REVIEW

Mass-balanced trophic and loop models of complex benthicsystems in northern Chile (SE Pacific) to improvesustainable interventions: a comparative analysis

Marco Ortiz Æ Matthias Wolff

Received: 23 May 2007 / Revised: 5 December 2007 / Accepted: 26 February 2008 / Published online: 15 March 2008

� Springer Science+Business Media B.V. 2008

Abstract The capacity to withstand perturbations and

the propagation of direct and indirect effects of

harvesting were explored in seagrass and sand–gravel

subtidal subsystems of northern Chile using Ecopath II,

Ecosim and Loop Analysis theoretical frameworks. The

relative Ascendancy and Redundancy from Ecopath II

and Ecosim models and the holistic stability measure

(Fn) given by Loop Analysis, all suggest that the sand–

gravel subsystem is the more resistant and its fishery

more sustainable. This outcome is relevant since the

theoretical frameworks used are based on different

assumptions but arrive at similar conclusions. If the

fishery is included in the qualitative ecological models,

which were found locally stable only when the fishery is

self-controlled. While this conclusion is not new, its

relevance here is that it emerges from qualitative

multispecies modelling (Loop Analysis). Based on our

model predictions, the biomass removal of the sea star

Meyenaster gelatinosus would increase the standing

stock of the commercial scallop Argopecten purpuratus

only in the seagrass habitat, whereas the same man-

made intervention may have an opposite effect in the

sand–gravel habitat. We recommend to enunciate

holistic models based on the theoretical framework

used in the current work, which explore the reality from

different perspectives assuming different givens. Based

on these holistic explorations alternative and comple-

mentary management scenarios could be designed.

Keywords Ecopath � Ecosim �Mixed Trophic Impacts � Loop Analysis �Multispecies management � Northern Chile

Introduction

Since population models have not been sufficiently

successful in predicting the consequences of man-made

interventions in ecological systems (e.g. fisheries, pest

management, diseases and immunisation practices)

there is a need to consider the use of alternative

multispecies ‘‘holistic’’ modelling approaches (Larkin,

1977; Levins & Vandermeer, 1990; Levins, 1994,

1998b; Hilborn et al., 1995; Patten, 1997; Roberts,

1997; Levins & Lopez, 1999; Walters et al., 1999;

Robinson & Frid, 2003; Hawkins, 2004; Pikitch et al.,

2004; Arias-Gonzalez et al., 2004). At least two differ-

ent theoretical frameworks have been widely applied to

analyse and understand the underlying processes in

Handling editor: T. P. Crowe

M. Ortiz (&)

Instituto de Investigaciones Oceanologicas, Facultad de

Recursos del Mar, Universidad de Antofagasta,

PO Box 170, Antofagasta, Chile

e-mail: mortiz@uantof.cl

URL: www.uantof.cl/recursos_mar/mortiz/mortiz.htm

M. Wolff

Charles Darwin Research Station, Puerto Ayora,

Santa Cruz, Galapagos, Ecuador

e-mail: matthias.wolff@fcdarwin.org.ec

123

Hydrobiologia (2008) 605:1–10

DOI 10.1007/s10750-008-9362-8

complex natural aquatic systems. The Ecopath II

modelling approach considers the flows of energy or

matter between interconnected parts (variables, popula-

tions, functional groups) while Loop Analysis grasps the

qualitative nature of the interactions. The steady-state

Ecopath II (Christensen & Pauly, 1992) modelling

software is a useful tool by which the population

dynamics of the species or functional groups, their food

spectrum, trophic relationships, spatial distribution and

fisheries activities are simultaneously considered. The

potential role of mass-balance models for the manage-

ment of different aquatic systems has been previously

discussed (Christensen & Pauly, 1998; Jarre-Teich-

mann, 1998; Pauly et al., 2000; Christensen & Walters,

2004). Furthermore based on the density and diversity of

flows, systems can be characterised following ecological

theory of Ulanowicz (1986, 1997), and the propagation

of direct and indirect effects can be evaluated by the

Mixed Trophic Impacts (Ulanowicz & Puccia, 1990), a

routine of Ecopath II and also by Ecosim (Walters et al.,

1997). The other theoretical framework, termed Loop

Analysis (Levins, 1974, 1998a; Puccia & Levins, 1985),

is a useful qualitative technique to estimate the local

stability (sustainability) of the systems and to assess the

propagation of direct and indirect effects as response to

external perturbations (Ramsey & Veltman, 2005). This

approach has been applied widely in different fields of

the natural sciences (Li & Moyle, 1981; Giavelli &

Bodini, 1990; Levins & Vandermeer, 1990; Whitlatch &

Osman, 1994; Lane, 1998; Ortiz & Wolff, 2002c, 2004;

Ortiz, 2003; Ortiz & Stotz, 2007; Ortiz, 2007) and has

shown a high degree of predictability (after perturbation)

of natural phenomena (Briand & McCauley, 1978; Lane

& Bloiun, 1985; Lane & Collins, 1985; Lane, 1986;

Hulot et al., 2000; Ortiz, 2007).

Due to the difficulty in carrying out replicated

experiments to estimate the sustainability and the

propagation of direct and indirect effects of fishing

activities on the community or ecosystem level

(Lewontin & Levins, 1998; Maron et al., 2001), the

current study is the first attempt to compare quanti-

tative and qualitative small-scale models of benthic

subsystems along the Chilean coast and to recom-

mend adaptive human interventions. Based on these

models we characterise the food webs according to

Ulanowicz’s and Levins’s theoretical frameworks to:

(1) estimate the resistance of each subsystem to

external perturbations, and (2) assess the propagation

of higher-order effects within the subsystems.

Materials and methods

Description of the habitats

The models constructed represent the benthic subsys-

tem located at the southern extreme of Tongoy Bay

(30�150S–71�310W) (Northern Chile) (Fig. 1). Within

this benthic area, named management area of Puerto

Aldea, the seagrass and sand–gravel habitats concen-

trate the highest subsystem production (Ortiz & Wolff,

2002a) and support an intensive harvest of the red algae

Chondrocanthus chamissoi (ca. 114 t yr-1), the scal-

lop Argopecten purpuratus (ca. 16 t yr-1) and the crab

Cancer polyodon (ca. 0.4 t yr-1). Tongoy Bay is an

important upwelling centre (Daneri et al., 2000; Mon-

tecinos & Quiroz, 2000), which supplies nutrients to

the ecosystem and prevents the establishment of a

stable thermocline during summer through an inflow of

upwelling water into the bay. Surface water temper-

ature reaches 13�C as minimum in winter and 17�C as

maximum during summer (Jesse & Stotz, 2002).

The models were constructed to grasp the trophic

relationships for the most relevant species (commer-

cial resources) inhabiting the benthic communities.

Flows derived from epiphytes, microphytobenthos

and bacteria; and those leading to fishes, seals and

birds were not considered due to insufficient scientific

information. We are aware that realism is thus

reduced by our model configuration, but think that

the most relevant interdependencies and flows are

reflected. Since the configuration of all models

followed the same principle, this systematic error

should still allow for a comparative analysis.

Ecopath II, steady-state approach

It represents a steady-state modelling approach in

which the production of the system compartments is

balanced by consumption and exports (Fig. 2a, b).

The model uses a set of linear equations (one for each

species i or group of species). The basic mathematical

function can be expressed as:

dB�idt¼ Pi � ðBi �M2iÞ � Pi � ð1� EEiÞ � EXi; ð1Þ

where *, at steady state (=0); Bi, the biomass of i

(g m-2); Pi, the production of i (g m-2 yr-1); M2i,

mortality by predation of i (yr-1); EEi, the ecotrophic

efficiency of i (%); 1 - EEi, other mortalities of i

2 Hydrobiologia (2008) 605:1–10

123

(yr-1); EXi, the export of i (g m-2 yr-1). The

immigration and emigration are considered zero.

Furthermore, the direct and indirect impacts of

different management strategies on the communities

were evaluated by the Mixed Trophic Impact (MTI)

(Ulanowicz & Puccia, 1990) routine of Ecopath II

(Christensen & Pauly, 1992). For more details about

the benthic models see Ortiz & Wolff (2002a).

Ecosim, dynamic mass-balance approach

It describes a dynamic extension of the above

approach based on the initial conditions estimated

by Ecopath II. The mathematical ground of Ecosim

models consists of the biomass dynamics described in

the form of coupled differential functions as Eq. 1.

Additionally it uses the following function:

Cij ¼aij � vij � Bi � Bj

ð2vij þ aij � BjÞ; ð2Þ

where Cij is the consumption rates of j by compart-

ment i, aij represents the instantaneous mortality rate

on prey i caused by one unit of predator j biomass.

Also aij can be interpreted as the rate of effective

search by predator j for prey i. Each aij could be

estimated directly from the corresponding Ecopath II

models by: aij ¼ Qi=Bi � Bj (Qi, total consumption of

i). The vij represents the transfer rate between

TongoyBay

GuanaquerosBay

Coquimbo

BayPacificOcean

Study area

COQUIMBO

N

30° S

71° 20` W

5 km

500 m

Seagrass Sand-gravel Sand Mud

Pto.Aldea

CHILE

Upwelling

1

2

3

ab

c

Fig. 1 (a) Main littoral

types along the Chilean

coast: 1, dominated by

exposed compact rocky

shores; 2, dominated by

exposed sandy shores and 3,

mostly insular systems. (b)

The principal bay systems

of the IV Region of

Coquimbo (Chile). (c)

Study area of Puerto Aldea

located at southern of

Tongoy Bay

Hydrobiologia (2008) 605:1–10 3

123

Phytoplankton

B=28.0P/B=250.0

Ch.chamissoi

B=5.5 P/B=6.0

Rodophyta

B=6.0P/B=5.5

Ulva sp.

B=5.0P/B=6.0

H.tasmanica

B=450.0P/B=1.5

Detritus

Zooplankton

B=18.0P/B=40.0

A.purpuratus

B=90.0P/B=2.08

Taliepussp.B=1.3P/B=1.5

Infauna

B=65.0P/B=4.4

SmallEpifauna

B=29.5P/B=3.7

L.magallanica

B=0.6 P/B=0.7

P.barbiger

B=1.6P/B=1.95

M.gelatinosus

B=20.5P/B=1.2

H.helianthus

B=0.5P/B=0.6

C.polyodon

B=10.0P/B=1.1

LargeEpifauna

B=2.2 P/B=1.25

1

2

3

4

Seagrass habitat model

Q = 95.0

Q=20.9

Q=1.1

Q=102.5

Q=1.8

Q=12.35

Q=15.84

Q=368.75

Q=2880.0

Q=955.5

Q=891.0

Catches=0.01

Catches=7.5

Catches=0.15

**

Phytoplankton

B=36.0P/B=256.0

Ch.chamissoi

B=564.8P/B=6.0

Rodophyta

B=230.0P/B=5.5

Ulva sp.

B=70.0P/B=6.0

Detritus

Zooplankton

B=19.0 P/B=40.0

A.purpuratus

B=71.54P/B=2.08

C.trochiformis

B=90.0P/B=0.8

Tegula sp.

B=150.0P/B=2.2

Taliepus sp.

B=1.7P/B=1.5

Infauna

B=60.0P/B=4.4

P.chilensisB=70.0P/B=3.2

Small Epifauna

B=20.0P/B=3.7

L.magallanicaB=2.98P/B=0.7

P.barbiger

B=29.28 P/B=1.95

M.gelatinosus

B=46.76P/B=1.2

H.helianthus

B=0.43 P/B=0.6

C.polyodon

B=25.6P/B=1.1

LargeEpifauna

B=6.54 P/B=1.25

1

2

3

4Sand-gravel habitat model

Q=8.94

31.26=Q2.342=Q

Q=289.87

Q=250.0

Q=770.0

Q=882.0

Q=3040.00.5841=Q52.807=Q

Q=16.1

Q=891.0

Catches=0.15

Catches=7.5

Catches=113.9

M. gelatinosusH. helianthus

Q=233.8

Q=0.99

Small Epifauna

**

a

b

4 Hydrobiologia (2008) 605:1–10

123

compartment i and j. This parameter determines if the

control is top-down, mixed or bottom-up (Walters

et al., 1997). In the current study a mixed flow

control mechanism was used. For more details of the

models see Ortiz & Wolff (2002b).

Loop Analysis, qualitative approach

The loop models show the relationships as sign,

indicating the type of influence each variable has

upon another, that is, positive, negative or zero

(Fig. 3a, b). For instance, in ecological relationships,

(+,-) denotes a predator–prey or parasite–host

interaction, (-,-) represents competition between

two species, while (+,+), (+,0) and (-,0) represent

mutualism, commensalisms and amensalism, respec-

tively. Each variable is represented by a large circle

and edges representing direction and type of inter-

actions, i.e. if at one extreme there is an arrow, it

means positive effect, a circle means negative and

nothing means null effect. Loop Analysis is based

on the correspondence between differential equa-

tions near equilibrium and matrixes and their loop

diagrams. Therefore, in the benthic system the

element aij of the matrix and the loop diagram

represent the effect of variable j on the growth

variable i when the equation:

dXi

dt¼ fi � X1;X2; . . .;Xn; C1;C2; . . .;Cnð Þ; ð3Þ

where the change in time of the variable Xi is a

function fi of other interconnected variables Xn and

parameters Cn, is solved at equilibrium. The link from

Xj to Xi is similar to the aij in Levins (1968) as

follows:

aij ¼ofiðXÞx�

oXj; ð4Þ

where X* evaluated at equilibrium. The element of

the graph representing the link from j to i is sign (aij),

(positive, negative or zero) where the function sign

(X) is 1 when X [ 0, 0 when X = 0 and -1 when

X \ 0.

Local stability, as determined by the Routh–

Hurwitz criteria, translates into loop terms as Con-

dition 1, when Fk \ 0, for all k, i.e. Fk corresponds to

the negative feedback at every level which must

exceed the positive feedback. Condition 2: negative

feedback at higher levels cannot be too large

compared to a negative feedback at lower levels to

conserve the qualitative stability properties of the

systems. An approximation for this condition is a

sequence of inequalities, where the general expres-

sion is the following: Fn-2 Fn-1 + Fn-3 Fn [ 0. The

feedback for each level can be also calculated by the

estimation of the characteristic polynomial related to

the Jacobean interaction matrix, where the polyno-

mial now can be written in terms of the feedback

notation as: F0kn þ F1k

n�1 þ F2kn�2 � � � þ Fn�1kþ

Fn ¼ 0 where F0 : -1 and the Fn is the feedback of

the entire system (n = total number of variables in

the system). It is assumed that the system is locally

stable when Fn is negative. The stronger the negative

feedback Fn becomes, the greater will be the

resistance to external change (Levins, 1998a). Based

on this local stability criterion it is possible to

estimate the degree of resistance to perturbations (as

a measure of sustainability) of the system and

simultaneously explore strategies for its increase.

If the parameters [Cn in Eq. 3] of the system are

changing slow enough for the variables to track the

movement of the equilibrium, then the equilibrium

values of the variables, which are changing in

magnitude, and the direction of that change can be

evaluated as follows:

oXi

oCh¼

P ofjoCh�P

k

pðkÞij � F

ðcompÞn�k

Fn; ð5Þ

where Ch is the hth parameter that is changing as an

environmental impact (impact entering at h), ofj=oCh

is the effect of Ch parameter change on the state of

the jth variable, pij(k) is the path from the jth to the ith

b Fig. 2 Quantitative trophic models for the seagrass (a) and

sand–gravel (b) complex benthic systems. Vertical position of

each box approximates trophic level. The box size is in

proportion to the square root of the population or compartment

biomass. Biomass (g wet weight m-2), productivity (P/B)

(yr-1) and consumption (Q) (g wet weight m-2 yr-1) are

given (after Ortiz & Wolff, 2002a). (Note: For seagrass model

** means detritus is consumed by M. gelatinosus, H.helianthus, L. magallanica, C. polyodon, P. barbiger, Large

Epifauna, A. purpuratus, Small Epifauna, Infauna and Zoo-

plankton. For sand–gravel model ** means detritus is

consumed by M. gelatinosus, H. helianthus, L. magallanica,

C. polyodon, P. barbiger, Large Epifauna, A. purpuratus, C.trochiformis, Tegula sp., P. chilensis, Small Epifauna, Infauna

and Zooplankton)

Hydrobiologia (2008) 605:1–10 5

123

variable and includes k variables, Fn-k(comp) is the

feedback of the complementary subsystem. This

subsystem is formed by those variables not on the

path of pij(k); and Fn is the feedback of the whole

system, which integrates all variables of the system

(Puccia & Levins, 1985; Levins, 1998a). For details

about the model see Ortiz & Wolff (2002c). Recent

extensions of the theoretical aspects of Loop Analysis

are given by Jorgensen et al. (2000) and Dambacher

et al. (2002, 2003).

Results

Table 1 contains the resistance and/or sustainability

estimations for quantitative and qualitative ecological

subsystem models. Based on the results obtained by

Ecopath II and Loop Analysis the sand–gravel habitat

seems to be the most resistant or sustainable subsys-

tem. It is important to note that similar tendencies are

shown by Ulanowicz’s and Levins’s indices.

Although the trophic and loop models did not have

exactly the same configuration (see Figs. 2, 3), we

believe that they represent the principal variables and

ecological interactions underlying each subsystem.

The propagated direct and indirect effects as

response to a negative perturbation on the sea star

Meyenaster gelatinosus are shown in Table 2. This

species is considered by fishermen ‘‘undesirable’’

because it preys upon the commercial scallop Argo-

pecten purpuratus (Fig. 1). A similar response, using

the Mixed Trophic Impacts, Ecosim and Loop

Analysis approaches, is predicted for just seven

variables. In the seagrass model an increase in the

standing stock of the scallop A. purpuratus is

predicted at a reduction of the starfish M. gelatinosus.

However, its removal from the sand–gravel habitat,

Fig. 3 Qualitative ecological models for the seagrass (a) and

sand–gravel (b) complex benthic systems. Holistic sustainabil-

ity measures (Fn and 2� criterion) under two fishermen self-

dynamics. The capital letters correspond to management

scenarios, A, increasing the standing stock of juvenile scallops

(ApJ); B, increasing standing stock of recruits (ApR); C, D and

E, partial removal of the starfish predators L. magallanica(Lm), H. helianthus (Hh) and M. gelatinosus (Mg), respec-

tively; F, increase the available substrate (artificial) for

increasing algae settlement and h, harvest. The soft lines

indicate postulated relationships based on limited data (after

Ortiz & Wolff, 2002c)

b

F16

LE 14

Mg13

Hh12

Lm11

Ht10

SE9

CpA8

CpJ 7

I6

MF5

PP 4

ApR3

ApJ2

ApA1

Seagrass habitatEco-social model

Pb15

variables 14 and 15

h

h

AB

C

D

E

F16

F16

Fn = - 12.0; 2° criterion > 0

Fn = + 42.0; 2° criterion < 0

F21

LE 14

Mg20

Hh19

Lm18

SE13

CpA8

CpJ 7

I12

MF15

PP 4

ApR3

ApJ2

ApA1

Sand-Gravel habitatEco-social model

Pb17

S5 Ct

6

Pch9

OM10

ChCh 11

T sp16

A

h h

h

B C,D,E,F

variables:8,13,14,16,17,18,19,20

F21

F21

Fn = - 24.0; 2° criterion > 0 Fn = + 168.0; 2° criterion > 0

a

b

6 Hydrobiologia (2008) 605:1–10

123

yielded different responses by the different models

applied: while Mixed Trophic Impact (Ecopath II)

and Ecosim predicted a positive effect on the scallop,

the effect was negative when Loop Analysis was

used. Another effect of the removal of the sea star,

predicted by the two models, would be an increase in

the predatory crabs Cancer polyodon and Paraxan-

thus barbiger in the seagrass and sand–gravel

habitats, respectively. The molluscs Calyptraea

trochiformis and Tegula sp. would be positively

affected in the sand–gravel habitat.

Discussion

The coincidence between the measures ‘‘relative

Ascendency’’ (Ascendency/Capacity) and Redun-

dancy given by Ulanowicz (1986, 1997) and the

holistic stability measure (Fn) given by Levins

(1998a) shows that these indices may be consistent

as key measures of sustainability for natural systems.

This convergence appears quite relevant considering

that the models used here did not include connections

to other ecosystem compartments. Additionally,

through Loop Analysis we could extend the natural

ecological systems by integrating the activities of the

Table 2 Qualitative predictions for each variable (species and

group of species) in the seagrass and sand–gravel ecological

systems based on Mixed Trophic Impacts (routine of Ecopath

II), Ecosim (using mixed flow control mechanism) and Loop

Analysis, as response to the negative impact on the predatory

sea star M. gelatinosus

Ecological benthic system /model

Mg Hh Lm Cp Pb LE Ap Ct Te sp. Pch SE I Ht Chch R Ul sp. PP D FSeagrassMixed Trophic Impacts (Ecopath II) + + + + +– + + 0ECOSIM (with mixed flow control) –

– ––––

+ 0 + + + + + 0 0Loop Analysis 0 – – + – + +Sand-gravelMixed Trophic Impacts (Ecopath II) + + + + + + + + + + 0 0 0 0ECOSIM (with mixed flow control) + 0 + + + + + + 0 0 0 0 0 0 0 0 +Loop Analysis + + + + + + +

Species/groupsQualitative predictions

0

++

0 +0

0

–– –

–

– –––

–

–

– –

– –

–

The dark areas indicate similar expected responses. Mg, Hh and Lm represent the sea star species Meyenaster gelatinosus, Heliasterhelianthus and Luidia magallanica, respectively; Cp and Pb are the crabs Cancer polyodon and Paraxanthus barbiger, respectively;

LE includes the remainder crabs species such as Guadichaudia gaudichaudia, Hepatus chilense and Platymera gaudichaudia; Ap is

the scallop A. purpuratus; Ct represents the mollusc Calyptraea trochiformis; Te sp is the snail Tegula sp.; Pch represents the sea

squirts Pyura chilensis; SE includes small gastropods such as Nassarius sp., Nucula sp., Turritella sp., Mitrella sp. and the

polyplacophora Chiton sp.; I is the infauna which comprises polychaetes and other buried bivalves; Ht is the seagrass Heterozostera

tasmanica; Chch represents the rhodophyta Chondrocanthus chamissoi; R includes other rhodophyta; Ul sp. represents Ulva sp.; PP is

primary productivity (phytoplankton); D represents detritus and F is the fishermen (after Ortiz & Wolff, 2002a, c)

Table 1 Summary of holistic measures related to resistance to

perturbations or local stability (two criteria) for each benthic

system

Indices Seagrass Sand-gravel

Ecological benthic system

Ulanowicz (1986, 1997)

Ascendency A/C (%) 31.1 30.4

Redundancy (%) 51 53.8

Levins (1974, 1998b)

Loop Analysis Fn \ 0 -1 -96

Second criteria [ 0 No No

Extended systems

Fn \ 0

(a) -12 -24

(b) 42 168

Second criteria [ 0

(a) Yes Yes

(b) No No

The relative Ascendency (%) (A/C) and Redundancy (%) sensu

Ulanowicz (1986, 1997) and the holistic measures of

sustainability based on two criteria of local stability (sensu

Levins, 1974, 1998b) for ecological and extended (including

Fisherman as variable) model systems are also shown; (a) and

(b) represent the fishermen with a self-damped and self-

enhanced dynamic in extended model, respectively. Values in

bold indicate the most resistant or sustainable system

Hydrobiologia (2008) 605:1–10 7

123

fishermen into the models. Under this condition the

extended sand–gravel system is the most sustainable

one, but local stability is only reached if the fishery is

self-controlled, that is, if fishing effort and/or catch

quota are constrained. While non-linear quantitative

theoretical studies on the fishery effects on multispe-

cies systems have arrived at similar conclusions (May

et al., 1979; Beddington & May, 1980; Beddington &

Cooke, 1982; Azar et al., 1995), the relevant point

here is that the need for a regulation of fishing effort

and catch quota also emerged from a qualitative

multispecies modelling approach.

The positive responses of the competitor and prey

species (cascading effects) can be interpreted as

compensatory mechanisms, which may negatively

impact the stability of the modelled system. Com-

munities and ecosystems are subjected to several

types of natural perturbations, which may eventually

impact on the stability of the entire system, driving it

to some other moving equilibrium (Levins, 1998c).

Thus, if our objective is not only to increase the

standing stock of the commercial species studied

here, but also to conserve the natural systems, which

they inhabit, this response must be avoided. One way

may be trough fishing the crab C. polyodon and the

mollusc C. trochiformis as well (both are of com-

mercial importance). However, to establish a

definitive additional harvest it would be necessary

to monitor the trajectory of both systems under the

condition of a removal of the sea star. According to

the Ecopath II results, a removal of ca. 50% of

biomass of the sea star M. gelatinosus would possibly

be without changes in the system’s holistic properties

(i.e. Ecological Efficiency, Gross Efficiency and

Respiration/Biomass rate).

The models applied here confirm the need to

consider multispecies inter-relationships should be

considered if our interest is to advise a sustainable

fishery. External system perturbations like harvesting

can produce unexpected system responses, such as

the replacement of a predator or competitor, or

changes in the dominance of prey populations in

absence of predators, all responses widely reported

for perturbed systems. Even though other man-made

interventions, such as the simultaneous removal of

‘‘undesirable’’ predator species, may theoretically be

sustainable in population models, these abstractions

offer us only a proximate response without the

integration of ultimate and long-term effects. The

quantitative and qualitative theoretical frameworks

here presented, captured just a part of the different

types of interspecific relationships, which enabled us

to explore and answer with high robustness ecolog-

ical questions. We thus conclude that the above

modelling approaches should be used in other

ecological systems, especially, if our aim is to assess

the sustainability of different management options for

multispecies fisheries (Hilborn et al., 1995; Walters

& Korman, 1999; Walters et al., 1999).

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