the effect of a crab predator (cancer porteri) on secondary producers versus ecological model...

AQUATIC CONSERVATION: MARINE AND FRESHWATER ECOSYSTEMS

Aquatic Conserv: Mar. Freshw. Ecosyst. 18: 923–929 (2008)

Published online 13 September 2007 in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/aqc.869

The effect of a crab predator (Cancer porteri) on secondaryproducers versus ecological model predictions in Tongoy

Bay (south-east Pacific coast): implications formanagement and fisheries

MARCO ORTIZ*Instituto de Investigaciones Oceanologicas, Facultad de Recursos del Mar, Universidad de Antofagasta,

Antofagasta, Chile

ABSTRACT

1. The present study compares the propagation of effects observed as a response to changes in the abundance ofa top predator (top-down cascading effect) in a benthic community within the south-east Pacific upwellingecosystem of northern Chile, with predictions derived from quantitative and qualitative multispecific models.2. Results with Loop Analysis achieved 71.4% of predictive certainty; indicating that this technique is useful

for assessment of the effects of human intervention related to the mud-bottom ecosystem tested. On the otherhand, Ecosim using bottom-up flow control mechanism achieved only 14.3% certainty. In an intermediate range,predictions obtained using the Mixed Trophic Impacts and Ecosim models using top-down, mixed and flowcontrol mechanisms estimated by the program, achieved 57.1% certainty.3. The results obtained have important implications for the management of communities and ecosystems since

human interventions can be studied using holistic models with an end result of evaluating the eventual changesthat they propagate.Copyright # 2007 John Wiley & Sons, Ltd.

Received 2 October 2006; Revised 22 March 2007; Accepted 15 April 2007

KEY WORDS: benthic community; top-down effects; Mixed Trophic Impacts; Ecosim; Loop Analysis models

INTRODUCTION

A main theme of the Fourth World Fisheries Congress in

Vancouver, Canada, May 2004 ‘Reconciling Fisheries with

Conservation’, emphasized the increasing importance in recent

years of ecosystem-based fisheries management and use of

Ecopath II (Christensen and Pauly, 1992) and Ecosim (Walters

et al., 1997) software. These models represent trophic webs

specific for each ecosystem which permit prediction of the

effects produced by the application of different harvest

scenarios in marine ecosystems (Christensen and Pauly, 2004;

Pikitch et al., 2004). Application of a holistic focus in the study

of disturbed ecosystems has become increasingly

recommended in recent years (Robinson and Frid, 2003;

Hawkins, 2004; Pikitch et al., 2004), and also for testing

*Correspondence to: M. Ortiz, Instituto de Investigaciones Oceano-logicas, Facultad de Recursos del Mar, Universidad de Antofagasta,PO Box 170, Antofagasta, Chile. E-mail: [email protected]

Copyright # 2007 John Wiley & Sons, Ltd.

hypotheses related to biodiversity-ecosystem functioning

(Hawkins, 2004). The qualitative models based on Loop

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

however, have not yet been intensively applied in fisheries

research, in spite of their usefulness in describing systems and

their high degree of certainty in predictions of responses due to

disturbance (Briand and McCauley, 1978; Lane and Blouin,

1985; Lane, 1986; Hulot et al., 2000). The possibility of

verifying predictions of changes expected in nature is

particularly difficult in coastal and large marine ecosystems.

These systems are largely open, and driven by import and

export of materials and exchange between populations via

propagule dispersal (Giller et al., 2004).

Most quantitative trophic holistic models are typically

directed towards the description of the properties and

characteristics of ecosystems by contrasting past with present

conditions (Pauly and Christensen, 1995; Jarre-Tiechmann,

1998). A different situation has occurred with the use of Loop

Analysis, which has been applied to the study and prediction of

changes in natural and artificial aquatic and terrestrial systems

(mesocosms) (Briand and McCauley, 1978; Lane and Blouin,

1985; Lane, 1986, 1998; Hulot et al., 2000) and their response to

disturbance. The present study describes seasonal changes of

biomass of different species and functional groups inhabiting a

subtidal mud system located in Tongoy Bay (northern Chile) as

a consequence of the decrease in abundance of a top predator

(Cancer porteri). Comparisons are made between predictions

obtained from quantitative trophic models constructed for the

system using Mixed Trophic Impact (Ulanowicz and Puccia,

1990) routine of Ecopath II and Ecosim, and a qualitative

model using Loop Analysis.

METHODS

Description of trophic groups (species) and model

conditions

The subtidal system (>12m depth) under study is occupied by

various species and/or functional groups of macrofauna (Jesse

and Stotz, 2002; Ortiz et al., 2003), of which the main species

variables selected for construction of the models included: the

crab species Cancer porteri, Cancer coronatus (both

unexploited) and Cancer polyodon (occasionally exploited).

One of the major observations and measurements described

for this system reported that the crab Cancer porteri decreased

significantly in biomass during the summer, migrating to

greater depths (Jesse and Stotz, 2002); crabs in lesser

abundance Hepatus chilense and Platymera gaudichaudi

(with the other crabs making up the ‘Large Epifauna’

functional group); two species of starfish Meyenaster

gelatinosus and Luidia magallanica, plus two species of

gastropod Nassarius gayi and Linucula sp. forming the

‘Small Epifauna’ functional group; and the ‘Infauna’

functional group, formed of the polychaetes and sub-

sediment bivalves. The occasionally exploited scallop

Argopecten purpuratus was also included (Figure 1).

Variations in the abundance all model variables and/or

functional groups were evaluated seasonally (Table 1).

The quantitative model was constructed using mean annual

biomass magnitudes for each of the variables (Ortiz and Wolff,

2002). In the case of the mass-balance trophodynamic model

by Ecosim, which is based on the Ecopath II steady-state

model, an increase of total seasonal mortality (50%) was

assumed (entered) for C. porteri, thus simulating a decrease in

its biomass (Jesse and Stotz, 2002). The qualitative model by

Loop Analysis (Figure 1) was constructed using the steady-

state trophic model (Ecopath II) as a baseline in which the

flows were replaced by negative effects on the prey and positive

effects for the predators. It should be noted that most of the

variables included self-enhanced dynamics for motile and

exploited organisms and self-damped for organisms with

spatial limitations.

Ecopath II modelling approach

The balance of biomass for the different species and/or

functional groups present in the mud habitat system was

determined using Ecopath II software (Figure 1), which is used

for each of the variables as a set of linear differential equations

established with the aim of balancing the flows which enter and

exit each compartment. Once the model is balanced, the Mixed

Trophic Impact (MTI) routine of Ecopath II was applied,

which allows estimation of the direct or indirect effects of the

variables of the model as a response to disturbance of a

particular species and or functional group of the system.

For each variable i in the model, Ecopath II uses a set of

linear equations in order to balance the flows in and out of

each compartment. The basic equation can be represented as:

dB�

dt¼ Pi � ðBiMiÞ � Pið1� EEiÞ � EXi ð1Þ

where � ¼ at steady state, Pi¼ the production of i (gm�2 yr�1),

Bi¼ biomass of i (gm�2), Mi¼ mortality by predation of i

(yr�1), EEi=ecotrophic efficiency of i (%), 1� EEi¼ other

mortalities of i (yr�1), EXi¼ export of i (gm�2 yr�1).

Therefore, the total production by variable i is balanced by

predation from other groups ðBiMiÞ; by non-predation losses

ðPið1� EE1ÞÞ; and losses to other systems ðEXiÞ: Predationmortality depends on the activity of the predator and it can be

expressed as the sum of consumption by all predators j preying

upon the species i, i.e.:

BiMi ¼ BjQj

BjDCji ð2Þ

M. ORTIZ924

Copyright # 2007 John Wiley & Sons, Ltd. Aquatic Conserv: Mar. Freshw. Ecosyst. 18: 923–929 (2008)

DOI: 10.1002/aqc

where Qj=Bj ¼ consumption/biomass ratio of the predator j

(yr�1), and Dji=Cji ¼ fraction of the prey i in the average diet

of predator j. The input parameter values entered and

estimated by Ecopath II software are summarized in Table 2.

Ecosim modelling approach

Subsequently, the Ecopath II (balanced model) was analysed

using Ecosim software (version 5.1), which is based on coupled

Table 1. Average seasonal biomass (gwetweightm�2) (� standard deviation) of six species of macrofauna (secondary producers) inhabiting themud benthic habitat

Species Biomass (gwwm�2) (mean� SD)

Seasons (years 1996–1997)

Winter Spring Summer Autumn

Cancer porteri 26.9� 23.1 42.9� 26.4 12.6� 29.1S 15.9� 17.2Cancer polyodon 5.8� 5.5 4.1 � 4.3 12.9� 13.5S 5.9� 6.5Cancer coronatus 4.4� 4.1 8.8 � 5.1 3.6� 1.9S 8.8� 4.5Meyenaster gelatinosus 1.0� 3.7 0.8� 2.1 2.2� 4.3NS 0.3� 0.6Luidia magallanica 0.5� 1.2 0.8� 1.7 0.1� 0.1NS 0.4� 1.1Argopecten purpuratus 0.7� 1.8 7.7� 10.4 2.4� 3.2S 4.5� 6.1

S ¼ significant changes; NS ¼ not significant.

1

2

3

4

1112

10 7

9

82

1 36

4

5

1

2

3

4

1112

10 7

9

82

1 36

4

5

1

2

3

4

1112

10 7

9

82

1 36

4

5

Prey-predator trophic matrix (%)Prey/Predator Mg Lm Cpol Cpor Cc LE Ap SE I Zoo Phy D Mg Lm Cpol Cpor Cc LE Ap SE I Zoo Phy DPrey/Predator

1 Meyenaster gelatinosus (Mg)2 Luidia magallanica (Lm)3 Cancer polyodon (Cpol)4 Cancer porteri (Cpor)5 Cancer coronatus (Cc)

12345

Note: Characteristic polynomial associated to interaction matrix, which must be multiplied by-1 due to F0 = -1

2161323372964687731678145262337932279618 +−+−+−+−+−+− λλλλλλλλλλλThe refore, F = -216 (the interaction matrix is locally stable).

79

6, 8, 10

Mud qualitative model

79

6, 8, 10

79

6, 8, 10Fn = -216

1

2

3

4

1112

10 7

9

82

1 36

4

5

1

2

3

4

1112

10 7

9

82

1 36

4

5

1

2

3

4

1112

10 7

9

82

1 36

4

5

1

2

3

4

1112

10 7

9

82

1 36

4

5

1

2

3

4

1112

10 7

9

82

1 36

4

5

1

2

3

4

1112

10 7

9

82

1 36

4

5

Mud trophic model

1

2

3

4

1112

10 7

9

82

1 36

4

5

Cancer coronatus (Cc)

8 Small Epifauna (SE) 0.56 0.15 0.20.48 0.45

0.25 0.02

1 Meyenaster gelatinosus (Mg) 0.022 Luidia magallanica (Lm) 0.013 Cancer polyodon (Cpol) 0.14 Cancer porteri (Cpor) 0.156 Large Epifauna (LE) 0.05

0.050.1

7 Argopecten purpuratus (Ap) 0.1 0.02 0.01

0.12

0.19

0.03

50.00.650.39.0)I(anuafnI951.050.0)Z(notknalpooZ1051.050.058.0)P(notknalpotyhP11

12 Detritus (D) 0.31 0.1 0.33 0.3

0.50.1

0.17 0.15 0.23 0.65 0.050.95

12345

12345

2161323372964687731678145262337932279618 +−+−+−+−+−+−

12345

2345

2345

Prey-predator interaction matrix

+ + 0 0 0 000 0 0 0

0 0 0 00 0 0 0

+

+

++

+

+

+

+ 0 0 0 +2 - 0 0 + 0 0 +

0 0 + 0 + + + 0 0 +4 0 0 0 + 0 + + 0 0 +5 0 0 - 0 + 0

00+ 0 0 +

6 Large Epifauna (LE) 0 0 - 0 0 + + 0 0 +7 Argopecten purpuratus (Ap) - 0 - 0 -

---- - - -

- - - -

- + 0 0 0 + +8 Small Epifauna (SE) - 0

0

-0

- 0 + + + + +9 Infauna (I) 0 - 0 - + + + +

10 Zooplankton (Z) 0 0 - - 0 + +11 Phytoplankton (P) 0 - - - - + 012 Detritus (D) - - - - - 0 -

2161323372964687731678145262337932279618 −+−+−+−+−+− 2161323372964687731678145262337932279618 −+−+−+−+−+−λ

79

6, 8, 10

79

6, 8, 10

79

6, 8, 10Fn = -216

79

6, 8, 10

79

6, 8, 10

79

6, 8, 10

10

1

2

3

4

56

7

8

9

11 12

6, 8, 10Fn = -216

Figure 1. Trophic (after Ortiz and Wolff, 2002) and qualitative models describing direct interactions among species and functional groups in thebenthic mud habitat within the south-east Pacific upwelling ecosystem. Diet and interaction matrices used for Ecopath II and Loop Analysis

respectively. The characteristic polynomial, pðlÞ; related to the qualitative interaction matrix and Fn value are also shown.

CASCADING EFFECTS AND MODEL PREDICTIONS 925


DOI: 10.1002/aqc

differential equations and consumption function (transference

rate):

Cij ¼aijvijBiBj

ð2vij þ aijBjÞð3Þ

where Cij ¼ consumption rates of i by variable j, Bi ¼ biomass

of prey i, Bj ¼ biomass predator j, aij ¼ represents the

instantaneous mortality rate on prey i caused by one unit of

predator j, and vij ¼ represents the transference rate between

variable i and j, it also determines if the flow control

mechanism is top-down, bottom-up or mixed, ranging from

1.0 for bottom-up, to values much greater than 1.0 for top-

down, and a value of 2.0 means a mixed control. It is

important to indicate that for simulations using the Ecosim

model the following control mechanisms were considered: (1)

bottom-up (v ¼ 1:0), (2) top-down (with v ¼ 4:0 and v ¼ 8:0),(3) mixed control (v ¼ 2:0), and (4) flow control estimated by

Ecosim. One year was the simulation time considered to assess

the instantaneous responses after an increase of 50% of total

seasonal mortality for C. porteri.

Loop Analysis modelling approach

With the qualitative model, the nodes (Figure 1) represent the

variables which are bound together by trophic relations

determined using the coefficients of the Jacobian matrix for

dynamic systems which are near or in a moving equilibrium.

The connection between variables i and j can terminate in an

arrow or circle, indicating the direct positive or negative effect,

respectively. The main fundamental of Loop Analysis is the

estimation of the local stability of the system using the balance

of feedbacks at different levels of complexity and identifying

the propagation of direct or indirect effects as a response to

disturbance entering the system through one or other of the

variables.

Loop Analysis is based on the correspondence among

differential equations near equilibrium and matrices and their

loop diagrams. Therefore, in the benthic system the element aijof the matrix and the loop diagram (Figure 1) represents the

effect of variable j on the growth variable i, when the following

equation is solved for a moving equilibrium:

dXi

dt¼ fiðX1;X2; . . . ;Xn;C1;C2; . . . ;ChÞ ð4Þ

where Xn represent the variables and Cn the parameters. The

link from Xj to Xi is similar to the aij in Levins (1968), where

aij ¼ @fiðXÞ�=@Xj (* evaluated at equilibrium), where the

function (aij) is ‘+1’ when aij>0, 0 when aij ¼ 0; and ‘�1’when aij 5 0. It is relevant to state that this equation is

applicable only to predicting effects of small perturbations in

the local vicinity of the equilibrium, where linearity of effects

can be assumed. Feedback at level k, where k is the number of

variables, is calculated by, Fk ¼Pk

m¼1 ð�1Þmþ1Lðm; kÞ and

Lðm; kÞ is the product of m disjunct loops whose combined

total length is k. Feedback has the same value as the

determinant of order k in the interaction coefficient of

the Jacobian matrix. In other words, Fk is the coefficient of

the (n�k)th term in the characteristic polynomial equation.

The feedback for each level can be also calculated by the

estimation of the characteristic polynomial, pðlÞ; related to the

interaction matrix, where the polynomial now can be written in

terms of the feedback notation as:

pðlÞ : F0ln þ F1l

n�1 þ F2ln�2 þ � � � þ Fn�1lþ Fn ¼ 0

where F0 � �1 (the feedback of the system of order 0). For

more details see Puccia and Levins (1985: 162–164). Local

stability, as a moving equilibrium, determined by the Routh–

Hurwitz criteria (Puccia and Levins, 1985), is translated into

loop terms as follows. Condition 1: Fk50, for all k, i.e. the

negative feedback at every level must exceed the positive

Table 2. Parameter values entered (in bold) and estimated (standard) by Ecopath II software for the benthic mud habitat (C ¼ catches; B ¼ biomass;P=B ¼ productivity; Q=B ¼ consumption; EE ¼ ecological efficiency, GE ¼ gross efficiency, FI ¼ food intake, NE ¼ net efficiency, R ¼ respiration;

A ¼ assimilation (after Ortiz and Wolff, 2002)

Species or functional groups C B P/B Q/B EE P/C FI NE R/A P/R R/B

Meyenaster gelatinosus } 1.08 1.2 5 0.083 0.24 5.4 0.3 1.225 0.245 4.9Luidia magallanica } 0.58 0.7 2.3 0.133 0.304 1.33 0.38 0.62 0.614 1.14Cancer polyodon 0.05 7.35 1.1 9.5 0.87 0.116 69.82 0.145 0.855 0.169 6.5Cancer porteri } 23.7 0.5 4.5 0.9 0.111 106.7 0.139 0.861 0.161 3.1Cancer coronatus } 6.35 1.8 9.5 0.939 0.189 60.33 0.237 0.763 0.31 5.8Large Epifauna } 15 1.25 9.5 0.946 0.132 142.5 0.164 0.836 0.197 6.35Argopecten purpuratus 0.01 4 2.08 9.9 0.82 0.21 39.6 0.263 0.737 0.356 5.84Small Epifauna } 21 3.7 12.5 0.985 0.296 262.5 0.37 0.63 0.587 6.3Infauna } 96 4.4 14.7 0.973 0.299 1411 0.374 0.626 0.598 7.36Zooplankton } 18 40 160 0.312 0.25 2880 0.313 0.688 0.455 88Phytoplankton } 28 250 500 0.428 0.5 14000 0.5 0.5 1 250Detritus } 1.0 } } 0.221 } } } } } }

M. ORTIZ926


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feedback. Condition 2: this condition is a sequence of

inequalities, where the general expression is the following: Fn�2

Fn�1 þ Fn�3Fn > 0 (Levins, 1998a). This expression includes

higher-order feedbacks, which means that the negative

feedbacks at higher levels must be not too strong compared

to the negative feedbacks at lower levels in order to conserve

the qualitative stability properties of the systems. It is

important to note that this expression is not a sufficient

condition for stability and therefore must be just considered as

an approximation to the second condition of stability. Fn is the

feedback of the entire system (n ¼ 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 is, the

greater the resistance to external changes will be (Levins,

1998a). Based on this local stability criterion, it is possible to

estimate the sustainability of the system and simultaneously

explore strategies of stabilization.

If the parameters [Cn in equation (4)] 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:

@Xi

@Ch¼

P @fj@Ch

Pk pðkÞij F

ðcompÞn�k

Fnð6Þ

where Ch is the hth parameter that is changing as an

environmental impact (impact entering at h); @fj=@Ch is the

effect of Ch parameter change on the state of the jth variable;

pðkÞij is the path from the jth to the ith variable and includes k

variables; FðcompÞn�k is the feedback of the complementary

subsystem. This subsystem is formed by those variables not

on the path of pðkÞij ; and Fn is the feedback of the whole system,

which integrates all variables of the system. For more details

see Puccia and Levins (1985), Levins (1998a) and Ramsey and

Veltman (2005).

The qualitative interaction matrix is based on the diet matrix

used for the Ecopath II quantitative trophic model (Figure 1).

Maple V (student edition) software was used to calculate the

characteristic polynomial, pðlÞ; (related to the interaction

matrix), Fn (feedback of the entire system) and to assess direct

and indirect effects. It is important to indicate that diet and

interaction matrices represent different ways to describe

community interactions, therefore they are not completely

equivalent.

Statistical procedures

One-way analysis of variance was used for assessment of the

seasonal variations of biomass for all species and functional

groups considered. Some logarithmic transformations of

biomass were performed to correct for heterocedasticity

(Underwood, 1997). An SNK-test was applied to detect the

differences attributable to season (Underwood, 1997).

RESULTS

During the summer of 1996 the dominant species of crab in the

mud system habitat Cancer porteri decreased significantly by

50% in biomass (ANOVA, p50.05). Other crab species such

as Cancer coronatus and Cancer polyodon, which share the

same habitat, showed significant inverse changes in their

biomass levels (ANOVA, p50.05) (Table 1). Regarding other

species studied, the two species of starfish Meyenaster

gelatinosus and Luidia magallanica showed inverse variations

in biomass, although these were not significant (ANOVA, p ¼0:43 and p ¼ 0:67 respectively). The scallop Argopecten

purpuratus also underwent a significant decline in abundance

(ANOVA, p50.05) (Ortiz et al., 2003). The infauna, another

functional group, demonstrated a notable recovery following

intense feeding activity by C. porteri and C. coronatus (Jesse

and Stotz, 2002) although robust quantitative information on

this is not available. As a further informational note, the

feeding behaviour of these crab species includes ‘sediment

mining’ where excavations of up to 20 cm in depth are made in

efforts to prey on polychaetes, gastropods and bivalves from

below and laterally, often leaving patches of several square

metres of substrate without infauna.

Comparisons of instantaneous responses (predictions)

obtained with quantitative (Table 3) and qualitative models

(Table 4) with results of direct observations in the field

(Table 1) showed the best qualitative results with the Loop

Analysis with certainty of effectiveness reaching 71.4% (with a

negative holistic feedback, Fn ¼ �216; see Figure 1). Ecosim

using bottom-up flow control achieved only 14.3% certainty

(Table 4). In an intermediate range, predictions obtained using

the Mixed Trophic Impact and Ecosim models, with the other

flow control mechanisms, achieved 57.1% certainty (Table 4).

These results are relevant since they show the importance of

applying multispecific qualitative and quantitative modelling

strategies for predicting the changes in the populations as a

consequence of natural disturbance.

DISCUSSION

It has recently been postulated that a superposition occurs

between the niches of C. porteri and C. polyodon (competition)

(Jesse and Stotz, 2002), which could in part explain the

negative relation in the abundance observed between them.

The increase of M. gelatinosus in mud habitat could also be

explained by a certain degree of interference with the species of



DOI: 10.1002/aqc

dominant crabs. Certainly the decrease of C. porteri during

summer, which could be a response to a rise in water

temperature (Arnzt and Fahrbach, 1986) and/or a decrease

in the density of its infaunal prey (Jesse and Stotz, 2002),

would allow for the expansion of the distributional limits of

other predators such as C. polyodon and M. gelatinosus (Jesse

and Stotz, 2002). These predators in turn dominate in other

system habitats (seagrass and sand-cobble-gravel) near the

mud habitat system (Jesse and Stotz, 2002; Ortiz et al., 2003).

The Loop Analysis theory emerges as the more manageable

and less complicated in its application since it does not need

the volumes of quantitative information required by the

Ecopath II and Ecosim models. Although it is not possible

to estimate quantitative changes using Loop Analysis, nor

evaluate scenarios with different levels of harvest, it is a very

useful tool for answering questions such as ‘What if?’ in

relation to the propagation of effects having sufficient

certainty. Loop Analysis models have shown up to 100%

certainty in other natural systems (Briand and McCauley,

1978; Lane, 1986; Hulot et al., 2000) and thus the 71.4% of

prediction certainty achieved in the present study can be

explained by at least the following two situations: (1) if the

system studied is largely open, and (2) other types of ecological

interactions such as competition, mutualism and

commensalism were not included in the qualitative model,

which not only promotes realism but also can increase the

certainty of the predictions. In the present study, other types of

interaction were not included in the qualitative model owing to

the lack of robust biological knowledge.

The results obtained have important implications for the

management of ecosystems since human interventions can be

studied using holistic models with an end result of evaluating

the eventual changes which they propagate. In the present

contribution the loop model showed the best outcomes

(between observed and predicted biomass changes) compared

to the quantitative version, it is relevant since qualitative

Table 3. Biomass changes (initial and final) after simulation using Ecosim model based on different flow control mechanisms (n). QR ¼ qualitativeresponses

Species/groups Bottom-up control(n ¼ 1:0)

Top-down control(n ¼ 4:0)

Top-down control(n ¼ 8:0)

v estimated by Ecosim Mixed flow control(n ¼ 2:0)

Bi Bf QR Bi Bf QR Bi Bf QR Bi Bf QR Bi Bf QR

Cancer porteri 22 640 21 590 � 22 630 21 360 � 22 628 21 343 � 22 628 21 350 � 22 602 21 370 �Cancer polyodon 7 350 7 350 0 7 350 7 360 + 7350 7 360 + 7350 7 360 + 7350 7 359 +Cancer coronatus 6 350 6 350 0 6 350 6 370 + 6350 6 370 + 6350 6 370 + 6351 6 367 +Meyenastergelatinosus

1 080 1 080 0 1 080 1 083 + 1080 1 083 + 1080 1 083 + 1080 1 082 +

Luidia magallanica 580 580 0 580 581 + 580 581 + 580 581 + 580 581 +Argopectenpurpuratus

4 000 4 000 0 4 000 4 002 + 4000 4 003 + 4000 4 002 + 4000 4 001 +

Infauna 96 000 95 990 � 96 153 96 911 + 96 177 97 007 + 96 147 96 660 + 96 108 96 677 +

Table 4. Observed and predicted changes of abundance using Mixed Trophic Impacts, Ecosim (with different flow trophic control), and LoopAnalysis

Changes Cpor Cpol Cc Mg Lm Ap Inf Match %

Observed changes � + � + � � +PredictionsQuantitative trophic modelsMixed Trophic Impacts (Ecopath II) + + + + + � + 4/7 57.1Ecosim (bottom-up flow control) � 0 0 0 0 0 � 1/7 14.3Ecosim (top-down flow control; n ¼ 4:0) � + + + + + + 4/7 57.1Ecosim (top-down flow control; n ¼ 8:0) � + + + + + + 4/7 57.1Ecosim (flow control estimated by Ecosim) � + + + + + + 4/7 57.1Ecosim (mixed flow control; n ¼ 2:0) � + + + + + + 4/7 57.1

Qualitative modelLoop Analysis � + 0 + + � + 5/7 71.4

Cpor ¼Cancer porteri, Cpol ¼Cancer polyodon, Cc ¼Cancer coronatus, Mg ¼Meyenaster gelatinosus, Lm ¼Luidia magallanica, Ap ¼Argopectenpurpuratus, Inf ¼ infauna:

M. ORTIZ928


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models emerge as an alternative and/or complement to

numerical abstractions, allowing the inclusion of variables

that are not readily measurable and that differ in physical

form. Likewise, the loop models are inexpensive, which makes

them available to non-scientists (Levins, 1998a).

As far as the flow control mechanism which should be used

in Ecosim models, the results obtained show that bottom-up

would not describe with high certainty the propagation of

effects into the systems. Top-down, mixed and flow control

mechanisms estimated by Ecosim showed similar nominal

predictions (Table 4). Based on these results, Ecosim

simulations should be developed considering at least a mixed

flow control, since the prey and predator species are in co-

evolution and any separation between them is nothing more

than a false dichotomy in ecology, which distorts our capacity

for understanding (Levins, 1998b).

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DOI: 10.1002/aqc

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