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Fisheries Research 87 (2007) 46–57

Sociometric analysis of the role of penaeids in the continental shelffood web off Veracruz, Mexico based on by-catch

L.G. Abarca-Arenas a,∗, J. Franco-Lopez b, M.S. Peterson c,N.J. Brown-Peterson c, E. Valero-Pacheco d

a Instituto de Investigaciones Biologicas, Universidad Veracruzana, Dr. Luis Castelazo s/n, Col. Industrial Animas, Xalapa, Veracruz, Mexico, CP 91190, Mexicob Laboratorio de Ecologıa, FES-Iztcala-UNAM. Av. De los Barrios s/n, Los Reyes Iztacala, Tlalnepantla, Edo. de Mexico, Mexico CP 54090, Mexico

c Department of Coastal Sciences, The University of Southern Mississippi, 703 East Beach Drive, Ocean Springs, MS 39564, USAd Posgrado en Neuroetologıa, Instituto de Neuroetologıa, Universidad Veracruzana, Apartado Postal 566, Xalapa 91001, Veracruz, Mexico

bstract

Continental shelf macrofauna are impacted by trawling and associated by-catch activities. These activities have been predicted to change theacrofaunal community structure and the resulting food web. Four food webs (three seasonal and one pooled) were constructed using shrimp

y-catch samples from 21 surveys from 1991 to 1994. Network sociometric analyses were performed on the webs in order to explore structuralharacteristics focusing on the role of penaeids. The number of nodes varied from 43 to 73. The out-degree centrality value for the combined webas the highest. For the penaeid node, the windy season centrality was the highest (47%) and the rainy season the lowest (11%). The numberf cutpoints by season was: windy four, dry two, and three for the combined web. Using the lambda sets analysis; penaeid is a key node for the

tructural cohesion of the trophic network. The rainy season food web is the most homogeneous and penaeid is an important node such that itslimination would cause a major structural and functional disruption to the network. These modeling exercises suggest over-fishing by trawlersould impact the continental shelf community structure and thus significantly change the existing trophic relationships.2007 Elsevier B.V. All rights reserved.

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eywords: Centrality; Food webs; Gulf of Mexico; Networks; In-degree; Out-d

. Introduction

Coastal fisheries are of great benefit to the economy andhe society in Mexico. Total annual landings of coastal fin-sh and shellfish in 1997 in Mexico were around 1.5 million

onnes (CONAPESCA, 2003). Furthermore, the shrimp fish-ry has been one of the most important extractive industriesn both Mexican coasts. During the last 5 years, a decrease inhrimp captures has been reported mainly in the Campeche Bankone (CONAPESCA, 2003). Additionally, trawling for shrimpas been demonstrated as a destructive method not only for theenthic fauna but for many fish species (Yanez-Arancibia andanchez-Gil, 1988; Hall, 1999; Keller, 2005). Worldwide, theortion of the total by-catch that is returned to the sea (i.e. global

iscards) was estimated in 1992 as 11.2 million tonnes for thehrimp fishery (Hall, 1999; Jennings et al., 2001), and the USulf of Mexico shrimp fishery discards 10.3 kg fish of for each

∗ Corresponding author. Tel.: +52 228 841 8910.E-mail address: luisgaa@gmail.com (L.G. Abarca-Arenas).

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165-7836/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.fishres.2007.06.019

; Trophic relations

ilogram of shrimp captured (Alverson et al., 1994). For theexican portion of the Gulf of Mexico, the latest estimate was

2 kg of by-catch for each kilogram of shrimp (Yanez-Arancibiand Sanchez-Gil, 1988).

Trawl fisheries for shrimp and demersal finfish account forver 50% of total estimated discards, from this, tropical shrimprawl fisheries have the highest discard rate accounting forround 27% of total estimated discards (Keller, 2005). In recentears, a reduction in discards has been observed, due to theromotion of using more selective fishing gears and discardegulations. However this proportion is higher for the finfishsheries (40%) than for the shrimp fisheries in the case of theulf of Mexico (Keller, 2005). The high by-catch numbers rep-

esent a problem for the fishery managers since most of theime this capture is not reported, and the data are not taken intoccount during fisheries assessments (Hall, 1999).

From an ecological perspective, the damage to the seafloor

nd the associated fauna due to trawling has been well doc-mented (Albert and Bergstad, 1993; Diamond et al., 1999;orse and Watling, 1999; Bianchi et al., 2000; Diamond et

l., 2000; Jennings et al., 2001; Sanchez and Olaso, 2004).

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L.G. Abarca-Arenas et al. / Fi

urthermore, there are also negative impacts on the pelagicauna (Sainsbury, 1987, 1988; Sainsbury et al., 1997). Few ofhe studies devoted to fish community structure deal with therophic relationships of the community components (Albert andergstad, 1993; Stobutzki et al., 2001; Abarca-Arenas et al.,004). Studies at the ecosystem hierarchical level are needed inrder to better understand both the target species role and theverall effect of by-catch removal on the whole system. Thispproach to studying the fishery would produce the possibilityf sounder management (EPAB, 1999; Pikitch et al., 2004) asell as a better understanding of communities and ecosystems

elated to the fisheries.Food web analysis has been a well-documented tool to

chieve a fisheries ecosystem approach as well as to under-tand the ecosystem under various scenarios (Arreguın-Sanchezt al., 1993a, 1993b; Pauly et al., 1998, 2000). One advantage ofhis type of analysis is the parallel understanding of the ecosys-em under different scenarios. Although published food webso not provide a true representation of all interacting species,good amount of information on the structure and function of

cosystems has been obtained. Among this is the possibility ofxtracting the information necessary to identify those specieshat play an important role in the ecosystem, also known as key-tone species (e.g. Dunne et al., 2002; Jordan and Scheuring,002; Luczkovich et al., 2003).

Although shrimp utilize the productive estuarine and coastalursery habitat as post-larvae and juveniles, their importance tosheries occurs once they return to the open ocean as adults.owever, little is known regarding the ecological role of shrimpn the open ocean food web. This is an important aspect consid-ring the decline that the shrimp population density has had overhe years. Understanding the shrimp’s role in trophic interactionsould help fisheries managers recommend sound exploitationolicies that will take into account the interaction of shrimpith other species of the ecosystem. The aim of this work was

o define the structural role of shrimp in four food webs, threeeasonal and one for the pooled data set. We used the central-ty, betweenness and lambda sets indices as proposed by theocial sciences (Wasserman and Faust, 1994). This was doneith the idea to explore the application of methods from otherisciplines in resolving ecological problems. We found that thepplication of sociometric indices resulted in an important toolor the structural and functional analysis of trophic networks.

. Area description

Predator and prey samples were taken offshore of thelvarado lagoon system (between 18◦45′′ and 19◦00′′N and5◦40′′ and 85◦57′′W, located NE of the Campeche Bank), anmportant region for the shrimp fishery. The region has threeeasonal periods: “nortes” or windy, from October to February

ith occasional high winds (up to 100 km/h) and some rain; thery season, from March to June, and the rainy season from Julyo September. A significant amount of freshwater comes to therea during the rainy season, mainly from the Papaloapan Riveratershed adjacent to the zone.

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s Research 87 (2007) 46–57 47

. Data source

The food webs analyzed were assembled from the stomachontents of fishes captured as by-catch during shrimp fishingff the Alvarado coast. The capture methods, as well as theethods used to describe and analyze the stomach contents of

ll species, are considered in greater detail in Abarca-Arenast al. (2004). Briefly, fishes were collected for stomach contentnalysis on 21 sampling dates between May 1991 and November994 from commercial shrimp trawling boats. Two-hour nightlyruises were conducted twice during each sampling time. Sixampling dates corresponded to the rainy season, six to the dryeason, and nine to the windy season. More than 6000 fishesere analyzed from the entire collection, representing 10% of

he total by-catch captured from the shrimp trawling. From theotal of 159 fish species collected, those representing ≥10% ofhe abundance were used for the present work, totaling 51 fishpecies for all seasons.

After seasonal tables of fish species and their food items weressembled, it was noticed that some of the prey were identifiedt too general a level, i.e. crustaceans. In order to eliminate theseinds of items, and reduce the loss of data, we assigned these preytems proportionally to their respective type (Abarca-Arenas etl., 2004). That is, if “crustacean pieces” was an item, then thatercentage was assigned proportionally to other crustaceans inhe diet like shrimp, crab, lobster, etc. This method eliminatespossible bias when statistical analyses were performed, as it

educes the variability in prey items introduced by non-specificdentifications. Once the food items were ordered, the feedingreferences of the fish prey were tabulated from the literatureAbarca-Arenas and Valero-Pacheco, 1993; Arreguın-Sanchezt al., 1993a, 1993b; Browder, 1993; Chavez et al., 1993; Vega-endejas et al., 1993).

With these data, predator–prey matrices were assembled sea-onally and for all data pooled across seasons. For each matrix,he rows are the predators and the columns are the prey. A num-er one indicates that a predator on row i preys on a species inolumn j, and is called an adjacency matrix. Adjacency matricesere used for all the network analyses as described below. Eachatrix can also be represented as a graph where each species

epresents a node that is linked to other species (see Fig. 1). Theink between two nodes or species is called an edge and can beither undirected or directed. In the former case, the relation-hip between the two nodes involved has no inherent direction,uch that the adjacency matrix is perfectly symmetric. That is,he relation between species A and B is the same as the rela-ion between species B and A. The latter case is represented byn arrow pointing from the prey to its predator. This kind ofdjacency matrix is, in general, asymmetric because the rela-ion between species A and B might not be the same as the oneetween B and A. For example, if species A preys on species Bhe opposite does not necessarily happen (see Fig. 1a and b).

. Network analysis

Species involved extensively in relationships with others inhese food webs are called prominent, because they are embed-

48 L.G. Abarca-Arenas et al. / Fisheries Research 87 (2007) 46–57

F . A non-directed network will show no arrows between the species. (b) Adjacencym n-degree centrality (IDC) and out-degree centrality (ODC) for the network in (a) and( 1.

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ig. 1. (a) Directed network showing the interaction between five species, A–Eatrix showing the relationship between species of a five-species network. (c) I

b) and their normalized values computed by dividing the IDC and ODC by n −

ed in the network. In order to measure which species arerominent, several indices have been proposed that measure howentrally located a species is within the network. Some indicesre better suited for non-directed networks, others are betteror directed networks, and some other indices are adequate foroth kinds. Independently of the kind of network, the centralityndex of each node is calculated and they are used to calculatehe network centrality. These calculations are used to identifyhe existence of one or more species with a high centrality value.f the network has one or more species with high centrality, it iseterogeneous while a network with no such species is homo-eneous. The variance of the individual centrality is anothereasure commonly used, and some authors prefer this method

o measure centrality.Centrality indices are based, in part, on the number of nodal

ies in a network. A network in which all nodes point to andre connected to only one node is called a “star” networkHanneman, 2001; Watts et al., 2002) (Fig. 2a). This particu-ar network has a centrality degree of one, and the “star” nodeas a degree of the number of species, minus one. Thus, for anyther kind of network, the centrality value would be standard-zed on the degree of a “star” network with the same numberf nodes. An extreme of this kind of network is a circular oneFig. 2b) where a node is connected to the adjacent one, which ishen connected to another, and so on. The last node is connectedo the first node.

For undirected graphs, counting the links is enough. But forirected graphs, where a node may link to the outside or haveinks entering the network from the outside, it is possible to cal-ulate a centrality value for these cases and these are termed in-egree centrality (IDC) and out-degree centrality (ODC), respec-ively (see Fig. 1c). In this case, the adjacency matrix is asymmet-

ic. In the case of the food webs, those links leaving a node rep-esent being eaten by another node or species while an incomingink represent preying on a second node or species. In most of theases, the values for the IDC and ODC are different, and the net-

Fig. 2. Examples of two extreme types of networks. (a) Star network, node oneis connected to all other nodes and these to no other and (b) circle network whereone node is connected to the adjacent and so on.

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ork centrality will be different as well. Finally, for asymmetricdjacency matrices, it is possible to symmetrize it and calculaten index for undirected graphs. All indices were calculated usinghe program UCINET 6 for Windows (Borgatti et al., 2002).

.1. Degree centrality

For undirected graphs the following index was used:

D(ni) =S∑

j=1

xij =S∑

j=1

xji, (1)

here CD is the Centrality Index for species ni, and Xij, Xji, arehe links that represent the relation between species i and j.

Because this value depends on the number of nodes or speciesf the network, a standardized version was used as follows:

′D(ni) = CD(ni)

S − 1, (2)

here S is the number of species in the network; this index isndependent of the number of species, and thus can be comparedcross networks of different sizes. A node with a large value isn direct contact or adjacent to many other nodes.

For directed graphs both equations are used twice, one forhe output links, the ODC, of each node and one for the inputinks, the IDC.

Taking into account the individual species centrality degreesf the network, it is possible to calculate group centralization.hen a large value of group centralization is obtained, there is

n indication that a single species is central. Thus, the group cen-ralization measures how variable or heterogeneous the speciesentralities are. It can be considered as a measure of dispersionr variability.

Considering CD(n*) as the maximum observed value of cen-rality in the network, the group centrality is calculated by

D =∑S

i=1[CD(n∗) − CD(ni)]

(S − 1)(S − 2)(3)

here n* is the value of the maximum centrality for species n.The limits of the group centrality are 0 and 1. The former

alue indicates that all species have the same centrality (circularetwork Fig. 2b), and the food web is relatively homogeneous.n contrast, a value of 1 represents one species dominating allthers in the network and represents a network where one nodes central to all others as in a star network (Fig. 2a).

Another statistical value commonly used is the variance ofhe species’ degree:

2D =

∑Si=1(CD(ni) − CD)2

S, (4)

here CD is the mean centrality value over all the species; theariance of the individual centrality values can be used as aeasure of the network’s homogeneity (Wasserman and Faust,

994).sn

s Research 87 (2007) 46–57 49

.2. Betweenness centrality

This index measures the extent to which a particular speciesies between two or more species of the network. That is, apecies has a central position in the network if it is betweeneveral species. In a food web, an intermediary species couldepresent an important position in the flow of matter from onepecies to another or from one trophic level to the next, even ift is not connected to many other species. If gjk is the number ofeodesic (i.e. the number of species from j to k) linking speciesand k containing species i, with one species acting as the inter-ediary, then the betweenness index for species ni is the sum of

ll pairs of species not including the ith species:

B(ni) =∑

j<kgjk(ni)

gjk

. (5)

In this equation, CB is the betweenness centrality index forpecies i distinct from j and k. If the value of this index is zerohen species ni falls on no geodesics, i.e. it is not an intermedi-ry. The maximum value for this index is (S − 1)(S − 2)/2. Thetandardized formula for the betweenness centrality is

′B(ni) = 2

[CB(ni)

(S − 1)(S − 2)/2

], (6)

esulting in values between 0 for no betweenness of the speciesnd 1 for a species which is between all pairs of species.

If CB(n*) is the largest realized species betweenness indexor the web analyzed, then the food web betweenness centralityndex is

B = 2∑S

i=1[CB(n∗) − CB(ni)]

(S − 1)2(S − 2), (7)

ith a minimum value of 0 when all species have exactly theame value of the betweenness index. A high value of this indexill indicate that few of the species in the food web are betweenany others, or, in another sense, few species are intermediary

n the matter flow between species of the trophic network.

.3. Block analysis

In an attempt to reduce the dimensionality of the food webs, alock model was performed on each of the networks (Borgatti etl., 2002). A block model is a simplified version of the multire-ational network that represents the general feature of the foodeb’s structure. The final result is a matrix containing species

hat are structurally similar. Blocking a network carries with ithe discovery of cutpoints. A cutpoint is a node (a species in thiseb), that, if removed, will result in the network being divided

nto two or more other networks. It is possible for a network toave more than one cutpoint or to have no cutpoints.

.4. Lambda sets

A network can be divided into different number of sets orubgraphs, each with a certain number of lines connecting eachode. Each of these subgraphs is termed LS Sets. Within each of

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Table 1List of species and other items used in the food webs for the Alvarado, Veracruzcoastal shelf

Season Code Name

D, R 1 Achirus lineatusD, W 2 Anchoa hepsetusD, R, W 3 Anchoa mitchilliD, R 4 Anchovia rostralisW 5 Caranx hipposR 6 Cetengraulis edentulusD 7 Citharinchthys spilopterusD, R, W 8 Chloroscombrus chrysurusD, R, W 9 Conodon nobilisR, W 10 Cyclopsetta chittendeniD, R, W 11 Cynoscion arenariusD, R, W 12 Cynoscion nothusD, R, W 13 Diapterus auratusW 14 Diapterus rhombeusR, W 15 Diplectrum bivittatumW 16 Diplectrum formosunD, R, W 17 Engyophrys sentaW 18 Eucinostomus melanopterusW 19 Gymnotorax nigromarginatusD, R, W 20 Haemulon aureolineatumR 21 Harengula clupeolaD, R, W 22 Harengula jaguanaD, W 23 Hoplunnis macruraD, W 24 L. graellsiW 25 Lobotes surinamensisW 26 Lutjanus campechanusD, R, W 27 Micropogonias furnieriW 28 Myrophys puntatusW 29 Ophidion welshiW 30 Polydactilus octonemusD, R, W 31 Porichthys porosissimusR, W 32 Prionotus rubioD, R, W 33 Pristipomoides aquilonarisD, W 34 Sardinella auritaD, R 35 Saurida brassiliensisR, W 36 Scorpaena plumeriD, W 37 Selar crumenophthalmusR 38 Selene setapinnisR, W 39 Selene spixiiD 40 Selene vomerD, R, W 41 Sphyraena guachanchoR, W 42 Stellifer lanceolatusW 43 Stenotomus caprinusR, W 44 Syacium gunteriW 45 Syacium papillosumW 46 Symphurus plagiusaD, R, W 47 Synodus foetensD, W 48 Trachurus lathamiD, R, W 49 Trichiurus lepturusR, W 50 Umbrina coroidesD, R, W 51 Upeneus parvusD, R, W 52 B. cantori

Prey itemsD, R, W 53 CopepodsR, W 54 PlanktonD, R, W 55 SquidD, R, W 55 Penaeid shrimpR, W 57 Amphipods

0 L.G. Abarca-Arenas et al. / Fi

he LS Sets there is a certain amount of connectivity and there islso an amount of connectivity between the LS Sets that shapehe whole network. Considering this last property, it is possibleo measure the strength of connectivity between the various setshich is called the Lambda Sets. The line connectivity of nodesand j, denoted as λ(i,j) if i and j belong to different sets, isqual to the minimum number of lines that must be removedrom the graph in order to leave no path between the two nodes.he smaller the value of λ(i,j) the more vulnerable are nodes ind j to be disconnected from the graph by removing the lines.he higher the number of λ(i,j) the higher the number of lines

hat should be removed in order to disconnect i and j. In the casef the food webs, a large value of the lambda index will suggestspecies with a high connectivity between the set to which it

elongs and other sets.

. Results

Of the 159 fish species captured during the 4-year period, 27pecies were used for the dry season, 28 for the rainy season, and4 for the windy season. For the pooled data, 51 fish species werenalyzed (Table 1 ). From these species, a total of 21 differentomposite food items were identified (Table 1).

For the rainy season, a total of 46 nodes or species (predatornd prey) were used for the food web analysis (Table 1). A totalf 133 links between the nodes were recorded, representing aean value of 2.89 links per node. Of all species, two (plant

emains and algae) were basal, meaning they prey on no otherpecies. A total of 21 top species were obtained, representingsh that were not preyed upon by any other species. The final3 species were intermediary, being both predators and prey.

For the 63 predators and prey species in the windy seasonood web (Table 1), a total of 205 links were observed with aean value of 3.26 links per species. Of all the species 2 were

asal, 37 top, and 24 intermediate. The dry season food webTable 1) was composed of 43 predator and prey species with aotal of 156 links, and a mean value of 3.63 links per species. Ofll the species 2 were basal, 20 were top, and 21 species werentermediate. The overall food web was composed by a total of3 predator and prey species with a total of 369 links, resultingn 5.05 links per species as a mean. Of all species 2 were basal,6 intermediate and 35 top.

.1. Centrality

Our results showed shrimp as the species with the highestumber of output links. This is represented as a high value for theDC index of this species, second after detritus for each season

Table 2). For the pooled data matrix, shrimp fell to the fourthlace, after squid, caridean shrimp and detritus. These resultsre an indication of the high pressure that predators have onhrimp. This pressure is apparent after observing an increase ofhe ODC when the number of species of the food web increases,

.e. the windy season centrality value and number of species ishe highest. On the other hand, the IDC for shrimp was very lowor all seasons (Table 2), mainly due to their highly specializedeeding habits.

W 58 TanaidsW 59 IsopodsD, R, W 60 StomatopodsD, R, W 61 Polychaetes

L.G. Abarca-Arenas et al. / Fisheries Research 87 (2007) 46–57 51

Table 1 ( Continued )

Season Code Name

D, R, W 62 MysidaceanR, W 63 BrachiuraD, R, W 64 Portunus spinicarpusD 65 Caridean shrimpR, W 66 Fish larvaeD, R 67 Fish remainsD, R, W 68 MollusksD, W 69 BivalvesD, R 70 GasteropodsD, R, W 72 DetritusD, R, W 73 Plant remainsD, R, W 74 Algae

The list represents all species used for the pooled food web; species occurringdw

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Table 3Food web and shrimp betweenness index for each season and seasons pooled

Food web (%) Shrimp

Rainy 12.22 3.531WDP

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uring each season are indicated with D: dry season, R: rainy season, and W:indy season.

Histograms for each season’s IDC and ODC are presented ingures three to four. It is clear a fast decay of the ODC for thell season but steeper for the windy one. The IDC values droplower and several of the species present similar values.

The food web with the highest centrality was the one for theindy season (43.8%; Table 2). The centrality values for thether two seasons were similar to each other but lower than theindy season. Species like shrimp and fish larvae were dominant

s food sources, based on their high centrality, during the windyeason. That is, these two species presented the highest ODCalues. The remaining two seasons presented a different picture.everal species with similar ODC values were present, althoughone had values as high as that of shrimp and fish larvae for theindy season food web.The centrality index for the pooled food web was relatively

igh, more than 56% (Table 2). This value was affected by theetritus and squid high centrality values. Interestingly, shrimp

o not appear to have a central role when all food webs areooled; they are replaced in the rank list by squid.

Examination of the variance of the centrality values showedhat the windy season food web was the most heterogeneous with

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able 2entrality values and variance for each food web by season and pooled

Rainy

ODC (%) 29.43IDC (%) 8.99

2ODC 17.34IDC 2.04

ish larvaeODC 8.89IDC 4.44

quidODC 11.11IDC 2.22

ETODC 35.56IDC 0

enaeid shrimpODC 33.33IDC 6.67

aridean shrimpODC –IDC –

verall network centrality values (%), as well as those for key species such as penaeiDC: out-degree centrality; IDC: in-degree centrality; S2: variance; DET: detritus: n

indy 11.40 4.448ry 12.60 3.257ooled 11.89 2.376

relatively high variance (39%; Table 2). The centrality vari-nces were low (<18%) for the other seasons, from which it maye concluded that the food web is relatively homogeneous withespect to the ODC and IDC values. A large difference is evidenthen comparing the seasonal centrality variances with that of theooled food web (Table 2). The value for the variance suggestshat the pooled food web is highly heterogeneous, primarily dueo the high difference of centrality values for a few species (e.g.etritus, squid) compared to the rest of the species. That is, aew species are central while the rest are peripheral species.

For the betweenness index (the amount a species falls as anntermediary between two or more other species), the valuesbtained were small, ranging from 11% to 13% (Table 3).ince the models represent food webs, and the links connectingach species represent flow of matter, the small values ofetweenness represent an almost direct relation between preynd its predator. The smaller value for the shrimp node suggestsn almost direct linkage between the food taken by the shrimpsnd their predators.

.2. Blocking

For the rainy season, no blocks were found, meaning that theood web cannot be divided into different sub-webs. Thus, noutpoints were computed for this season (Table 4). For the windyeason food web, seven blocks were identified (Table 4), and

our species were considered as cutpoints (copepods, penaeids,sh larvae, and algae). The dry season food web blockingesulted in four blocks and two cutpoints (penaeids and fishemains; Table 4). The pooled data food web presented five

Windy Dry Pooled

43.84 29.59 56.0314.33 14.97 26.2739.96 14.49 113.07

5.04 3.56 21.0448.38 – 5.56

4.84 – 6.9414.51 9.52 51.39

1.61 2.38 2.7829.03 35.71 41.6714.51 21.43 046.77 26.19 41.66

4.83 7.14 12.5– 7.14 45.83– 11.9 6.94

ds, fish larvae, squid, detritus and caridean shrimp are shown.ot present.

52 L.G. Abarca-Arenas et al. / Fisheries Research 87 (2007) 46–57

Table 4Number of blocks and cutpoints of the food web for each season and seasonspooled, including the species identified as cutpoints

Season Blocks Cutpoints

Rainy 0Windy 7 Copepods, penaeids, fish larvae, and algaeDry 4 Penaeids, and fish remainsP

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ooled 5 B. cantori, squids, and caridean shrimps

locks and three cutpoints (Bregmaceros cantori, squids, andaridean shrimp; Table 4). The blocking algorithm is a similarechnique to the cluster analysis widely used in ecology, whichepresents a high degree of complexity as the number of clus-ers increases. The resulting block analysis for the food webshowed the windy season as the most complex of all due tohe number of blocks discovered, representing a higher levelf hierarchization within the windy season food web as com-ared to the other two seasons as well as to the pooled dataFigs. 3–5).

In order to exemplify the effect of eliminating one of thepecies marked as cutpoint, figures six and seven represent theood web for the dry season as an example. The original ODCood web (Fig. 6a), is compared to the food web (Fig. 6b) aftereleting the node representing the penaeid shrimps. For the IDCig. 7a represents the original food web while Fig. 7b the foodeb after the penaeid shrimps deletion. The species Lepophid-

um graellsi (node 24) is completely disconnected from the restf the food web as a consequence of the shrimp deletion. On thether hand, the number of links and the position of other speciesn the ODC and IDC ranking changes as well.

.3. Lambda sets

During the rainy season, the relationship between penaeidsnd detritus was most important for maintaining the networktructure, with detritus having a secondary importance (Table 5).or the windy season food web, fish larvae and penaeids were

he nodes with the most important relationships. The dry

eason food web showed the most important relationshipas between fish remains and detritus, followed closely byenaeids (Table 5). In the pooled food web, the most importantelationship was between squid and detritus followed byenaeid and caridean shrimp.

able 5ambda sets for each season and for seasons pooled

eason Lambda sets

ainyPenaeids and detritusPlant remains

indy Fish larvae and penaeids

ryFish remains and detritusPenaeids

ooled dataSquids and detritusPenaeids and caridean shrimp

6

waaiwtasiip

c

ig. 3. Out- and in-degree centrality distribution for the species of the windyeason. Species codes are as in Table 1. Notice that not all species codes areresented for clarity.

. Discussion

Centrality is a major component in different kinds of net-ork analysis approaches such as social networks (Wasserman

nd Faust, 1994) and the World Wide Web (WWW) (Barabasi etl., 2000; Albert et al., 1999). The importance of centrality laysn identifying the principal components within a social groupith which individual and/or group behavior is explained. In

he case of the WWW, the study of centrality resulted in thenalysis of hubs (computers with a high degree of traffic) andubsequently to the fragility of the WWW (Albert et al., 2000)n case of attacks from hackers. The possibility of characteriz-

ng hubs within a system of computers allows the possibility torepare the WWW from different attacks.

In the case of food webs, centrality has been related to theoncept of keystone species (Sole and Montoya, 2001; Dunne

L.G. Abarca-Arenas et al. / Fisheries Research 87 (2007) 46–57 53

Fig. 4. Out- and in-degree centrality distribution for the species of the rainysp

eshophs2wt(stAnf

Fig. 5. Out- and in-degree centrality distribution for the species of the dry season.Sf

ftitrpegotwn

eason. Species codes are as in Table 1. Notice that not all species codes areresented for clarity.

t al., 2002; Girvan and Newman, 2002). In this approach, theuggestion is that those species with a high number of links (i.e.,igh ODC and IDC) could be considered as a keystone speciesf the community (Albert et al., 2000). But this brings an inter-retation problem: should a keystone species be the one with aigh ODC or the one with a high IDC? This issue has been con-idered by Albert et al. (2000; see also Jordan and Scheuring,002), who proposed that a keystone species should be the oneith the highest connectivity, thus representing the most impor-

ant species in the community. On the other hand, Jordan et al.1999) and Jordan (2001) proposed a method to identify a key-tone species using weighed trophic networks and not solelyhe presence or absence of a link between them. Furthermore,

llesina and Bodini (2004) show that species connectivity notecessarily indicates its importance as a structural node in theood web.

sas

pecies codes are as in Table 1. Notice that not all species codes are presentedor clarity.

Our results showed a relatively high value of the ODC indexor shrimp in every food web analyzed. However, this was nothe case for the IDC value. Detritus was dominant for the IDCndex; representing the importance that organic recycling has onhe ecosystem. However, an elevated out-degree value also rep-esents the high pressure on the shrimp population from theirredators. The windy season was the season with the high-st ODC value for penaeids, as well as the season with thereatest number of fishes. These two values are related to eachther considering that fish species are mostly opportunistic inheir feeding habits. Thus, an increase in the shrimp populationill trigger an increase in their mortality by fish predation asoted for the windy season compared with the other two sea-

ons. Interestingly, the food web for the pooled data presentedsmaller value for the penaeid ODC than that of the windy

eason. That is, the overall population mortality for shrimp

54 L.G. Abarca-Arenas et al. / Fisheries Research 87 (2007) 46–57

Fig. 6. Food web representation for the dry season for the out-degree centrality: (a) with and (b) without the penaeids shrimps. Nodes are arranged from the lowest(top) to the highest (bottom) values of the degree. The species codes are as in Table 1.

L.G. Abarca-Arenas et al. / Fisheries Research 87 (2007) 46–57 55

F a) wit .

cb

s

ig. 7. Food web representation for the dry season for the in-degree centrality (o the highest (bottom) values of the degree. The species codes are as in Table 1

ould be greater during the windy season than on a yearlyasis.

Relating network centrality with the homogeneity of thepecies relationships using the variance results (Wasserman and

Fghp

th and (b) without penaeids shrimps. Nodes are arranged from the lowest (top)

aust, 1994), the rainy and dry seasons were the most homo-eneous of all food webs analyzed. The windy season waseterogeneous in this respect mainly due to the dominance ofenaeids as prey of many species. The dominance by penaeids

5 sherie

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6 L.G. Abarca-Arenas et al. / Fi

ased on the ODC index produced a bias on the food web index,hus inflating the value. The pooled food web had by far theighest value of ODC variance, denoting a high dominance byew species. In particular, detritus and squid dominated the foodeb structure on an annual basis.The relatively high homogeneity of the food webs is closely

elated to the low betweenness values found for each food web.lthough penaeids presented a high centrality, their position in

he food web does not make them an important intermediary ofhe matter flow. This might be true as well for the other relativelyighly central species, since the overall food web betweennessalues were low. The low betweenness values also indicate thathe food chains are short, which agrees with other studies onood webs (e.g. Williams et al., 2002). It is expected that if a foodeb has several central species these will act as intermediaries

o others, increasing the betweenness values (Hanneman, 2001)nd thus the chain length. The food webs analyzed here wereow in their centrality properties and thus by consequence theetweenness values were also low.

The number of blocks found in a food web is an indication ofhe structural homogeneity of that web. As the number of blocksncreases in a network, the relationship between its componentsecomes more complicated and heterogeneous. Our data showedhe rainy season, with a low S2, had no blocks and no cutpoints.hat is, the food web for this season is very homogeneous and

he species relationships are structurally compact. In contrast,he windy season presented the highest number of blocks andpecies acting as cutpoints. This web had the most potentialubgroups of any of the webs analyzed. When data for all sea-ons was aggregated, an intermediate number of blocks wereecorded, and penaeids were not a cutpoint, contrary to resultsn the windy and dry seasons.

These blocking and cutpoint results resemble what was foundy Abarca-Arenas and Ulanowicz (2002; see also Bersier andugihara, 1997; Krause et al., 2003) after aggregating species for

he Chesapeake Bay food web. Their results showed that, as thepecies were combined into single trophic species, the amountf information decreased, as the theory dictates. However, cer-ain combinations of species aggregations actually increased thenformation. That is, the quality of species lumping is an impor-ant factor in order to define the structure and functionality of

food web. The increase in the number of species, as in theooled data food web, did not increase the blocking or numberf cutpoints as could be expected. The windy season food web,ith less species, was more susceptible to division than the oneith higher species number.Analyzing the resulting lambda sets of species for each food

eb we found that the above analysis is congruent. Several of thepecies responsible for maintaining the structural characteristicsere also found as key in the relational structure. This means

hat species like squid and penaeids seem to be responsible forhe structural and functional cohesion of the food webs.

The values obtained by the various centrality indices indi-

ated an important position of penaeids within all food websnalyzed. Penaeids as a food source for fish is an important itemn every season of the year. The food web dynamics showed aariable structure among the different seasons of the year. The

A

s Research 87 (2007) 46–57

esults showed that a yearly-based food web does not resemblehat is happening each season with the species relationships

nd hence with the food web structure.This is also reflected, after the penaeid shrimps deletion in

ne season as an example, resulted in a depletion of the numberf links between species, and the isolation of one of the species.his results on a change in the structural properties of the foodeb and most probably on its functioning.Harvey et al. (2003) found that an understanding of species

nteractions as influenced by intensive fishing is a key to respon-ible management. Unfortunately, this is not an easy task. Theore we try to understand the species interactions within an

cosystem, more questions are proposed. Topological structuref complex networks is a key factor in understanding speciesnteractions (Arii and Parrott, 2004). Our results showed thentricate relationships existing within the coastal shelf commu-ity as well as their temporal variation. We discovered thathrimp, besides being an important human resource, are anmportant link in the trophic network of the area. We showedhat depletion of shrimp biomass could negatively impact theverall community structure and function of the area. With thisn mind, people responsible for the fishery policies should takento account the important role that shrimp has in the ecosystem.

Further work needs to be done to determine quantitatively theole of shrimp in the community food web. A keystone speciess not only the species with the highest number of predators; theiomass of the species is a factor that should also be taken intoonsideration. Furthermore, weak interactions might be as orore important than strong ones in defining the food web struc-

ure and its dynamics. Currently, the food webs examined herere being analyzed using the amounts of matter flowing frompecies to species. The combination of this ongoing analysis andhe analysis presented here will result in a better understandingf the role of penaeids in the trophic network.

Finally, the application of sociometric indices resulted inn important tool for the structural and functional analysis ofrophic networks. Of the whole universe of tools used by soci-logist to analyze social networks, just a handful of them werepplied. A continuous exploration on these tools certainly willroduce sound ecological hypotheses that will help us under-tand the structure, functioning, and evolution of ecosystems.

cknowledgments

We appreciate the help of the crew of the CETMAR-Alvaradoessel during the sampling. Travel expenses were paid in party the Grant No 00-06-010v from SIGOLFO-CONACyT toGAA.

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