Dynamical simulation of mass-balance trophic models for benthic communities of north-central Chile:...

Ecological Modelling 148 (2002) 277–291

Dynamical simulation of mass-balance trophic models forbenthic communities of north-central Chile: assessment of

resilience time under alternative management scenarios

Marco Ortiz *, Matthias WolffZentrum fur Marine Tropenokologie (ZMT), Center for Tropical Marine Ecology, Fahrenheitstrasse 6, D-28359 Bremen, Germany

Received 14 February 2001; received in revised form 7 September 2001; accepted 11 October 2001

Abstract

Within Tongoy Bay (north-central Chile), four different habitats (seagrass, sand-gravel, sand and mud) wereidentified and subsequently considered as subsystems for the construction of trophic mass-balance models. By usingthe ECOSIM software package of Walters et al. (Ecosystems, 2 (1997) 539), different management scenarios weresimulated for these subsystems and for an overall integrated system (combining all habitats) in order to explorestrategies of sustainable resource use. System Reco�ery Time (SRT) as well as single species responses differed withthe scenario simulated. The most important findings were: (1) an increase in the harvest of the scallop Argopectenpurpuratus would not drastically affect the global properties of the systems; (2) a depletion of its principal predator,the sea star Meyenaster gelatinosus, greatly improved the availability of scallops in the subsystem seagrass,sand-gravel as well as in the integrated model; (3) a biomass reduction of the snail Xantochorus cassidiformis wouldproduce only a small negative impact on the SRT, while a simulated harvest on the clam Mulinia sp. drasticallychanged the system properties. This clam may thus be considered as a keystone species; (4) predictions of themaximum sustainable yield (MSY) of the scallop were lower than those obtained by single species approaches. Oursimulations allow us to conclude that: (1) a strong fishery of the scallop predator, the sea star M. gelatinosus, wouldgreatly increase the yield of the scallop and the other populations or resources of the systems; (2) trophic massbalance models and their simulated scenarios offer great possibilities for the planning of interventions or manipula-tions of natural systems. © 2002 Elsevier Science B.V. All rights reserved.

Keywords: ECOSIM; Trophic relationships; Upwelling system; Bottom-up; Mixed and top-down controls; Fishing mortality

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1. Introduction

The intensive growth in the development ofecosystem models during the last decade has per-mitted us to theoretically explore our scientificunderstanding of natural processes and to assessalternative management polices (Jørgensen, 1992).

* Corresponding author. Fax: +49-421-238-0030.E-mail addresses: [email protected] (M. Ortiz),

[email protected] (M. Wolff).

0304-3800/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved.

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M. Ortiz, M. Wolff / Ecological Modelling 148 (2002) 277–291278

The overexploitation of most aquatic resourceshas lead to a transformation of ecological andeconomical systems and has produced a situationwhich concerns not only the scientific community,but also environmentalist, fisheries managers, andfishermen.

While many reductionistic population modelshave been developed to study these complex sys-tems, the disillusion about the predictive capabil-ity of these single species assessment strategies hasincreased (Walters et al., 1999). Their principaldisadvantage is that they need to consider thepopulations under study in isolation from bothbiotic and abiotic surroundings (Larkin, 1977;Levins and Lewontin, 1985; Paine, 1984; Hilbornet al., 1995; Patten, 1997; Roberts, 1997; Levins,1998a; Walters et al., 1999). Although some ofthese models seem appropriate in situations ofclear stock–recruitment relationships, they onlygrasp proximate properties of the populations anddo not make neither implicit nor explicit consider-ations about the ‘health’ conditions of the ecosys-tems where these species inhabit. Thus, if we wantto approach the global properties of these com-plex natural systems, the boundaries of our ab-stractions must be expanded towards itsexternalities, that is, integrating more variables,interactions and their dynamical behaviour.

Although the stability and structural propertiesof ecosystems have been widely analysed anddiscussed in the literature, especially in regard tothe complexity of food webs (MacArthur, 1955;Odum, 1969; Holling, 1973; Levins, 1974; May,1974; DeAngelis, 1975; Pimm, 1982; Briand, 1983;Briand and Cohen, 1984; Ulanowicz, 1986; Pimmand Kitching, 1987; DeAngelis et al., 1989; Law-ton, 1994; Vasconcellos et al., 1997; Peterson etal., 1998; Tokeshi, 1999), few studies have beenfocused on the holistic dynamical modelling (mul-tispecies) and on the prediction of alternativemanagement polices in overexploited systemaround the world (Mackinson et al., 1997). So farmost studies done along the Chilean coastline arebased upon the population dynamics of the com-mercial species (Santelices, 1989; Santelices andDoty, 1989; Vasquez, 1995; Stotz, 1997; Stotz andGonzalez, 1997; Castilla, 2000) and lie essentiallywithin the above-mentioned reductionisticabstractions.

One way to integrate and to study complexnatural ecosystems is through the modelling oftrophic or matter/energy flow. Christensen andPauly (1992), developed the ECOPATH II software,by which steady-state mass-balances and flowsbetween interconnected (by depredation) com-partments can be quantified. Furthermore, basedon the theories of Odum (Odum, 1969) andUlanowicz (Ulanowicz, 1986, 1997) it is possibleto describe and compare systems in terms of theirdevelopment (maturity) or degree of growth (sizein term of flows), capacity to withstand externalperturbations, stability and direct– indirect impactof the species or groups on the remainder com-partments. Although ECOPATH II produces asteady state picture of the trophic flows, it repre-sents an important baseline for further dynamicalsimulations.

A dynamical extension of ECOPATH II, termedECOSIM, was developed by Walters et al. (1997).Based on this approach simulations can be madeabout the response of the entire system to differ-ent perturbations and to different exploitationregimes, under assumptions of bottom-up, mixedor top-down flow control mechanisms. In a recentcontribution, Mackinson et al. (1997), in compar-ing the trophic impacts of harvesting small pelagicfish in three different upwelling ecosystemspointed out the following results: (1) after anintensive exploitation of small pelagic fishes, thestanding stocks of their food and competitorsincreased, and their predators decreased; (2) foodlimitation by bottom-up control cannot explainthe replacement in abundance from anchovy tosardine species in the Peruvian system; and (3)estimations of fishing mortality for maximum sus-tainable yield (MSY) in small pelagics under as-sumptions of bottom-up control were higher thanthose obtained under top-down control.

The present contribution is based on steady-state trophic models previously constructed by theauthors for Tongoy Bay (north-central Chile)(Wolff, 1994) and for habitat subsystems usingECOPATH II software. The analysis of food webinto habitat or subsystems follows the recommen-dations suggested by May (1974), Paine (1980,1984), Hall and Raffaelli (1993) in regard to thatthe stability of the systems would be increased if

M. Ortiz, M. Wolff / Ecological Modelling 148 (2002) 277–291 279

the food webs are organised into subsystems.These mass-balance trophic models allowed todescribe the species structure and trophic flowswithin each subsystem (seagrass, sand-gravel andsand habitat) and whole system, and to do somepreliminary impact analysis by Mixed TrophicImpact (Ulanowicz and Puccia, 1990).

The main objective of this paper is to assessdynamically the resilience time of each subsystemand whole system as response to different strate-gies of resource exploitation (harvest pressure)and to estimate fishing mortality corresponding tomaximum sustainable yield (FMSY) for the mostvaluable species, the scallop Argopecten purpura-tus, under assumption of bottom up, mixed andtop down flow control mechanisms. As studies ofHunter and Price (1992), Jordan et al. (1999),Menge (2000) suggest that a control is mixed(both bottom-up and top-down) we further ex-plore the simulations results based on this as-sumption. Moreover, we believe that alonebottom-up and top-down processes in communi-ties may be considered as another false dichotomythat dominates in ecological sciences (sensuLevins 1998a).

2. Material and methods

2.1. Subtidal benthic system of Puerto Aldea,Tongoy Bay

The study area of Puerto Aldea (Fig. 1) corre-sponds to one of 168 management areas estab-lished along the Chilean coast (Castilla, 2000).These areas are assigned to fishermen organisa-tions to maximise, within sustainable boundaries,the production and exploitation of commercialresources. In this area the following habitats canbe recognised: (1) seagrass meadows; (2) sand-gravel; (3) sand; and (4) mud. A complete bioticand abiotic description of these habitats was doneby Jesse (2001).

Tongoy Bay and the subtidal benthic system ofPuerto Aldea are protected from the prevailingsouth-west winds by Lengua de Vaca peninsula;all beaches are classified as of the intermediatemorphodynamic state (Ortiz and Stotz, 1996).

The upwelling center near Punta de Vaca (Daneriet al., 2000; Montecinos and Quiroz, 2000) isamong the most important one of northern Chileand supplies nutrients to the ecosystem and simul-taneously prevents the establishment of a stablethermocline during summer through permanentintrusions of upwelling water to the bay. Temper-ature of bottom water ranges between 13 and17 °C in winter and autumn, respectively (Jesse,2001).

2.2. ECOSIM, dynamic mass-balance approach

Our dynamical simulations are based on theECOSIM software, starting from the initial condi-tions estimated by ECOPATH II models for thebenthic system under study. The mathematicalground of ECOSIM models consists of the biomassdynamics described in form of coupled differentialequations as:

dBi

dt=gi �

j

Cji−�j

Cij+Ii− (Mi+Fi+Ei)Bi, (1)

where Bi is the biomass of compartment i (g/m2),gi is the growth efficiency of i, Cji is the consump-tion rates of j by compartment i [gi �j Cji=Bi(P/B)i, where P/B is production rate of i ], Cij is theconsumption rates of i by compartment j, Ii is theimmigration rate of i, Mi is the total mortality ofi, Fi is the fishing mortality of i, Ei is emigrationrate of i (I and E were both considered zero inthis study), and additionally,

Cij=aij �ij Bi Bj

(2�ij+aij Bj), (2)

where aij represents the instantaneous mortalityrate on prey i caused by one unit of predator jbiomass. Also aij can be interpreted as the rate ofeffective search by predator j for prey i. Each aij

could be estimated directly from the correspond-ing ECOPATH models by: aij=Qi/(BiBj) (Qi= totalconsumption of i ). The �ij represents the transfer-ence rate between compartment i and j. Thisparameter determines if the control is top-down,bottom-up or mixed, ranging from 1.0 for top-down to 0.0 for bottom-up control. A value of 0.3


represents a mixed control. Table 1 summarisesthe initial parameters entered for each benthicmodel system and calculated by ECOPATH II. Thesteady-state flow models for each benthic systemwere constructed showing the biomass (B), pro-duction rate (P/B) and total consumption (Q) ofeach compartment and flows between them (Fig.2a–d).

Based on previously constructed steady-stateECOPATH II models, ECOSIM permits to generate

dynamical biomass predictions of each systemcompartment i which is affected directly byfishing, depredation, changes in food supplies,and indirectly, by fishing on other groups. Usingequilibrium simulations where equilibriumbiomass is plotted over a range of fishing mortal-ity values, it is possible to estimate—under alarge-scale approach— the maximum sustainableyield for the harvested compartments. For moredetails see Walters et al. (1997).

Fig. 1. (a) The main littoral types along the Chilean coast: (1) dominated by exposed rocky shores; (2) dominated by exposed sandyshores; (3) mostly insular systems. (b) The principal bay systems of the IV Region of Coquimbo (Chile). (c) Study area of PuertoAldea located at southern of Tongoy Bay.


Tab

le1

Cat

ch[C

](g

/m2),

biom

ass

[B]

(g/m

2),

prod

ucti

onra

te[P

/B]

(per

year

),co

nsum

ptio

n[Q

/B]

(per

year

),an

dfis

hing

mor

talit

y[F

](p

erye

ar)

valu

esfo

rth

ese

agra

ss,

sand

-gra

vel,

and

sand

habi

tats

,an

dfo

rw

hole

(com

bine

d)ar

ea

Par

amet

eren

tere

dan

dca

lcul

ated

byE

CO

PA

TH

IISp

ecie

s

Sand

-gra

vel

mod

elSe

agra

ssm

odel

Sand

mod

elW

hole

mod

el

CB

P/B

Q/B

FC

BP

/BQ

/BF

FC

BP

/BQ

/BF

CQ

/BP

/BB

–46

.76

1.2

5–

–17

.31.

25

––

21.6

1.2

M.

gela

tino

sus

5–

–20

.51.

25

––

0.43

0.6

2.3

––

–2.

31.

10.

62.

3–

H.

helia

nthu

s–

0.5

0.6

–2.

980.

73

––

0.61

0.6

2.3

–L

.m

agal

lani

ca–

–1.

30.

73

–0.

60.

73

–0.

1525

.61.

19.

50.

006

0.05

17.4

81.

19.

50.

003

0.01

50.

35C

.po

lyod

on10

1.1

9.5

0.04

9.5

1.1

100.

15–

3.5

0.5

4.5

–C

.po

rter

i–

6.35

1.8

9.5

––

C.

coro

natu

s2.

51.

89.

5–

P.

barb

iger

–1.

6–

29.2

81.

951.

959.

9–

–4

1.95

–9.

9–

9.9

––

6.54

1.25

2.2

9.5

––

61.

25–

9.5

Lar

geE

pifa

una

–1.

25–

5.5

1.25

9.5

9.5

–

0.6

9.74

1.5

5.5

X.

cass

idif

orm

is0.

060.

62.

281.

55.

50.

269.

990

0.08

7.5

71.5

42.

082.

089.

90.

10.

9940

2.08

7.5

9.9

0.02

15.9

955

2.08

A.

purp

urat

us9.

90.

29

––

–1.

71.

59.

5–

–0.

651.

59.

5–

1.3

1.5

Tal

iepu

ssp

.9.

5–

150

1.2

9.9

––

241.

29.

9–

Mul

inia

sp.

–90

0.8

9.9

–C

.tr

ochi

form

is–

370.

89.

9–

–15

02.

29.

9–

–T

egul

asp

.38

2.2

9.9

––

703.

211

––

203.

211

–P

.ch

ilens

is–

203.

712

.5–

–43

3.7

12.5

––

––

183.

712

.5–

Smal

lE

pifa

una

12.5

3.7

29.5

––

–60

4.4

14.7

––

104.

54.

414

.7–

–60

4.4

14.7

–65

4.4

14.7

Infa

una

H.

tasm

anic

a–

–11

01.

5–

–45

01.

5–

–11

3.9

564.

86

–0.

2–

36

––

–11

46

78.6

6–

1.45

–C

h.ch

amis

soi

–5.

5–

––

230

5.5

––

–6

5.5

––

–11

05.

5–

–6

5.5

–R

odop

hyta

–70

6–

––

36

––

–U

l�a

sp.

50–

6–

–5

6–

––

1940

160

––

1840

160

––

–16

018

4016

0–

Zoo

plan

cton

–18

40P

hyto

plan

cton

––

3625

0–

––

3425

0–

––

2825

0–

–28

250

––

Inbo

ldar

eth

een

tere

dda

taan

din

stan

dard

are

the

calc

ulat

edby

EC

OP

AT

HII

.(N

ote:

Imm

igra

tion

[I]

and

emig

rati

on[E

]pa

ram

eter

sof

Eq.

(1)

wer

eco

nsid

ered

=0)

.


Fig. 2. The food web for: (a) seagrass; (b) sand-gravel; (c) sand habitat; and d) whole (combined) area. The biomass [B ] (g/m2),production rate [P/B ] (per year), consumption rate [Q/B ] (per year), and catches (g/m2) values are shown. Vertical positionapproximates trophic levels. The box size is proportional to the square root of the compartment biomass.

2.3. Definitions

Stability is the capacity of a system to returnto a state of equilibrium after perturbations(Holling, 1973; Levins, 1974). Based on Odum’stheory of ecosystems (Odum, 1969), ecologicalstability is considered as an exclusive propertyof mature systems, which evolve towards an in-crease of size and diversity until certain limitsare imposed by the available resources. On theother hand, Ulanowicz’s theory (Ulanowicz,1986, 1997) states that ecosystems organisation,in terms of Relative Ascendency (A/C) and Re-dundancy (internal flow of Overhead), may bethe most important attributes associated with

system stability. A bottom-up control means thatthe flow of energy between two compartments islimited by food resources or controlled by thepreys; top-down control holds that the flow isregulated by the predators (Patten, 1997). Re-silience is the speed at which the entire systemreturns to its original state after it has beenstressed and displaced from that state (Pimm,1982). Resistance describes the ability of the sys-tems to withstand displacement (Begon et al.,1990). Thus stability includes both resilience andresistance. In the present study we assume thatSystem Reco�ery Time (SRT) as obtained byour simulations is a measure of the internal sta-bility of the systems.


Fig. 2. (Continued)

2.4. The scenarios

Only two parameters, the fishing mortality (Fi)and the transference rate (�ij), were modified dur-ing the simulations. Fig. 3 shows the fishing sce-narios that were simulated for each habitat andthe whole area. All parameter modifications (dis-turbances) were done for the period between the2nd and 4th year of the total simulation (20years). For the scallop A. purpuratus and the snailXanthochorus cassidiformis (harvested popula-tions), fishing mortality was increased by 100%from the baseline in order to create an extremesituation where both species are severely depleted(by over fishing). For the remainder populations,50% depletion was simulated, which represents anintermediate intensity of fishing, as these speciesdo not have commercial importance until present.

For all scenarios, the dynamical simulations weredone with bottom-up (�ij=0.1–0.2), mixed (�ij=0.3) and top-down (�ij=0.4–1.0) control assump-tions. However, the results will be described onlyfor mixed control.

3. Results and discussion

3.1. Dynamical simulations of biomass

Fig. 4 shows the possible dynamical responsesof biomass in the seagrass habitat under eachscenario and the combined impacts. The longestSRT was obtained when the sea star M. gelati-nosus was depleted (Scenario II). This, however,would have a positive effect on the scallop A.purpuratus and also its competitors (i.e. the crab


Fig. 2. (Continued)


Fig. 3. Simulated fishing scenarios or management options in:(a) seagrass habitat; (b) sand-gravel habitat; (c) sand habitat;and (d) whole area. For harvested and not harvested speciesan increase of 100 and 50% of fishing mortality (F), respec-tively, was considered.

single reduction of M. gelatinosus (through collec-tion by fishermen, who consider this species as‘undesirable’ because it feeds upon the scallops)might not be adequate because dramatic systemresponses (proliferation of competitors) are to beexpected. An alternative or additional policy maybe to simultaneously exploit C. polyodon and H.helianthus. By doing so, the positive effects onboth species (competitors) would be counteractedand the overall top-down control by the predatorson the scallops would be significantly decreased.

In the sand-gravel habitat observed responsesare similar. An increase of fishing for M. gelati-nosus would have a large impact on the SRT andon the other compartments. A large positive effectcould be observed for its preys, A. purpuratus andCalyptraea trochiformis, and for its competitor H.helianthus (Fig. 5). Contrary to the previous habi-

Fig. 4. Dynamical responses of biomass behaviour in seagrasshabitat subject to 2 years of increased fishing for each scenariounder a mixed controlling (�=0.3). SRT as a measure ofsystem’s stability (see text).

Cancer polyodon and the asteroid Heliaster he-lianthus). A similar pattern can be observed forthe simulation with all scenarios combined. Thesystem recovers quickly under an increase offishing of A. purpuratus (Scenario I). Based onthese results, a management plan focused on a


Fig. 5. Dynamical responses of biomass behaviour in sand-gravel habitat subject to 2 years of increased fishing for eachscenario under a mixed controlling (�=0.3). SRT as a mea-sure of system’s stability (see text).

keystone species (Paine, 1966, 1969, 1984; Mills etal., 1993; Jordan et al., 1999). The importance ofMulinia sp. seems due to its high throughput ofenergy, its high degree of connectivity within thetrophic web and its intermediate trophic position.

Fig. 7 shows the possible dynamical trajectoryof biomass for all compartment in the combinedmodel as a response to each scenario. A negativeimpact on M. gelatinosus would produce thelargest effect on the SRT and the other compart-ments if it is compared to other individual manip-ulations. The other extreme was observed for X.cassidiformis, which had the smallest effect on theentire system. In this expanded model a harvest

Fig. 6. Dynamical responses of biomass behaviour in sandhabitat subject to 2 years of increased fishing for each scenariounder a mixed controlling (�=0.3). SRT as a measure ofsystem’s stability (see text).

tat, only a removal of H. helianthus seems indi-cated as an additional management option. Anincrease of the harvest on A. purpuratus wouldonly have a small impact on the system and to theother compartments (Fig. 5).

Fig. 6 illustrates the responses in the sand habi-tat. An increase in fishing (F) for the snail X.cassidiformis would produce a small effect onboth the SRT and the other species populations.An exploitation of the clam Mulinia sp., however,produces large direct and indirect effects on thesystem properties; most of the predators would bedepleted, except for the positive effect on M.gelatinosus. These findings point to the impor-tance of Mulinia sp. within the food web andsuggest that this clam may be considered as a


Fig. 7. Dynamical responses of biomass behaviour in whole area subject to 2 years of increased fishing for each scenario under amixed controlling (�=0.3). SRT as a measure of system’s stability (see text).


on Mulinia sp. would not have the large effect onthe remainder populations, as was found in thesand habitat (Fig. 6). An increased fishing of theother populations showed similar responses as forthe habitat simulations.

Based on our results, an increase of fishing onthe commercial scallop A. purpuratus would haveonly a small effect on the systems when comparedto the other manipulations. Even though a de-crease in biomass of the asteroid M. gelatinosuswould produce a proximate positive effect on thescallop in the three models, a removal of thisspecies as a management tool must be carefullyanalysed because it may directly favour its com-petitors species. This replacement among preda-tors under selective fishing may be explained bythe dominance of direct and indirect interactionsgoverned by competition, depredation, mutualis-tic and ammensalistic mechanisms (Lawlor, 1979;Higashi and Patten, 1986, 1989; Billick and Case,1994; Wootton, 1994; Menge, 1995; Fath andPatten, 1999). These switches were described forother ecological simulations with surprisingly sim-ilar predicted and observed responses (Mackinsonet al., 1997; McClanahan and Sala, 1997). How-ever, it is important to note that Mackinson et al.(1997) obtained these similar responses only if theecosystem was top-down controlled. Under condi-tions of bottom-up control, no switch betweenpredators could be observed.

These positive responses on competitor species(or cascading effects) can also be viewed as adominance of positive feedback which may drivethe system to some other moving equilibrium(sensu Levins, 1998b). Thus, if our objective is notonly to increase the production of A. purpuratus,but also to conserve the natural system in which itinhabits, this positive feedback must be avoided.One way to depress these positive feedbacks maybe by fishing the other competitors species as well.The crabs C. polyodon must be exploited in theseagrass habitat and the asteroid H. helianthusmust be removed both in seagrass and sand-gravelhabitats. Comparable alternative management po-lices were suggested by McClanahan and Sala(1997) working on a Mediterranean infralittoralrocky-bottom ecosystems.

A further harvest on Mulinia sp. cannot berecommended due to the unexpected high ordereffects that it would produce on the remainderpopulations of the system. Even though the wholemodel, with the additional components and paths,shows a buffer effect if Mulinia sp. is exploited,this simulation outcome may not be realistic be-cause this species extends on a narrow sand beltalong the beach, which is distant or more discon-nected to the seagrass and the sand-gravelcommunities.

Based on our results, we think that any man-agement policy must be supported by ecologicalmodels of the kind presented here, which repre-sent each particular community or subsystemwhere the target species is inserted. It also seemsimperative to consider the environmental hetero-geneity of larger systems and to account for dif-ferent habitats (Hunter and Price, 1992; Walterset al., 1999). This is especially important since itimplies, for instance, that for each managementarea assigned to fishery organisations along theChilean coast (Castilla, 2000), specific modelsmust be developed which grasp the most relevantecological interactions and allow the evaluation ofdifferent management options for the sustainableuse of the resources.

Table 2 resumes the SRT obtained for bothbottom-up, mixed and top-down controlling. Forall scenarios, bottom-up control showed thesmallest SRT in comparison to top-down control,which under extreme condition produces oscilla-tion behaviour for all the compartments.

3.2. Fishing mortality corresponding to themaximum sustainable yield (FMSY)

Fig. 8 shows the maximum sustainable fishingfor A. purpuratus obtained by the equilibriumsimulations in the whole area. This combinedmodel suggests that a maximum fishing pressureof 0.86 can be supported by the system. Themaximum fishing mortality for the seagrass andthe sand-gravel habitat are shown in Table 2. Thevalues obtained in the present work are near butsomewhat smaller than those proposed by Stotzand Gonzalez (1997) who estimated a fishing mor-tality of about 1.19 for the same species in the


Table 2Summary of the SRT and fishing mortality at maximum sustainable yield (FMSY) for A. purpuratus for each model and scenariounder top-down, mixed and bottom-up controls

Habitats Control (�)

Top-down Mixed Bottom-up

1 0.8 0.6 0.4 0.3 0.2 0.1

SeagrassSRT Os 40.8 15.2 9.4 7.5 6.5 5.5Scenario I A. purpuratusFMSY Multiples 0.94 1.03 1.03 1.06 1.24 1.71SRT OscillationsScenario II 95.7M. gelatinosus 37.2 16.4 11.9 8.6 7.2SRT Oscillations 55.5 20.3H. tasmanica 10.2Scenario III 9.9 9 8.5SRT Oscillations 85.6 37.8 17.4 10.4All (I+II+III) 8.5 8.4

Sand-gra�elSRT Oscillations 65.7Scenario I 25.9A. purpuratus 10.1 7.7 6.2 5.5FMSY Multiples 0.17 0.28 0.52 0.7 1 1.5SRT Oscillations 97.6 36.4M. gelatinosus 16.3Scenario II 12.4 7 6.1

All (I+II) SRT Oscillations �100 39.6 17.2 12.5 8.6 7.3

SandSRT Oscillations Oscillations OscillationsX. cassidiformis 7.4Scenario I 5.6 4.5 4.3SRT Oscillations Oscillations Oscillations 11.2Scenario II 9.5Mulinia sp. 8.4 8SRT Oscillations Oscillations Oscillations 15.4 12.4All (I+II) 11.3 11

Whole areaSRT Oscillations �100 34.6A. purpuratus 15.7Scenario I 10.5 7.5 6.2FMSY 0.29 0.34 0.45 0.68 0.86 1.1 1.57SRT Oscillations �100 35.6M. gelatinosus 17.7Scenario II 11.7 8.3 7.1SRT Oscillations �100 15.4 9.5 9.7Scenario III 9.4H. tasmanica 9.1SRT Oscillations 50.4 20.5X. cassidiformis 11Scenario IV 8.6 6.5 5.5SRT Oscillations �100 24.4 14.9 10.9Scenario V 8.5Mulina sp. 7SRT Oscillations �100 37.5 17.4 11.8 9.4All scenarios 9.1

The flow control is determined by the parameter of vulnerability (�) of Eq. (2) (see text).

same study area. This higher value could be theresult of a bottom-up control assumption. Undermixed and top-down control mechanisms, maxi-mum fishing for each model were small (Table 2).Based on these results, we conclude that anymanagement strategy based on single species pop-ulation models may over-estimate sustainable ex-ploitation rates of the target species. Instead,scientist and managers should also consider simu-lations of multispecies models of trophic interac-tions for planning sustainable interventions andmanipulations in natural systems. The dynamicalsimulations carried out allowed to see how theeffects of depletion of the biomass of some speciesin each subsystem propagate in time and pro-duced relevant cascading effect in the remainder

populations. Even though the responses observedwere in terms of quantifiable biomass, the com-plex interactions among species in each commu-nity, however, make it unlikely to predict theexact amount of change. Therefore, under thesecircumstances a qualitative analysis, by which wecan only generalise about directions of changeand relative comparisons, seems to be recom-mended. There are, nonetheless, some sources ofmistake, which are directly related to the interpre-tation of simulations already made. Walters et al.(1997) addressed some limitations and weaknessesof ECOSIM. Firstly, the equilibrium assumptionsof ECOPATH II play a important role because thedata quality are directly related with the reliabilityof the period of time over which the simulations


Fig. 8. Equilibrium simulations of fishing mortality at maxi-mum sustainable yield (FMSY) for A. purpuratus in the wholearea under mixed control (�=0.3).

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