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Ecological Modelling 221 (2010) 2918–2926
Contents lists available at ScienceDirect
Ecological Modelling
journal homepage: www.elsevier.com/locate/ecolmodel
Topological analysis of the ecological importance of elasmobranch fishes: A food
web study on the Gulf of Tortugas, Colombia
Andrés F. Navia a,b,c , Enric Cortés d,∗ , Paola A. Mejía-Falla a,b
a
Fundación Colombiana para la Investigación y Conservación de Tiburones y Rayas, SQUALUS, Carrera 79 No 6-37, Cali, Colombia
Grupo de Investigación en Ecología Animal, Departamento de Biología, Universidad del Valle. A.A. 25360, Cali, Colombia
c
Programa de Doctorado en Ciencias Marinas, Centro Interdisciplinario de Ciencias Marinas, A.P. 592, La Paz, B.C.S. Mexico
d
National Oceanographic and Atmospheric Administration, National Marine Fisheries Service, Panama City, FL 32408, USA
b
a r t i c l e
i n f o
Article history:
Received 17 March 2010
Received in revised form 31 August 2010
Accepted 7 September 2010
Available online 1 October 2010
Keywords:
Sharks
Skates
Rays
Food webs
Key species
Mesopredators
a b s t r a c t
We built a trophic network based on a matrix of interspecific trophic relationships to assess the role of
elasmobranch fishes in shaping community structure of the Gulf of Tortugas in the Colombian Pacific
Ocean. We analyzed diet similarities to define trophic components (nodes) – rather than taxonomical
groups – in the network. We evaluated the ecological function of species or trophic entities through
topological analysis of their structural importance in trophic networks by applying one local and several
mesoscale network indices. We found that top predatory elasmobranchs play an important ecological
role in top-down control and in propagating indirect effects through the system owing to high values of
the node degree, centrality and topological importance indices. However, invertebrates and teleost fishes
had higher connectivity and topological importance than other elasmobranchs in the network before and
after removal of top predators from the system. Results from our study thus suggest that elasmobranchs
at intermediate trophic levels – commonly referred to as “mesopredators” – are not so important in all
complex coastal ecosystems as previously reported.
Published by Elsevier B.V.
1. Introduction
A central theme in the study of trophic networks is how
interspecific relationships affect ecosystem dynamics and stability (Pimm, 2002; De Ruiter et al., 2005). The importance of these
interactions has given rise to the development of concepts such as
multispecies management (May et al., 1979; Yodzis, 2000) or system perspective (Grant et al., 1997), which recognize the need to
understand the interactions of not only one species, but of most or
all species to model more accurate responses to the dynamics of
each system under study (Jordán et al., 2006).
Despite the supposed importance of elasmobranchs in marine
trophic network interactions (Stevens et al., 2000; Wetherbee and
Cortés, 2004), there are very few studies that have assessed the
effect of elasmobranch predation on populations of their prey
(direct effects), with a few exceptions that have examined interactions with marine mammals. For example, Lucas and Stobo (2000)
and Bowen et al. (2003) suggested that sharks played an important
role in the decline of sea lions in Sable Island, and McCosker (1985)
proposed a top-down effect of sharks on pinnipeds. García-Gómez
(2000) suggested that top shark species are important density reg-
∗ Corresponding author. Tel.: +1 850 2346541x220; fax: +1 850 2353559.
E-mail address: [email protected] (E. Cortés).
0304-3800/$ – see front matter. Published by Elsevier B.V.
doi:10.1016/j.ecolmodel.2010.09.006
ulators because when their biomass decreases that of some of their
prey increases significantly.
It has been proposed that ray predation can have a strong impact
on benthic prey (Thrush et al., 1994; Myers et al., 2007), to the
extent of creating population sinks in specific locations (Peterson
et al., 2001). Behaviorally mediated indirect interactions between
elasmobranch fishes and their prey have also been suggested as
mechanisms to understand community dynamics, whereby the
presence or absence of elasmobranch predators condition the
behavior and habitat use of their prey (“risk effect”; Heithaus and
Dill, 2002; Dill et al., 2003; Heithaus et al., 2008).
Some approaches to understanding the ecological role of
elasmobranch fishes, especially sharks, have used mass-balance
ecosystem models (e.g., Ecopath with Ecosim (Walters et al., 1997)),
based on assessment of direct density-dependent effects, and have
produced contrasting results. Manickchand-Heileman et al. (1988)
concluded that although sharks occupy the highest trophic levels in
the Gulf of Mexico, the effect of an increase in their population size
on the rest of the community is small. Kitchell et al. (2002) found
that oceanic sharks are not key species in the north central Pacific
Ocean, and Carlson (2007) also found that a population reduction
of sharks in Apalachicola Bay in the Gulf of Mexico did not result
in strong top-down effects such as trophic cascades. In contrast,
Stevens et al. (2000), García-Gómez (2000), and Fernández et al.
(2001) found that changes in abundance of different shark species
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A.F. Navia et al. / Ecological Modelling 221 (2010) 2918–2926
2919
resulted in changes of different magnitude and wide spectrum in
their respective communities.
Stevens et al. (2000) proposed that the strongest responses to
shark removals do not always take place in populations of their
main prey, and thus their regulatory role is not necessarily related
to the relative contribution of a prey to their diet (i.e., direct effects).
These authors recognized the need to characterize the trophic
interactions of these species and assess their importance as spreading mechanisms of indirect effects and thus in regulating marine
communities. Myers et al. (2007) identified batoids as major contributors to indirect trophic effects (i.e., a trophic cascade) in an
Atlantic marine ecosystem that became considerably unbalanced
as a result of exploitation of top predators, proposing an important
role of batoids as mesopredators.
Most of these analyses focused on functional approaches, i.e.,
quantification of the functional importance of species in a community (Libralato et al., 2006), to study the effect of a predator on
the population size of its prey, or, in some very specific cases, on
trophic cascade effects that do not consider other types of indirect effects (e.g., apparent competition, competitive exclusion),
which have also been identified as strong forces shaping community structure (Menge, 1995). A different option for analyzing
trophic networks is the structural perspective, i.e., quantification
of the positional importance of trophic groups in a trophic flow
network (Wassermann and Faust, 1994; Jordán, 2003; Jordán et
al., 2006), which allows identification of those species that play
an important role in structuring the ecosystem, referred to as key
species (Dunne et al., 2002a; Jordán and Scheuring, 2002). The
purpose of the present study was to assess the importance of elasmobranch species in the marine ecosystem of the central coast
of the Colombian Pacific Ocean using the structural approach of
topological analysis of trophic networks.
the studies examined, we built a matrix of prey presence–absence
in predator diets, as has been done in multiple trophic network
studies (Solé and Montoya, 2001; Dunne et al., 2002b; Allesina and
Bodini, 2004; Williams and Martinez, 2004; Benedek et al., 2007;
Appendix B). This matrix was analyzed with Jaccard’s similarity
index and the Unweighted Pair Group Method with Arithmetic
Mean (UPGMA) algorithm; a similarity value ≥0.7 was considered
significant for assigning a trophic niche or trophic components
(Macpherson, 1981). Once trophic components and other species
participating in the network were defined, we built a new matrix
of trophic interactions among those entities (Appendix C). We used
the network analysis software NetDraw 2.075 (Borgatti, 2002) to
visualize the matrix as a trophic network.
2. Materials and methods
2.3.2. Centrality indices
The first index is BC (betweenness centrality), which is based on
quantifying how often node i is on the shortest path between each
pair of nodes j and k. This index was computed using the UCINET
IV software package (Borgatti et al., 1996). The standardized index
for node i (BCi ) is:
2.1. Data
We built a trophic network using stomach content data of
species caught in the shrimp fishery operating in the Colombian
Pacific Ocean. This information was collected between 1990 and
2007 and is reported in 34 theses from the Universidad del Valle
(Appendix A). All research was conducted between Guapi Inlet
and Buenaventura Bay (2◦ 45 N, 78◦ 10 W–3◦ 50 N, 77◦ 20 W) in the
central coast of the Colombian Pacific Ocean and diet information
was recorded at least at the order level. Diet data for top predators were mostly not available from the study area and were thus
obtained from adjacent marine areas (Ecuador, Costa Rica or Mexico) as found in the literature. Information from 12,439 stomachs
belonging to 75 species was assembled.
2.2. Building the trophic network
To reduce bias caused by different levels of prey identification
(e.g., orders, families, genera) we initially set up a database in which
prey identification was standardized at the order or lower level and
available quantitative indices of prey importance were recorded
(e.g., frequency of occurrence, percent by number or weight, index
of relative importance; see Hyslop, 1980 for details). Since in
trophic network analyses it is more important to analyze trophic
components than single species (taxonomical groups), because the
former more accurately describe trophic interactions and reduce
functional redundancy in the food web (Jordán, 2003), we used
the available diet information to establish those groups from the
species analyzed. As a result of the inconsistency in use of numerical indices among studies and that no single index was used in all
2.3. Topological analysis
We used node degree as well as several intermediate-reach or
“mesoscale” indices, whose application in topological analysis has
been extensively discussed in multiple publications (Jordán, 2001;
Jordán and Scheuring, 2002; Jordán et al., 1999, 2006; AbarcaArenas et al., 2007; Gaichas and Francis, 2008), to assess the
positional importance of the different nodes in the trophic network
of the studied community and thus infer the positional importance
of the species or trophic components under study. These indices
are as follows.
2.3.1. Node degree (D)
This is the most easily applied but least informative index
because it only takes into account the number of other nodes connected directly to node i. Thus, the degree of node i (Di ) is the sum
of its prey (in-degree, Din,i ) and predators (out-degree, Dout,i ), and
was computed using NetDraw as Di = Din,i + Dout,i .
BCi =
2×
g (i)/gjk
j≤k jk
(N − 1)(N − 2)
where i =
/ j and k, gjk is the number of equally shortest paths
between nodes j and k, and gjk (i) is the number of these shortest paths to which node i is incident (gjk could be equal to 1). The
denominator is twice the number of pairs of nodes without node i.
This index thus measures how central a given node is in terms of
being incident to many shortest paths in the network. If BCi is large
for trophic group i, it indicates that the loss of this node will have
many rapidly spreading effects in the web.
The second centrality index used was CC (closeness centrality), which is based on the proximity principle and quantifies how
short the minimal paths from a given node to all other nodes are
(Wassermann and Faust, 1994). This index was also computed using
UCINET IV (Borgatti et al., 1996), and its standardized form (CCi ) is
expressed as:
CCi =
N−1
N
d
j=1 ij
where i =
/ j, and dij is the length of the shortest path between nodes
i and j in the network. This index thus measures how close a node
is to the rest of nodes. The smallest value of CCi will be for that
trophic group that upon being removed will affect the majority of
other groups.
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A.F. Navia et al. / Ecological Modelling 221 (2010) 2918–2926
Table 1
Network indices quantifying the positional importance of nodes (trophic entities or components) in the Gulf of Tortugas ecosystem with top predators included. Nodes are
listed by decreasing importance rank, based on the K index. K = topological importance index; Kbu = bottom-up importance index, Ktd = top-down importance index, Kdir = direct
effect importance index, Kindir = indirect effect importance index. Underlined values in bold are for elasmobranch fishes.
Rank
Code
Nodes or trophic component
Kbu
1
2
3
4
5
6
7
8
9
9
11
12
13
14
15
16
17
18
19
20
21
22
23
24
24
26
27
28
29
30
31
32
32
32
35
36
37
38
39
40
41
41
41
44
45
46
47
48
49
50
51
52
53
54
55
56
Cleu
Slew
Climb
Shri
Gcuv
Per
Bra
Pel
Det
Scom
Lutj
Alg
Clu
Pol
Zoo
Gas
Sto
Ceph
TC3
Ach
Ur
TC2
Cfalc
Dia
Dino
TC1
Mull
Ophii
Caran
Arii
Batra
Bran
Ost
Ang
Zx
Ano
Amph
Rl
Scia
Iso
Achan
Cyano
Rad
Ple
Gerr
Cni
Rv
Tetra
An
Prist
Bel
Aul
Scor
Sil
Sig
Gad
Carcharhinus leucas
Sphyrna lewini
Carcharhinus limbatus
Shrimps
Galeocerdo cuvier
Perciformes
Brachyura
Pelecypoda
Detritus
Scombridae
Lutjanidae
Algae
Clupeiformes
Polychaetes
Zooplankton
Gastropoda
Stomatopoda
Cephalopoda
TC3
Achiiridae
Urotrygon rogersi
TC2
Carcharhinus falciformis
Diatoms
Dinoflagellates
TC1
Mullidae
Ophiididae
Carangidae
Ariidae
Batrachoidiformes
Branchiopoda
Ostracoda
Anguilliformes
Zapteryx xyster
Anomura
Amphipoda
Rhinobatos leucorhynchus
Scianidae
Isopoda
Achantharia
Cyanobacteria
Radiolarians
Pleuronectiformes
Gerridae
Cnidaria
Raja velezi
Tetradontiformes
Aetobatus narinari
Pristigasteridae
Beloniformes
Aulopiformes
Scorpaeniformes
Siluriformes
Signatiformes
Gadiformes
0.00
0.07
0.07
5.31
0.00
6.67
4.49
4.71
4.27
0.44
0.07
4.07
1.98
1.90
3.56
2.51
2.29
2.90
0.27
0.06
0.13
0.06
0.00
1.71
1.71
0.21
0.07
0.63
0.44
0.00
1.33
1.30
1.30
0.49
0.00
0.80
0.59
0.13
0.20
0.48
0.70
0.70
0.70
0.64
0.20
0.52
0.00
0.19
0.00
0.00
0.32
0.30
0.19
0.13
0.12
0.07
2.3.3. Keystone index (Ki )
It is used to characterize the importance of species in ecosystems
according to their position in the trophic network; it is also known
as index of topological importance. This index considers information
additional to the nodes directly connected to one another and was
defined in detail by Jordán (2001) and Jordán et al. (2006). It is
expressed as:
Kj =
n
1
c=1
dc
(1 + Kbc ) +
m
1
e=1
fe
(1 + Kte )
where n is the number of predators eating species i, dc is the number
of prey of the cth predator and Kbc is the bottom-up keystone index
Ktd
Kdir
34.28
14.40
12.07
4.96
8.04
0.00
0.80
0.00
0.00
3.83
4.18
0.00
1.79
1.72
0.00
1.04
0.82
0.07
2.52
2.64
1.88
1.94
1.82
0.00
0.00
1.47
1.59
0.99
1.13
1.45
0.00
0.00
0.00
0.81
1.14
0.29
0.46
0.73
0.64
0.33
0.00
0.00
0.00
0.00
0.39
0.00
0.50
0.29
0.39
0.38
0.00
0.00
0.00
0.00
0.00
0.00
4.57
6.02
4.09
8.84
3.51
2.65
3.88
2.54
1.84
3.35
3.10
1.45
3.53
2.54
1.64
2.45
2.27
1.76
2.14
1.63
1.14
1.31
0.67
0.45
0.45
1.05
1.02
1.08
0.97
0.80
1.16
0.31
0.31
0.93
0.61
0.90
0.95
0.50
0.46
0.73
0.11
0.11
0.11
0.59
0.33
0.24
0.25
0.34
0.10
0.24
0.27
0.28
0.18
0.10
0.08
0.07
Kindir
29.72
8.46
8.05
1.42
4.53
4.02
1.42
2.17
2.43
0.92
1.15
2.62
0.24
1.07
1.92
1.10
0.84
1.22
0.65
1.07
0.87
0.69
1.16
1.26
1.26
0.64
0.64
0.54
0.59
0.65
0.17
0.99
0.99
0.37
0.53
0.19
0.10
0.36
0.38
0.09
0.59
0.59
0.59
0.04
0.26
0.28
0.25
0.14
0.29
0.14
0.05
0.01
0.01
0.03
0.04
0.00
K
34.28
14.48
12.14
10.26
8.04
6.67
5.30
4.71
4.27
4.27
4.25
4.07
3.77
3.61
3.56
3.55
3.11
2.97
2.79
2.70
2.01
2.00
1.82
1.71
1.71
1.68
1.65
1.62
1.56
1.45
1.33
1.30
1.30
1.30
1.14
1.09
1.05
0.85
0.84
0.82
0.70
0.70
0.70
0.64
0.59
0.52
0.50
0.49
0.39
0.38
0.32
0.30
0.19
0.13
0.12
0.07
of the cth predator. Symmetrically, m is the number of prey eaten by
species i, fe is the number of predators of the eth prey and Kte is the
top-down keystone index of the eth prey. For node i, the first summation of the equation quantifies bottom-up effects (Kbu ), whereas
the second summation quantifies top-down effects (Ktd ). After rearranging the above equation, the terms that contain the values of K
(Kbc /dc + Kte /fe ) refer to indirect effects (Kindir ), whereas those
that do not contain K (1/dc + 1/fe ) refer to direct effects (Kdir ).
The sums of these values of effects (Kbu + Ktd and Kindir + Kdir ) equal
K: Ki = Kbu,i + Ktd,i = Kdir,i + Kindir,i . In addition to informing about the
number of direct connections among nodes, the keystone index
informs on how these neighbors are connected to one another
(Jordán et al., 2006), emphasizing vertical interactions over hori-
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A.F. Navia et al. / Ecological Modelling 221 (2010) 2918–2926
zontal ones (e.g., trophic cascades vs. apparent competition). It also
characterizes positional importance, separating direct from indirect effects, as well as bottom-up from top-down effects in the
trophic network (Jordán, 2001).
Local extinctions can trigger secondary extinctions through
direct or indirect effects in trophic networks or may considerably
influence other coexisting populations (Pimm, 1980). Jordán (2005)
proposed that the centrality of a species is a good indicator of its
“positional importance” because it allows one to infer the number
of secondary extinctions that a species may trigger within a community interaction network, a finding corroborated by Quince et al.
(2005). This index, in principle, gives the number of species going
to secondary extinction after removing a certain species from the
network (Jordán, 2001, 2005). Thus, the higher the value of K, the
higher the probability of triggering extinctions (Jordán et al., 2002).
The keystone index was computed using the FLKS 1.1 software
package (Jordán, 2005; provided by F. Jordán), which is designed
for characterization of vertical positional importance of species in
food webs.
These mesoscale indices have been favored over other more
local statistics, such as the distribution of trophic connections
(Montoya and Solé, 2002; Dunne et al., 2002a), or more global
ones, such as food web connectance (Martinez, 1992) because the
latter for example reflect the global topology of the network but
do not provide information on the specific position of individual
nodes or their more distant interactions, thus preventing the analysis of important indirect effects, such as apparent competition and
trophic cascades (Holt and Lawton, 1994; Menge, 1995). Furthermore, mesoscale indices are recommended when the purpose of the
study is to understand relationships within a community (Jordán
and Scheuring, 2002) and especially when one wants to quantify
the relative importance of a given species with respect to the rest
of species in a system (Jordán et al., 2006). Quince et al. (2005) studied the dynamics of “keystone indices” and determined that they
are effective in predicting the importance of species in a trophic
network, in particular the basal species.
Our baseline analysis made use of the most detailed taxonomic
resolution possible (species or genus if available) of both predators
and prey, but we explored the potential effect of the level of taxonomic resolution used in the trophic network on the node degree
and the two centrality indices (betweenness, closeness) by grouping species into families (e.g., Scomberomorus sierra and Thunnus
albacares as Scombridae), with the exception of elasmobranchs,
which were left at the species level. Additionally, we assessed the
structural importance of sharks considered top predators in the
trophic network of the community under study (Galeocerdo cuvier,
Carcharhinus leucas, Carcharhinus limbatus, Carcharhinus falciformis
and Sphyrna lewini) by computing the node degree, centrality, and
the keystone indices with and without these species using the
aggregated dataset.
3. Results
We identified three sets of trophic components or trophic niches
based on the diet data used in the analysis of diet similarities. They
were included in the network as TC1 (Arius seemani, Centropomus
unionensis, Pomadasys panamensis), TC2 (Cyclopsetta querna, Polydactylus approximans, Polydactylus opercularis) and TC3 (Mustelus
lunulatus and Dasyatis longa). The first two trophic components
(TC1 and TC2) consist of teleost fishes, whereas TC3 is composed
of two mesopredatory elasmobranchs. Given the limited availability of diet information, especially for invertebrates, cluster analysis
was only applied to predators, leaving prey categories at the taxonomical level reported in the literature reviewed. Thus, the trophic
network we built consisted of 56 nodes (11 elasmobranchs, 24
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Table 2
Effect of taxonomic aggregation level on the node degree and the two centrality
indices used. Each index shows the first ten nodes identified with the two aggregation levels (no grouping: lowest taxonomic resolution; grouping: family level;
see text for details). Nodes appearing with and without grouping for each index
are denoted in bold. See Table 1 for meaning of abbreviations; Lp = Lutjanus peru;
Kp = Katsuwonus pelamis.
Degree
Betweenness
Closeness
No grouping
Grouping
No grouping
Grouping
No grouping
Grouping
Shri
Bra
Sto
Clu
Slew
Climb
Gcuv
Gas
Ceph
Cleu
Shri
Bra
Sto
Clu
Slew
Climb
Gcuv
Scom
Gas
Cleu
Shri
Bra
Sto
Slew
Clu
Cleu
Lp
Kp
FG3
Gas
Shri
Bra
Scom
Lutj
Sto
Clu
Slew
TC3
Climb
Gas
Shri
Bra
Slew
Sto
Climb
Clu
Gcuv
Cleu
TC3
Gas
Shri
Bra
Slew
Climb
Sto
Scom
Cleu
Clu
Gcuv
Gas
teleosts, 11 invertebrates, 3 zooplankton, 6 phytoplankton and
detritus; Table 1).
The model used to analyze the trophic network was robust to the
two different levels of taxonomic aggregation. The node degree and
the two centrality indices computed (betweenness and closeness)
coincided between 70% and 90% of the time in the composition
(i.e., nodes present) of the 10 most important nodes in the network
(Table 2). The structure of these nodes (i.e., ranking order) showed
more variability between grouping levels (30–80% coincidence in
the ranking order), but the differences in ranking within each index
compared were only of 1, 2 or 3 positions (Table 2).
3.1. Results with top predators
Based on node degree connectivity (D), shrimps were the node
with the largest value (30), followed by brachyura (crabs, 25) and
stomatopods (21). The first elasmobranch node in our analysis
(Sphyrna lewini) had a connectivity degree of 20, ranking fourth
in importance.
Centrality indices yielded similar results. Sphyrna lewini had
a BC index value of 98, ranking seventh in importance below
shrimps (373), brachyura (159), Scombridae (132), Lutjanidae
(109), stomatopods (100.5) and clupeiformes (100.2), while the
next elasmobranch node was TC3, ranking eighth (Fig. 1a). A somewhat different trend was observed with the CC index, with S. lewini
being the most representative elasmobranch node, ranking third
overall (148), followed by C. limbatus in 4th place, below shrimps
(136) and brachyura (141; Fig. 2a).
The index of topological importance (K) yielded the highest positional values for 3 nodes of top predatory sharks as key species
(Table 1), meaning that their removal would result in a high number of secondary extinctions in the network compared with other
species with lower index values. Shrimps, brachyura, pelecypoda
(bivalves) and detritus had high values of topological importance,
showing high representation of low trophic levels in the structure of
this food web. Our results also indicate that top predatory elasmobranchs in the studied community play a larger role in top-down
ecosystem control (see Ktd values in Table 1) than in bottom-up
control (as expected since they are top predators; see Kbu values
in Table 1) and that the direct effects they exert over other species
in the ecosystem are smaller than their role in dispersing indirect
effects (see Kdir vs. Kindir values in Table 1). The first mesopredatory
elasmobranchs (node TC3, M. lunulatus and D. longa) to appear in
the ranking (19) had very low topological importance, well below
smaller species with lower trophic level, such as gastropods, stomatopods, and clupeiformes to cite a few (Table 1).
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Fig. 1. Topological network of the Gulf of Tortugas trophic web based on the betweenness index (node size is proportional to BC). (A) All food web, (B) food web without
top predators. Nodes in light grey (bottom) refer to phytoplankton, zooplankton and detritus, white nodes to invertebrates, dark grey nodes to teleosts, and black nodes to
elasmobranchs (top).
3.2. Results without top predators
Shrimps were also the node with the largest value of node
degree connectivity (27), followed by brachyura (21) and stomatopods (19). The first elasmobranch node in this analysis (TC3)
had a connectivity degree of 10, ranking 12th in importance.
Without top predators in the analysis, the first elasmobranch
node (TC3) had a BC centrality index value of 82, ranking 7th in
importance below shrimps (391), brachyura (154), stomatopods
(123), Lutjanidae (121), Scombridae (120) and clupeiformes (83;
Fig. 1b). With the CC centrality index, TC3 was the most representative elasmobranch node, ranking only in 13th place (150; Fig. 2b).
After removal of top predators from the system, the list of
species with high topological importance (K) was substantially
modified, with invertebrates, such as shrimps, brachyura and
polychaete worms, and teleost fishes, such as Lutjanidae and
Scombridae, having the highest positional values. The first mesopredatory elasmobranchs (node TC3, M. lunulatus and D. longa) to
appear in the ranking again had very low topological importance,
with a rank of 15 (Table 3), but generally contributed more to direct
effects over their prey than in dispersing indirect effects (see Kdir vs.
Kindir values in Table 3), in contrast to the findings for top predatory
sharks described above.
4. Discussion
The elasmobranch species examined in the present study are
predatory, have high and intermediate trophic levels (3–4.5), and
are associated with benthic and demersal habitats, thus feeding
mainly on fishes and invertebrates of the benthic epifauna and endofauna in the study area. According to the node degree index (D),
four high-trophic level predatory shark species (S. lewini, C. lim-
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A.F. Navia et al. / Ecological Modelling 221 (2010) 2918–2926
2923
Fig. 2. Topological network of the Gulf of Tortugas trophic web based on closeness index (node size is inversely proportional to CC). (A) All food web, (B) food web without
top predators. Nodes in light grey (bottom) refer to phytoplankton, zooplankton and detritus, white nodes to invertebrates, dark grey nodes to teleosts, and black nodes to
elasmobranchs (top).
batus, G. cuvier, C. leucas), out of the 11 species of elasmobranchs
included in the analysis, had connectivity values that ranked among
the 10 highest. In contrast, sharks and rays at intermediate trophic
levels (TC3 and others) had low levels of connectivity with the other
system components, which is indicative of their reduced contribution to system stability.
The betweenness index (BC) indicated that sharks and rays do
not have important centrality values, i.e., they are not part of many
of the shortest paths between species in the network, and thus
their removal would not result in a large spread of direct or indirect
effects in the network. Results of the closeness centrality index (CC)
also suggest that, except for S. lewini, G. cuvier, C. limbatus and C. leucas, a large amount of steps or interactions are needed for effects
originating in elasmobranchs to reach most of the species in the
system, thus the dispersion of their indirect effects is slower than
that of the species with higher CC index values.
In terms of the top-down importance index, the largest value
obtained for elasmobranchs, corresponding to the top predators,
suggests that these species significantly contribute to population
regulation of their prey. In contrast, the mesopredatory M. lunulatus and D. longa occupy intermediate trophic levels and contribute
relatively little to population regulation of their prey, with the topdown effect being even weaker in the other elasmobranchs studied.
Surprisingly, top-down importance indices (Ktd ) of species not considered to be predators of high functional value, such as shrimps,
polychaete worms, and clupeiformes, were larger than those of
some of the mesopredatory elasmobranchs, indicating a larger than
expected regulatory effect of prey populations by these species.
Theoretically, elasmobranch species at trophic levels between
those of top predators and those of the lowest-level prey belong
to the so-called mesopredator group, which in the absence or
decreased abundance of top predators – especially sharks – would
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Table 3
Network indices quantifying the positional importance of nodes (trophic entities or components) in the Gulf of Tortugas ecosystem without top predators included. Nodes
are listed by decreasing importance rank, based on the K index. K = topological importance index; Kbu = bottom-up importance index, Ktd = top-down importance index,
Kdir = direct effect importance index, Kindir = indirect effect importance index. Underlined values in bold are for elasmobranch fishes.
Rank
Code
Species or trophic component
Kbu
Ktd
Kdir
Kindir
K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
24
26
27
28
29
29
31
32
33
34
35
36
36
36
39
40
41
42
43
44
45
46
47
48
49
50
51
Shri
Lutj
Per
Bra
Scom
Pel
Det
Alg
Pol
Ach
TC2
Gas
Zoo
Clu
TC3
Sto
Mull
Arii
Ceph
Ur
Ang
TC1
Ophii
Dia
Dino
Zx
Caran
Batra
Bran
Ost
Amph
Ano
Scia
Rl
Iso
Achan
Cyano
Rad
Rv
Tetra
Cni
Prist
Ple
An
Gerr
Bel
Aul
Scor
Sil
Sig
Gad
Shrimps
Lutjanidae
Perciformes
Brachyura
Scombridae
Pelecypoda
Detritus
Algae
Polychaetes
Achiiridae
TC2
Gastropoda
Zooplankton
Clupeiformes
TC3
Stomatopoda
Mullidae
Ariidae
Cephalopoda
Urotrygon rogersi
Anguilliformes
TC1
Ophiididae
Diatoms
Dinoflagellates
Zapteryx xyster
Carangidae
Batrachoidiformes
Branchiopoda
Ostracoda
Amphipoda
Anomura
Scianidae
Rhinobatos leucorhynchus
Isopoda
Achantharia
Cyanobacteria
Radiolarians
Raja velezi
Tetradontiformes
Cnidaria
Pristigasteridae
Pleuronectiformes
Aetobatus narinari
Gerridae
Beloniformes
Aulopiformes
Scorpaeniformes
Siluriformes
Signatiformes
Gadiformes
4.58
0.00
5.28
3.73
0.00
4.20
3.87
3.67
1.71
0.00
0.00
2.16
3.14
1.31
0.00
1.93
0.00
0.00
2.14
0.00
0.28
0.00
0.44
1.47
1.47
0.00
0.00
1.25
1.08
1.08
0.49
0.64
0.00
0.00
0.39
0.62
0.62
0.62
0.00
0.15
0.49
0.00
0.46
0.00
0.00
0.15
0.14
0.13
0.10
0.08
0.07
4.96
5.37
0.00
0.88
4.42
0.00
0.00
0.00
1.74
3.40
3.31
1.10
0.00
1.79
2.94
0.91
2.36
2.25
0.10
1.96
1.46
1.63
1.13
0.00
0.00
1.46
1.40
0.00
0.00
0.00
0.46
0.29
0.83
0.81
0.33
0.00
0.00
0.00
0.53
0.35
0.00
0.47
0.00
0.45
0.42
0.00
0.00
0.00
0.00
0.00
0.00
8.71
3.68
2.30
3.56
3.35
2.54
1.84
1.45
2.56
1.84
2.20
2.36
1.64
3.10
2.13
2.25
1.67
1.10
1.43
1.04
1.03
0.89
1.03
0.45
0.45
0.80
0.66
1.16
0.31
0.31
0.95
0.84
0.37
0.40
0.73
0.11
0.11
0.11
0.26
0.37
0.24
0.28
0.46
0.12
0.15
0.15
0.14
0.13
0.10
0.08
0.07
0.83
1.69
2.99
1.05
1.07
1.66
2.03
2.22
0.90
1.56
1.11
0.90
1.50
0.00
0.81
0.59
0.70
1.15
0.82
0.92
0.71
0.74
0.55
1.02
1.02
0.66
0.73
0.09
0.77
0.77
0.00
0.09
0.47
0.41
0.00
0.51
0.51
0.51
0.28
0.14
0.24
0.19
0.00
0.33
0.28
0.00
0.00
0.00
0.00
0.00
0.00
9.54
5.37
5.28
4.61
4.42
4.20
3.87
3.67
3.45
3.40
3.31
3.26
3.14
3.10
2.94
2.84
2.36
2.25
2.24
1.96
1.74
1.63
1.57
1.47
1.47
1.46
1.40
1.25
1.08
1.08
0.95
0.93
0.83
0.81
0.73
0.62
0.62
0.62
0.53
0.50
0.49
0.47
0.46
0.45
0.42
0.15
0.14
0.13
0.10
0.08
0.07
participate in secondary population regulation effects known as
trophic cascades (Myers et al., 2007), and in certain cases would
lead to severe population reductions of their prey (e.g., bivalves,
gastropods). According to our results no such mesopredatory elasmobranch species belong to a complex with important indirect
effects on ecosystem regulation (see Kindir values in Table 1) because
they occupy low or intermediate topological positions, in fact lower
than those of other species (shrimps, cephalopods, zooplankton)
that despite having higher values of the K index, could hardly be
considered mesopredators.
Our results agree with previous reports showing the importance
of top predators in regulating ecosystem dynamics (e.g., Stevens et
al., 2000), but contrary to what has been reported in other studies regarding the ecological importance of mesopredatory species
(Sánchez et al., 2005; Myers et al., 2007), elasmobranchs in the food
web we analyzed (e.g., M. lunulatus and D. longa) unexpectedly had
lower topological importance (K) than several species groups such
as shrimps, brachyura, clupeiformes, polychaete worms, and snappers, or even zooplankton, algae, and detritus. Several of these taxa
also had larger connectivity and centrality values and therefore
are predicted to have more influence on the stability of the studied system, as has been reported in other continental shelf food
webs (Abarca-Arenas et al., 2007). Our results suggest that if top
predators are present they exert a top-down ecosystem control in
the community studied, but in their absence there appears to be a
shift to a bottom-up control mechanism. Our findings thus differ
from those of Myers et al. (2007), who proposed trophic cascade
effects caused by the removal of large sharks and are more in line
with Jennings and Kaiser’s (1998) notion that effects ensuing the
removal of large predators are generally weak because the high
diversity in marine systems may oppose strong top-down effects.
Quince et al. (2005) proposed that the spreading mechanism of
indirect effects known as predator-mediated coexistence or keystone predation may become dominant after removal of a predator.
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A.F. Navia et al. / Ecological Modelling 221 (2010) 2918–2926
This is a mechanism whereby a predator allows inferior competitors to coexist with a superior competitor by predation of the
competitively dominant species. Thus, deletion of the predator can
lead to extinctions among some of its prey. This phenomenon has
been recorded in real communities (Paine, 1974; Navarrete and
Menge, 1996) and should be assessed in elasmobranchs, because, if
true, some competing mesopredators may become locally extinct
before they potentially give rise to trophic cascades as proposed by
Myers et al. (2007) and Heithaus et al. (2008).
Topological evaluation of demersal systems gains strength as
a technique because fishing has forced global structural changes
(Pauly et al., 1998), which can already be observed in the studied
ecosystem (Navia and Mejía-Falla, 2008). Thus, it is necessary to
strengthen this kind of analysis to validate or reject the traditional
view that the removal of a top predator will cause a drastic effect
in the rest of the community (Beddington, 1984).
An important difference between the structural analysis we presented and traditional mass balance models (functional indices), on
which the majority of studies that highlight the ecological importance of elasmobranchs are based (García-Gómez, 2000; Sánchez et
al., 2005), is that the former identifies and analyses in detail interspecific or functional-group trophic relationships without grouping
many species of different trophic levels in large categories, such
as “sharks” (Arreguín-Sánchez et al., 1993) or “sharks and rays”
(Silva et al., 1993; Sánchez et al., 2005). Topological analysis thus
has the advantage of allowing quantification of direct and indirect
effects and the role that each group in the trophic network has in
the various ecosystem control mechanisms.
Stevens et al. (2000) noted that reductions in shark abundance
caused large changes in abundance of other species, with the effect
in most cases being larger for less important prey of small sharks
or species not fed upon by sharks than for direct prey of top predators, which unexpectedly decreased in abundance in some cases.
Stevens et al.’s (2000) results suggest that such direct trophic cascades as proposed by Myers et al. (2007) and Heithaus et al. (2008)
are unlikely to occur in complex marine food webs such as the
one we studied and that propagation of the effects of reductions
in shark biomass through trophic networks is a complex process.
In this type of situation structural analysis of trophic networks may
provide more detailed tools than those available with Ecopath with
Ecosim approaches to explore the spreading mechanisms of direct
and indirect effects in trophic webs.
Jordán et al. (2008) stated that it is important to identify which
structural properties of a node (topological analysis) make it more
functionally important within a network and, conversely, which
functional indices provided by Ecopath with Ecosim (e.g. community importance or keystone index) are indicators of the structural
importance of species. Our study represents the first structural
analysis of the ecological importance of elasmobranchs in marine
food webs and serves as a starting point for a more complete study
incorporating the two approaches to help identify the mechanisms
that govern the dynamics of key species. In our study, however,
we were limited to using binary data to construct an unweighted
network, but future work should strive to use quantitative data to
build a weighted network that would allow for a better correlation
with the functional attributes of the species in the trophic networks
(Jordán et al., 2008).
Although results obtained in the present study may have been
influenced by the specific properties of the system under study
(Jordán, 2003; Jordán et al., 2006), we present a new perspective for
evaluating the ecological importance of sharks and rays in coastal
ecosystems and food webs that allows for a more detailed assessment – even at the species or trophic components level – of their
role in shaping community structure. With this approach we can
also ask questions that go beyond those answered by mass balance
analyses, and therefore it represents a starting point for future,
2925
more detailed assessments of the role that elasmobranch fishes
play in shaping the structure, dynamics and stability of marine
ecosystems.
Acknowledgements
We thank F. Jordán for making the FLKS 1.1 software package
available for our analysis and for advice in conducting this study.
AFN and PAM thank the Universidad del Valle and COLCIENCIAS,
and AFN thanks the CICIMAR and CONACYT for providing funding
for this study and their PhD degrees.
Appendix A. Supplementary data
Supplementary data associated with this article can be found, in
the online version, at doi:10.1016/j.ecolmodel.2010.09.006.
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