies are needed to pro-uce and test the hypotheses that could indeed improve thenderstanding of the belowground and dead biomass dynam-

cs.

. Conclusions

his work was an attempt to use a simulation model to ana-yze the sensitivity of the marine grass community to variousrocesses in the Venice lagoon ecosystem. The goal was tostimate the importance of individual factors for the overallystem dynamics, using a simplified model entirely based onata sets.

We have built a model that can well simulate growth andensity of the seagrass population in the Venice lagoon. Itakes into account the effect of light and temperature on. nodosa growth. Analysis of the basic model and its mod-

fications indicate that temperature and light are the majorhysical factors governing photosynthesis and growth of C.odosa in this ecosystem. The model suggests that the princi-al limiting factor is temperature, whereas light fluctuationsre important at the seasonal scale.

The analysis indicated some weak points to be improved.he environmental controls and physiological mechanismsoverning the coupling among photosynthesis, growth,ranslocation and reproduction remain poorly understood, aso the environmental factors and internal plant mechanismsontrolling the shoot senescence.

In our further studies we intend to look at the data fromater field studies on C. nodosa at the two other stations inhe lagoon that are quite different from those reported here.y analyzing and comparing the model output with the newata we may gain a better understanding of how the systemorks and how local environmental factors contribute to the

ystem behavior. Our work so far has shown that simulationodeling can improve our knowledge about system dynamics.

y testing model sensitivity, both to parameters, and struc-ure (formulas used), we can better guide our experiments,ocusing them on most crucial parameters and forcing func-ions.

e f e r e n c e s

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gostini, S., Pergent, G., Marchand, B., 2003. Growth and primary

production of Cymodocea nodosa in a coastal lagoon. Aquat.Bot. 76, 185–193.

ach, H., 1993. A dynamic model describing the seasonalvariations in growth and the distribution of eelgrass (Zosteramarina L.) I. Model theory. Ecol. Model. 65, 31–50.

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