Defining and Measuring Trophic Role Similarity in Food Webs Using ...

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312J. J. LUCZKOVICH ET AL.consumer groups: the red group includedscavenging dipterans Nepenthosyrphus sp. (10),Pierretia urceola (11), and two species ofAnotidae (14 and 15); whereas the predatoryinsects Misumenops nepenthicola (1), encyrtids(Trachinaephagus) (2) and Toxorhynchies klossi(3) comprised the yellow group. Both the yellowand red groups are sinks for energy in this web(they have no outgoing ties).Five pairs of species were exactly regularlyequivalent, with coefficients of 1.0 (5 and 6; 7and 8; 10 and 11; 12 and 13; and 14 and 15).These nodes are shown as slightly displaced fromone another in Fig. 6(a) to prevent themfromcompletely obscuring one another. These pairsof nodes have the same ties to the same classesof species, but not necessarily the same species. Inthis example, each pair is tied to the exact samespecies, considering both predators and prey, sothey are both regularly and structurally equivalent.The complexity of the feeding relations in thisfood web network at the level of species can nowbe simplified from the original 19 nodes into fivecolor classes. After pooling nodes in the samecolor class into a single node and redisplayingthe network of these pooled nodes, we createda regular-equivalence image graph. The imagegraph of the pitcher plant food web shows thenetwork structure in simplified form [Fig. 6(b)].For comparative purposes, we also haveanalysed the same food web data using Yodzis& Winemiller’s (1999) preferred similarity measure,the additive trophic similarity measure,which is a measure of structural equivalence(Fig. 7 F similarity data available from theauthors or at http://drjoe.biology.ecu.edu/regefoodweb).The two types of similarity measures,structural (additive similarities) and the regular(REGE coefficients) equivalence, produced twovery different views of similarities among thespecies (compare Figs 5 and 7). Whereas thehierarchical clustering based on REGE coefficientsgrouped the basal producers into the sameclass (drowned insects 18, organic debris 19) atan early step, in the additive similarity clusteringthey are not joined until the next to the lastagglomeration step (Fig. 7). According to theadditive similarity measure, the node for organicdebris (19) is more similar to the top predatorM. nepenthicola (1) than it is to drowned insects(18). The additive similarity measure produces anon-intuitive grouping of nodes in the food web.We can visualize the structural equivalence ofthe network if we compute the MDS coordinatesin two dimensions using the additive similaritymeasure and display these with the networktrophic links [Fig. 6(c)], as we did above with theREGE coefficients [refer to Fig. 6(a) for comparison].The food web depicted with nodespositioned according to the MDS coordinatesobtained from the additive similarity measuredoes not describe the flow of energy or materialsfromsources to sinks, as it did when REGEcoefficients were used. Indeed, the basal nodes(17–19) are not particularly close to one another,and they cannot be arranged in such a way thatthey all lie near one end of the graph. The toppredators nodes (1–3) are close to one anotherand on one side of the plot, but are also in closeproximity to one of the basal nodes (18). This isa characteristic of the additive measure, whichignores the direction of the ties. In fact, thearrows representing energy flow among nodes inFig. 6(c) do not all point in the same generaldirection, rather they cross back over oneanother, so there is no approximation of trophicposition that can be uncovered in their arrangementby MDS. A few pairs of nodes appear togroup together: these are species with identicalyellowmagentagreenredblue111017568712139141519163142181.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2Additive SimilarityFig. 7. An average-linkage cluster diagramof theMalaysian pitcher plant insect food web using the additivesimilarity measure of Yodzis & Winemiller (1999).
DEFINITION OF TROPHIC ROLE SIMILARITY 313predator and prey relations, which thus haveadditive similarities of 1.0 and identical MDScoordinates [nodes 5 and 6; 7 and 8; 10 and 11;12 and 13; 14 and 15 F all are shown slightlydisplaced fromtheir coordinate positions so thatthey do not overlap one another in Fig. 6(c)].These species are the same pairs that were notedto be exactly regularly equivalent above. Outsideof these species with identical ties in the network,the additive similarity measure did not uncoverany nodes with similar network ties or positionwithin the network, as the REGE coefficientsdid. The additive similarity measure groupedtaxa independent of the direction of the ties F amajor drawback. In addition, the top predatorsin the web M. nepenthicola (1) and T. klossi (3)are joined only after the fourth agglomerationstep (Fig. 7), although they both clearly feed onaquatic insects living in the pitcher plants(Fig. 3). They feed on the same kinds of insects,but not the exact same species of insects, so theyreceive a low similarity in the additive similaritymeasure. But they do feed on the same trophicrole class of insects (green), as can be seen in theMDS plot [Fig. 6(a)]. Also, (1) and (3) are joinedat the same step as the bacteria and protozoa(16), yet these insects are the predators on theaquatic insect larvae group (4–9 and 12,13),whereas bacteria and protozoa are the prey ofthe aquatic larvae. Again, the direction of theties is ignored by the additive similarity measure,which results in the same level of similarity forthese species that occupy very different trophicroles.Thus, the additive similarity measure appearedto do a poor job at uncovering trophicroles of insects in the pitcher plant food web,except in the cases where species had exactly thesame predators and exactly the same prey. Incontrast, REGE was far superior in findingsimilarity among species’ trophic roles, even ifthe species consumed different prey and wereconsumed by different predators.4.2. ST. MARKS, FLORIDA SEAGRASS CARBONFLOW WEBWe now turn to another example, using thesesame procedures to illustrate the method toaggregate trophically similar taxa in a complexfood web. The 51 compartments in the food webcollected by Baird et al. (1998) were analysed viathe REGE algorithm, generating a matrix ofcoefficients (available fromthe authors andon-line at http://drjoe.biology.ecu.edu/regefoodweb).Appendix B lists the names and numericalidentification codes for the compartments thatare discussed here; see Christian & Luczkovich(1999) and Luczkovich et al. (in press) for thecomplete species list for each compartment. TheREGE coefficients were submitted to hierarchicalclustering and R 2 values were computed foreach partition. For display purposes we selecteda partition with ten clusters, which achieveda much better R 2 than partitions with fewerclusters and explained nearly as much varianceas partitions with more clusters (see scree plot,Fig. 8).We used colors to identify the ten isotrophicclasses of consumers in the MDS plot [Fig. 9(a)]:the lime green group, which was the mainproducer, the seagrass Halodule wrightii (2); thedark green group, which included other benthicproducers [epiphytic algae (3) benthic algae (5)]and benthic bacteria (12); the cyan group, whichincluded phytoplankton (1) and bacterio-plankton(6); the white group, which includedzooplankton (8); the yellow group, whichincluded various benthic invertebrates (nodes 7,9, 13, 15, 17, 19, 21, 22, 25, 27, 28), some fishesR squared0.50.40.30.20 5 10 15 20 25Number of ClustersFig. 8. A scree plot of the R 2 as it varies with number ofclusters fromthe average linkage cluster analysis using theREGE coefficients derived fromfeeding relations andcarbon-flow values of the St. Marks National WildlifeRefuge Seagrass EcosystemFood Web
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