Uncovering food web structure using a novel trophic similarity measure

Ecological Informatics 30 (2015) 110–118

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Uncovering food web structure using a novel trophic similarity measure Peng Gao ⁎, John A. Kupfer Department of Geography, University of South Carolina, 709 Bull Street, Room 127, Columbia, SC 29208, USA

a r t i c l e

i n f o

Article history: Received 21 October 2014 Received in revised form 15 September 2015 Accepted 27 September 2015 Available online 3 October 2015 Keywords: Trophic role Serengeti Spatial guilds Body mass

a b s t r a c t Aggregation of species on the basis of their trophic relationships is a fundamental step for quantifying, visualizing and thereby uncovering the structure of food webs. Although the Additive Jaccard Similarity (AJS) has been widely used to measure trophic similarity between species, it has also been criticized for its limited ability to find species with equivalent trophic roles, especially when they do not share the same predators and prey. In this study, we proposed a new trophic similarity measure, the Extended Additive Jaccard Similarity (EAJS), which quantifies trophic similarity between species based not only on the similarity of their shared predators and prey at adjacent trophic levels but at all trophic levels throughout a food web. Average linkage clustering was then used to aggregate species in the mammalian food web for the Serengeti ecosystem in northern Tanzania and southern Kenya on the basis of both trophic similarity measures. Compared to groups identified on the basis of AJS values, groups derived using EAJS had greater within-group similarity in terms of species' trophic relationships and greater discrimination vs. those in other groups. Groups based on EAJS values also better reflected ecological factors known to structure food webs, including producerlevel habitat segregation and mammalian body mass. The advantage of EAJS lies in the fact that it is designed to consider species feeding relations in food webs that is not limited to adjacent trophic levels. Our approach provides a means for revealing the patterns of trophic relations among species in food webs and exploring known and unknown factors shaping food web structure. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Food webs have been and continue to be an important research focus in many areas of ecology because energy flows play a central role in structuring population dynamics and maintaining biodiversity and ecosystem integrity (De Ruiter et al., 2005; Allesina et al., 2015; Montoya et al., 2015). The search for order and simplicity within food webs has attracted the attention of researchers for over a century (Elton, 1927), including efforts to uncover their structural properties (e.g., Polis, 1991; Havens, 1992; Johnson et al., 2014), reveal the rules shaping their complexity (e.g., Williams and Martinez, 2000), and capture species roles and interactions within them (e.g., Luczkovich et al., 2003a, 2003b; Jordán, 2009; Baker et al., 2015; Gauzens et al., 2015). While the interactions among species that form the basis of food webs may be complex (Polis, 1991), food webs are non-random and highly patterned in nature (Pimm, 1982; Bascompte, 2009) and are often regulated by a limited number of biological processes. For example, Cohen et al. (1990) summarized five laws that shaped food web structures, while Williams and Martinez (2000) succeeded in predicting twelve properties of food webs using only two parameters: species number and connectance.

⁎ Corresponding author. Tel.: +1 8037775234; fax: +1 8037774972. E-mail address: [email protected] (P. Gao).

http://dx.doi.org/10.1016/j.ecoinf.2015.09.013 1574-9541/© 2015 Elsevier B.V. All rights reserved.

As with the taxonomic classification system used to order organisms, one efficient way of reducing the complexity of food webs to better understand them is to decompose them into groups of species according to certain criteria or definitions. Approaches from various disciplines have been adapted to aggregate species in food webs into groups in which species have similar traits or perform similar ecological functions. Concepts and approaches typically employed to study individual roles and interactions in social networks have also been used to analyze species roles and feeding relations in food webs. For example, the concept of regular equivalence, in which two individuals with similar ties to analogous individuals are seen to play similar roles in a network (White and Reitz, 1983), has been adapted to partition food webs into isotrophic groups in which species have the same or similar trophic roles. This study provides useful information to determine trophic roles of species in food web models and to compare food webs over time and across geographic regions (Luczkovich et al., 2003a, 2003b). Methods used to detect compartments have also been used to identify groups of species that have more feeding relations within the groups but fewer feeding relations across groups (Girvan and Newman, 2002; Krause et al., 2003). In social network analysis, compartments are equivalent to ‘communities’, defined in that context as groups of people having more ‘within group’ than ‘between group’ interactions (e.g., people in same villages or towns). From an ecological standpoint, compartmentalization is thought to contribute to food web stability (Melian and

P. Gao, J.A. Kupfer / Ecological Informatics 30 (2015) 110–118

Bascompte, 2002). Krause et al. (2003), for example, investigated the response of a food web to two disturbance scenarios and found that compartmentalization could reduce the impact of disturbance on the other compartments by constraining its impact to a single compartment. Statistical modeling provides another means for aggregating species to reveal patterns in food webs. Allesina and Pascual (2009) created a probabilistic model that simultaneously considered compartments and groups of species with similar patterns of interactions while Baskerville et al. (2011) used a Bayesian computational method to detect group structures in the plant–mammal food web from the Serengeti ecosystem. The latter study demonstrated the importance of habitat type on food web structure through its direct control on species patterns at the producer level and, more indirectly, on groups of associated herbivores and carnivores, suggesting the spatial coupling and energy channels related to different types of plant habitats in the Serengeti. Another approach to defining trophic groups starts by quantifying pairwise trophic similarities for each species based on their feeding relationships with other species. A clustering method is then applied to the similarity matrix, yielding any desirable number of trophic groups. Trophic groups identified in this way have gained attention in ecological studies, because trophic interactions directly affect community dynamics and ecosystem functioning (Petchey and Gaston, 2006; Baiser et al., 2011; Gauzens et al., 2013). One of the most influential and fundamental works involving the aggregation of species into trophic groups based on their observed trophic connections is provided by Yodzis and Winemiller (1999), who compared the performance of multiple criteria and clustering algorithms. They concluded that the use of the Additive Jaccard Similarity (AJS) index to capture species' roles as consumers and resources in food webs was superior to the use of multiplicative similarity and that average linkage and maximum linkage clustering methods produced the most consistent and ecologically-interpretable groups. One implicit limitation in using AJS to define trophic similarity is that it is based solely on first order feeding links while the feeding relations in second or more distant neighbors are not considered. This may limit the ability of AJS-based approaches to find species with equivalent trophic roles, if they do not share the same predators or prey (Luczkovich et al., 2003a, 2003b). We therefore propose a novel trophic similarity measure, Extended Additive Jaccard Similarity (EAJS), which extends AJS to consider all orders of trophic relationships in a food web. Specifically, we aggregated plant and mammal species in the Serengeti ecosystem food web into groups based on pairwise species similarity values calculated using AJS and EAJS. We then evaluated the aggregations of species based on AJS and EAJS using a cluster validity index and explored the biological and ecological factors which may account for the clustering of species.

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Feeding relationships were analyzed as binary linkages and thus were not proportional to feeding pressure (e.g., the degree to which a certain predator preys on various species). Although food webs that incorporate more detailed fluxes of energy and materials are available in some studies (e.g., Cross et al., 2011) and are recognized as the new generation of food webs (Thompson et al., 2012), those with binary linkages are dominant in food web studies because it is much easier to observe the existence of feeding relationships than to quantify the fluxes of energy among specific species. 3. Methods 3.1. Calculating pairwise species similarity values To aggregate species into groups and reveal food web structure, we first defined the similarity between each pair of species based on predator–prey relationships. We did so using two measures of species similarity: the Additive Jaccard Similarity (AJS) coefficient used by Yodzis and Winemiller (1999) and others, and a new trophic similarity measure, Extended Additive Jaccard Similarity (EAJS, described below). For two species i and j, AJS is defined as:

AJSði; jÞ ¼

a aþbþc

ð1Þ

where a is the total number of predator or prey species shared by species i and species j; b is the number of predator or prey species for species i but not species j, and c is the number of predator or prey for species j but not species i. Values equal 1.0 when two species share the same predators and prey, and decrease when species have few predator or prey species in common. EAJS differs in that it incorporates not only the similarity of shared predators and prey at adjacent trophic levels but at all the trophic levels associated with both species (Fig. 1). EAJS is calculated by iteratively searching for all predators and prey in bottom-up (species preyed upon by a prey species) and top-down (predators of a predator species) directions until no additional linkages are found. If a species appears on two or more levels (e.g., the species is the predator of species i and the predator's predator of species i), only the feeding relationship on the closer level is considered. In doing so, the predators and prey of species i and j at all trophic levels are identified. The AJS of species i and j is then determined at each equivalent level (e.g., the prey of species i and j, the

2. Study area and dataset We chose to examine the food web for the Serengeti, which covers an area of plains and open woodlands in northern Tanzania and southern Kenya. Famous for its biodiversity, including the largest herds of grazing mammals in the world (Sinclair and Norton-Griffiths, 1984), the Serengeti has been the site of several seminal studies in grassland and savanna ecology, including research examining environmental factors contributing to community organization (McNaughton, 1978) and patterns of predation (Sinclair et al., 2003). The feeding linkages used to define the food web were developed by Baskerville et al. (2011) based on published information (Casebeer and Koss, 1970; McNaughton, 1978; Cooper et al., 1999; Sinclair et al., 2003) and personal observation from the authors of Baskerville et al. (2011). The resulting food web was composed of 592 feeding links among 161 species, which included 129 plants, 23 herbivores, and 9 carnivores and omnivores. While these linkages were undoubtedly incomplete, they represent one of the best documented food webs available.

Fig. 1. Comparison of Additive Jaccard Similarity (AJS) and Extended Additive Jaccard Similarity (EAJS) for species A and B. AJS is calculated based on prey and predators only at adjacent trophic levels (predator level 1 and prey level 1), while EAJS is based on prey and predators at all the trophic levels (predator level 1, predator level 2 and prey level 1). Arrows represent the feeding relationship with the end pointing to the prey. Triangles indicate prey of species A or B and squares represent predators of species A or B at all trophic levels. Species in dark color are those prey or predators shared by both species A and B at each trophic level.

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predator's predator of species i and j), summed, and divided by the maximum number of levels for species i and j. Calculations of AJS and EAJS are illustrated in Fig. 1. As noted above, AJS is based only on the shared predators and prey at adjacent trophic levels. In this case, the number of shared prey is 1, the number of shared predators is 2, and the number of prey or predators that are not shared by species A and B is 4. Therefore, AJS equals 0.43 (i.e., (1 + 2) / (1 + 2 + 4)). EAJS (0.61) is the sum of AJS at each equivalent level (i.e., 1/3 at the prey level; 2/4 and 2/2 at predator levels 1 and 2 respectively) divided by the maximum number of levels (i.e., species A has 3 trophic levels of predators or prey). Note that the similarity between either species A or B and any species at its predator or prey levels is zero, because they don't have any predator or prey in common with species A or B at any equivalent level. We next used average linkage clustering (ALK) to aggregate species into groups using the pair-wise similarity matrices of species produced by AJS and EAJS. ALK defines the distance between two clusters as the average dissimilarity between all cross-cluster pairs of species. A dendrogram is then built by iteratively merging the species or groups which have the shortest distance. This approach is hierarchical, and any number of groups can be obtained by cutting the dendrogram until a desired number is reached.

While the Silhouette index provides a means for assessing the mathematical quality of groups, groups should capture ecologicallymeaningful relationships, as well. Allesina and Pascual (2009), for example, were able to partition food webs into groups and compartments by optimizing an Akaike Information Criterion function of species interactions and their assignment to groups, but the biological interpretation of such patterns was not examinated. The ecological and biological factors that structure food webs have been widely investigated; here, we focus on two factors: 1) habitat, under the premise that species within a habitat are more likely to share trophic linkages with other species in that habitat, rather than those outside it (e.g., Pimm and Lawton 1980), and 2) body size, which influences predator–prey relationships and has thus been incorporated as a primary factor in understanding food web structure (Paine, 1963; Williams and Martinez, 2000; Emmerson and Raffaelli, 2004; Stouffer et al., 2005; Petchey et al., 2008). The degree to which groups of producers were related to habitats was examined using Shannon entropy values. Primary habitats of the 129 plant species were assigned to one of eight classes (grassland, woodland, riparian, kopje, shrubland, thicket, disturbed, undetermined) by Baskerville et al. (2011). Shannon entropy was then used to measure the habitat signature in each group of plants, that is, the clustering of plants in different habitats among the groups. For group i, the Shannon entropy (Hi) is defined as:

3.2. Evaluation of food web groups

  X ni j ni j Hi ¼ − log j n ni i

Defining the similarity between each pair of species on the basis of AJS and EAJS will, in most cases, yield two different similarity matrices and thus two distinct clustering results. While there is no ‘better’ cluster result, we evaluated the results of the food web partitions derived using AJS and EAJS based on two criteria: 1) the quality of groups defined by the cohesion of species within groups and separation of species in different groups, and 2) the ability of the methods to identify groups distinguished by ecological factors known to structure food webs. These criteria address the statistical and ecological properties of the food web classification, respectively. We first evaluated the quality of clustering based on the two similarity matrices using a cluster validity index, the Silhouette index (Rousseeuw, 1987). The Silhouette index (S) is calculated as:

S¼

1 Xn ðbi −ai Þ i maxða ; b Þ n i i

ð2Þ

where n is the number of species in the food web, ai is the average distance between species i and all other species in its own group, and bi is the minimum of the average dissimilarities between i and species in other groups. ai thus measures the overall dissimilarity of species i to other species in the same group (the cohesion of the groups, with smaller values meaning higher cohesion), and bi measures the average distance of species i to species in the group that is most similar or closest to it (the separation of the groups, with larger values meaning better separation). When ai is greater than bi, the Silhouette index for species i is negative, suggesting that species i is more similar to species in other groups. When bi is greater than ai, it means that the average distance of species i to species in the ‘nearest’ group is larger than that of species i to other species in the same group. In this case, the Silhouette index measures the difference between the two distances, scaled to the former. Therefore, larger values suggest a higher ‘fidelity’ of species to their groups. In a comparative study of thirty cluster validity indices, Arbelaitz et al. (2013) examined index performance using real and synthetic datasets under different test conditions, such as different clustering methods, various cluster densities, and multiple levels of noise. The Silhouette index was recognized as the most suitable cluster validity index in terms of successful rates of recognizing the number of groups in the different datasets under various test conditions.

ð3Þ

where j is the habitat, ni is the size of group i, and nij is the number of plants that are assigned to habitat j in group i. A low Shannon entropy value indicates clustering of habitats in the group. The overall segregation of habitats for all groups of plants was measured by the sum of Shannon entropy of each group, weighted by the size of each group: H¼

X ni H i n i

ð4Þ

where n was the total number of plants in all groups. To test the statistical significance of habitat segregation in the groups, we calculated the p-value as the probability of a value lower than or equal to H drawn from randomized partitions with groups of identical size. To determine whether a group of plants was overrepresented by plants of a certain habitat (i.e., significant clustering of a habitat in a group), we calculated the p-value as the probability that a randomized group of the same size would have as many or more plants of the habitat (Baskerville et al. 2011). For animals, body mass is one of the most commonly cited factors that structures trophic relationships. Predators typically consume prey that are smaller than themselves, although larger predators eat prey with a wider range of body sizes than smaller predators (Cohen et al., 1993; Brose et al., 2006a; Brose et al., 2006b; Riede et al., 2011). In their study of predation patterns in the Serengeti, Sinclair et al. (2003) found that carnivores exhibited distinct patterns associated with the range of prey body mass, while herbivore groups were structured by the number of predators. These patterns or aggregations can be explained by carnivore or herbivore body sizes. For this study, we assembled the animal body mass values in this food web from Roberts (1951) and Sinclair et al. (2003). We examined whether groups of carnivores or herbivores found in our study could be explained by the body mass of carnivores or herbivores in two ways. First, we qualitatively checked whether the assignment of animals in our study were consistent with the patterns found by Sinclair et al. (2003). More quantitatively, we performed a chi-square test to examine whether the separation of carnivores could be explained by the body mass of prey they feed on. For this analysis, we separated the prey of carnivores into small mammals (typical adult body mass b 80 kg) and large mammals (typical adult body mass N 150 kg). No prey species in

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the sample study dataset had typical body mass values between 80–150 kg. 4. Results 4.1. Clustering results The clustering process is hierarchical, meaning that users can select any number of food web groups depending on the desired level of detail. Here, we discuss results for 18 groups, level of detail that had a high Silhouette index and resulted in ecologically-meaningful groups (as discussed below). Partitioning of the Serengeti food web into 18 groups based on EAJS values clearly distinguished three trophic levels: carnivores and omnivores (Groups 1–3), herbivores (Groups 4–11), and producers (Groups 12–18) (Table 1, Fig. 2). At the highest trophic level (carnivores and omnivores), Group 1 contained just one species, Caracal caracal, which has no predator and relies on a limited number of herbivores. In contrast, carnivores in Group 2 included large carnivores that utilize a broader range of prey. Group 3 contained all carnivores eaten by Panthera pardus. Eight groups were identified at the herbivore level. Of the first six groups, five (Groups 4, 5, 6, 8, and 9) were distinguished on the basis of specific predator or prey species. Species in Group 5 (Procavia capensis), Group 6 (Heterohyrax brucei and Papio anubis) and Group 9 (Giraffa camelopardalis and Syncerus caffer) are only eaten by one species (Caracal caracal, Panthera pardus and Panthera leo, respectively), while species in Groups 4 and 8 have two predators: Taurotragus oryx in (Group 8) is eaten by Panthera leo and Panthera pardus, and Pedetes capensis (Group 4) is eaten by Caracal caracal and Panthera pardus. Group 7 contained the largest number of herbivores, each of which has at least three predators. Finally, Groups 10 and 11 each contained

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only one species, Loxodonta africana and Hippopotamus amphibius, respectively, neither of which has a predator. At the primary producer level, Groups 17 and 18 were both composed of only one species (Olea spp. and Panicum repens) that is eaten by a particular consumer (Giraffa camelopardalis and Hippopotamus amphibius, respectively). In contrast, the consumers of plants in Group 13 included all of the herbivores and secondary consumers that eat these herbivores. Species in the remaining groups (Groups 12, 14, 15 and 16) were aggregated on the basis of primary and secondary consumers. There were only three primary consumers of species in Group 14 (Heterohyrax brucei, Papio anubis, and Loxodonta africana), but species in this group were similar mainly because Panthera pardus is their only secondary consumer, giving them the highest possible AJS value at the level of secondary consumer. In contrast, consumers of species in Group 12 were five totally different species (Alcelaphus buselaphus, Damaliscus korrigum, Kobus ellipsiprymnus, Pedetes capensis, and Procavia capensis). Five species (i.e., Caracal caracal, Crocuta crocuta, Lycaon pictus, Panthera leo, and Panthera pardus) were the secondary consumers of species in Group 12, of which Panthera pardus is the only one that overlaps with the secondary consumers of Group 14. In contrast to the food web identified using EAJS values, results using AJS identified only two groups at the level of carnivores and omnivores (Fig. 3, Table 2). Panthera pardus and its two prey (Acinonyx jubatus and Canis aureus) were assigned to the same group (Group 2) while the other two prey species of Panthera pardus were assigned to Group 1. The four prey species of Panthera pardus were all assigned to Group 3 based on EAJS (Fig. 2). Six herbivore groups were identified using AJS values, while those based on EAJS identified eight. AJS did not distinguish Loxodonta africana and Hippopotamus amphibius, which have no predators. EAJS, however, separated these species because Loxodonta africana

Table 1 Species membership in eighteen groups identified on the basis of Extended Additive Jaccard Similarity (EAJS) for the Serengeti food web. Carnivores or omnivores Group 1 Group 2 Group 3 Herbivores Group 4 Group 5 Group 6 Group 7 Group 8 Group 9 Group 10 Group 11 Producers Group 12 Group 13

Group 14 Group 15 Group 16

Group 17 Group 18

Caracal caracal Crocuta crocuta, Lycaon pictus, Panthera leo and Panthera pardus Acinonyx jubatus, Canis aureus, Canis mesomelas and Leptailurus serval

Pedetes capensis Procavia capensis Heterohyrax brucei and Papio anubis Aepyceros melampus, Alcelaphus buselaphus, Connochaetes taurinus, Damaliscus korrigum, Equus quagga, Nanger granti, Eudorcas thomsonii, Kobus ellipsiprymnus, Madoqua kirkii, Ourebia ourebi, Phacochoerus africanus, Redunca redunca, Tragelaphus scriptus and Rhabdomys pumilio Taurotragus oryx Giraffa camelopardalis and Syncerus caffer Loxodonta africana Hippopotamus amphibius

Andropogon schirensis, Cymbopogon excavatus, Digitaria ternata, Phragmites mauritianus, Psilolemma jaegeri, Sporobolus spicatus and Typha capensis Acalypha fruticosa, Acacia senegal, Acacia tortilis, Achyranthes aspera, Allophylus rubifolius, Aloe macrosiphon, Andropogon greenwayi, Aristida spp., Balanites aegyptiaca, Boscia augustifolia, Bothriochloa insculpta, Brachiaria semiundulata, Capparis tomentosa, Pennisetum ciliare, Chloris gayana, Commelina africana, Commiphora trothae, Combretum molle, Cordia ovalis, Croton macrostachyus, Cynodon dactylon, Digitaria diagonalis, Digitaria macroblephara, Digitaria scalarum, Dinebra retroflexa, Duosperma kilimandscharica, Echinochloa haploclada, Eragrostis cilianensis, Eragrostis exasperata, Eragrostis tenuifolia, Eustachys paspaloides, Ficus glumosa, Grewia bicolor, Grewia trichocarpa, Harpachne schimperi, Heteropogon contortus, Hibiscus spp., Hibiscus lunariifolius, Hoslundia opposita, Hyperthelia dissoluta, Hyparrhenia filipendula, Hyparrhenia rufa, Indigofera basiflora, Indigofera hochstetteri, Kalanchoe spp., Maerua cafra, Microchloa kunthii, Ocimum spp., Panicum coloratum, Panicum maximum, Pennisetum mezianum, Pennisetum stramineum, Sansevieria ehrenbergii, Sida spp., Solanum dennekense, Solanum incanum, Solanum nigrum, Sporobolus festivus, Sporobolus fimbriatus, Sporobolus ioclados, Sporobolus pyramidalis and Themeda triandra Acacia xanthophloea, Commiphora merkeri, Crotalaria spinosa, Digitaria velutina, Euphorbia candelabrum, Ficus thonningii, Heliotropium steudneri, Kigelia africana, Lippia ukambensis, Sarga versicolor, Tricholaena teneriffae and Ziziphus spp. Acacia seyal, Chloris roxburghiana, Digitaria milanjiana, Lonchocarpus eriocalyx, Panicum deustum, Setaria pallide fusca and Setaria sphacelata Abutilon spp., Acacia robusta, Albizia harveyi, Albuca spp., Aloe secundiflora, Blepharis acanthodioides, Chloris pycnothrix, Cissus quadrangularis, Cissus rotundifolia, Commiphora schimperi, Croton dichogamus, Cyperus spp., Cyphostemma spp., Diheteropogon amplectens, Emilia coccinea, Eragrostis aspera, Eriochloa nubica, Ficus ingens, Grewia fallax, Hypoestes forskaolii, Iboza spp., Ipomoea obscura, Jasminum spp., Kedrostis foetidissima, Kyllinga nervosa, Pappea capensis, Pavetta assimilis, Pavonia patens, Pellaea calomelanos, Phyllanthus sepialis, Pupalia lappacea, Rhoicissus revoilii, Sclerocarya birrea, Senna didymobotrya, Sansevieria suffruticosa, Sporobolus pellucidus, Sporobolus stapfianus, Turraea fischeri and Ximenia caffra Olea spp. Panicum repens

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Fig. 2. The Serengeti food web, with groups identified on the basis of Extended Additive Jaccard Similarity (EAJS) represented by different colors. Species are arranged by trophic level from plants (left) to herbivores (middle) to carnivores and omnivores (right). Different shapes indicate types of habitats of the plants including: (G)rassland, (W)oodland, (R)iparian, (K)opje, (S)hrubland, (T)hicket, (D)isturbed and (U)ndetermined. (For interpretation of the reference to colors in this figure legend, the reader is referred to the web version of this article.)

is terrestrial and eats a broad range of terrestrial plants, while Hippopotamus amphibius is an aquatic animal and feeds on nine aquatic plant species. AJS recognized five groups of plants (Groups 14–18 in Fig. 3) that only included one or two species. Plants in these five groups have only one or two particular consumers of their own, and they do not share any consumers. They were separated from other groups of plants because they do not share any consumers other than their particular consumers in common with other plants, and similarity of these plants to other plants is very low by the definition of AJS. 4.2. Cluster validity Groups derived from EAJS consistently had higher Silhouette index values than those from AJS at all levels of classification detail (Fig. 4). This suggests a higher quality of groups, in that species within groups were more similar to each other while species in different groups were more different from each other in terms of their trophic relationships in the food web. Compared to results based on AJS values, the groups of species found on the basis of EAJS also revealed more detailed patterns related to the

habitat segregation of plants and aggregation of animals associated with their body mass. Mean weighted Shannon entropy across the 7 groups of producers identified by EAJS (1.21) was significantly lower than expected by random chance (p b 0.0001), suggesting that plants associated with the same habitat type were significantly clustered in groups. Moreover, species assemblages in Groups 12, 13, and 16 were significantly overrepresented by species with affinities for specific habitat types (Group 12: riparian plants; Group 13: woodland plants; Group 16: kopje plants; all p b 0.005). Mean weighted Shannon of the 10 producer groups identified by AJS suggested an overall clustering of habitats within the groups of plants (1.12 vs. randomized mean value of 1.31, p = 0.00001), but no types of habitat were overrepresented in any individual group (p N 0.05). The grouping of species at the level of carnivores and omnivores (Groups 1–3) reflected the expectation that predators typically consume prey that are smaller than themselves and that larger predators eat prey with a wider range of body sizes than smaller predators. Carnivores in Group 2 (Crocuta crocuta, Lycaon pictus, Panthera leo, Panthera pardus) were large predators (N 50 kg) that feed on a wide range of mammals. In contrast, species in Groups 1 and 3 are smaller

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Fig. 3. The Serengeti food web, with groups identified on the basis of Additive Jaccard Similarity (AJS) represented by different colors. Species are arranged by trophic level from plants (left) to herbivores (middle) to carnivores and omnivores (right). Different shapes indicate types of habitats of the plants including: (G)rassland, (W)oodland, (R)iparian, (K)opje, (S)hrubland, (T)hicket, (D)isturbed and (U)ndetermined.

predators that typically prey on a narrower range of smaller mammals, except for Acinonyx jubatus and Canis aureus in Group 3. The former eats Connochaetes taurinus and the latter eats Equus quagga, both of which are greater than 150 kg. The chi-square test suggested that the three groups of carnivores were differentiated by the body mass of the herbivores they prey on (p = 0.012). The chi-square test suggested that the two types of herbivores' body mass (i.e., small and large) were not evenly distributed among the three groups of carnivores feeding on them (χ2 = 8.78; d.f. = 2; n = 38; p b 0.05). In contrast, the groups developed using AJS did not show the pattern that carnivores or omnivores were assembled on the basis of prey sizes, as those derived using EAJS did. At the level of herbivores, the number of their predators decreases from Group 7 to Group 11, as determined using EAJS. Each species in Group 7 has at least three predator species while those in Group 8 had

two and those in Group 9 had just one. Species in Groups 10 and 11 had no predators. Meanwhile the typical body mass of the species increases from Group 7 to Group 11. In their study of predation patterns of the Serengeti ecosystem, Sinclair et al. (2003) found that ungulates with mean body mass b150 kg are more vulnerable to predators. It is thus worth noting that all the species in Group 7 are b 150 kg, including all five species reported by Sinclair et al. (2003). The wider range of predators of species in Group 7 reflects the vulnerability of these species to predators. Sinclair et al. (2003) also found that the chance of species' mortality caused by predators decreases, as body mass of the species increase. Loxodonta africana (Group 10) and Hippopotamus amphibius (Group 11) are two large mammals with no predators due to their large body size. Once again, no such pattern was observed in groups found by AJS.

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Table 2 Species membership in eighteen groups identified on the basis of Additive Jaccard Similarity (AJS) for the Serengeti food web. Carnivores or omnivores Group 1 Group 2 Herbivores Group 3 Group 4 Group 5 Group 6 Group 7

Group 8 Producers Group 9 Group 10

Group 11

Group 12 Group 13 Group 14 Group 15 Group 16 Group 17 Group 18

Canis mesomelas, Caracal caracal and Leptailurus serval Acinonyx jubatus, Canis aureus, Crocuta crocuta, Lycaon pictus, Panthera leo and Panthera pardus

Papio anubis Heterohyrax brucei, Loxodonta africana, Madoqua kirkii and Procavia capensis Giraffa camelopardalis Pedetes capensis Aepyceros melampus, Alcelaphus buselaphus, Connochaetes taurinus, Damaliscus korrigum, Equus quagga, Nanger granti, Eudorcas thomsonii, Hippopotamus amphibius, Kobus ellipsiprymnus, Ourebia ourebi, Phacochoerus africanus, Redunca redunca, Rhabdomys pumilio, Syncerus caffer and Tragelaphus scriptus Taurotragus oryx

Andropogon schirensis, Chloris gayana, Cymbopogon excavatus, Phragmites mauritianus, Typha capensis Abutilon spp., Acalypha fruticosa, Acacia robusta, Acacia tortilis, Achyranthes aspera, Albizia harveyi, Albuca spp., Allophylus rubifolius, Aloe macrosiphon, Aloe secundiflora, Blepharis acanthodioides, Boscia augustifolia, Capparis tomentosa, Pennisetum ciliare, Chloris pycnothrix, Cissus quadrangularis, Cissus rotundifolia, Commelina africana, Commiphora merkeri, Combretum molle, Commiphora schimperi, Cordia ovalis, Croton dichogamus, Cyperus spp., Cyphostemma spp., Digitaria ternata, Digitaria velutina, Diheteropogon amplectens, Emilia coccinea, Eragrostis aspera, Eriochloa nubica, Ficus glumosa, Ficus ingens, Ficus thonningii, Grewia fallax, Grewia trichocarpa, Heliotropium steudneri, Hibiscus lunariifolius, Hoslundia opposita, Hypoestes forskaolii, Iboza spp., Indigofera basiflora, Ipomoea obscura, Jasminum spp., Kalanchoe spp., Kedrostis foetidissima, Kyllinga nervosa, Lippia ukambensis, Maerua cafra, Ocimum spp., Panicum maximum, Pappea capensis, Pavetta assimilis, Pavonia patens, Pellaea calomelanos, Pennisetum stramineum, Phyllanthus sepialis, Pupalia lappacea, Rhoicissus revoilii, Sclerocarya birrea, Senna didymobotrya, Sansevieria ehrenbergii, Sansevieria suffruticosa, Solanum dennekense, Solanum nigrum, Sporobolus pellucidus, Sporobolus stapfianus, Tricholaena teneriffae, Turraea fischeri, Ximenia caffra and Ziziphus spp. Andropogon greenwayi, Aristida spp., Balanites aegyptiaca, Bothriochloa insculpta, Brachiaria semiundulata, Croton macrostachyus, Cynodon dactylon, Digitaria diagonalis, Digitaria macroblephara, Digitaria scalarum, Dinebra retroflexa, Eragrostis cilianensis, Eragrostis tenuifolia, Eustachys paspaloides, Grewia bicolor, Harpachne schimperi, Heteropogon contortus, Hibiscus spp., Hyparrhenia filipendula, Hyparrhenia rufa, Indigofera hochstetteri, Microchloa kunthii, Panicum coloratum, Pennisetum mezianum, Sida spp., Solanum incanum, Sporobolus fimbriatus, Sporobolus ioclados, Sporobolus pyramidalis and Themeda triandra, Acacia senegal, Acacia seyal, Acacia xanthophloea, Commiphora trothae, Crotalaria spinosa, Digitaria milanjiana, Echinochloa haploclada, Euphorbia candelabrum, Kigelia africana, Olea spp., Panicum deustum and Sarga versicolor, Chloris roxburghiana, Duosperma kilimandscharica, Lonchocarpus eriocalyx, Setaria pallide fusca and Setaria sphacelata, Psilolemma jaegeri and Sporobolus spicatus Eragrostis exasperata Panicum repens Hyperthelia dissoluta Sporobolus festivus

5. Discussion Methods and approaches for reducing the complexity of food webs have grown in recent years because they provide a means for better understanding food web structure and stability and for projecting the potential effects of anthropogenic and natural disturbances on biodiversity and ecosystem integrity. In this study, we aggregated plant and mammal species in the Serengeti using average linkage clustering based on two trophic similarity measures, the Additive Jaccard Similarity (AJS) index and an Extended Additive Jaccard Similarity (EAJS) index. The difference between these two measures is that the latter considers not only the similarity of shared predators and prey at adjacent trophic levels, but rather at all trophic levels associated with the species. This broader interpretation of food web connectance provided by the way that EAJS determines similarity considers the interactions of one species with other species in the network as a whole, without limiting such interactions to immediate feeding relations. In this study groups produced using EAJS fit expectations based on ecological principles better than those derived by AJS at the producer level. For example, Sporobolus festivus was assigned to a single group by AJS (Group 18 in Fig. 3 and Table 2) mainly because it is only eaten by Aepyceros melampus and does not share any consumer other than Aepyceros melampus in common with other plants. The similarity between Sporobolus festivus and Sporobolus fimbriatus, which is eaten by Nanger granti and Eudorcas thomsonii, is zero according to AJS, because they share no consumer in common. AJS failed to capture their similar trophic roles as producers in the food web. In contrast, their similarity is 0.417 according to EAJS, because they share five secondary consumers, including all of the four species in Group 2 and Acinonyx jubatus in Group 3 in Fig. 2. They were thus assigned to the same group (Group

13 in Fig. 2 and Table 1). Overall, AJS underestimated the similarity among the plants in terms of their similar trophic roles as producers in the food web, especially when two plants share few or no consumers in common. The underestimation reduced the cohesion in the groups of plants and accounted for the lower Silhouette index compared to that derived from EAJS. The food web examined in this study did not include any biological information aside from a set of nodes representing species and links representing their interactions. However, the aggregation of species on the basis of EAJS was consistent with ecological expectations associated with: 1) preferred habitat types of plants, and 2) body mass of animals. Like Baskerville et al. (2011), who examined the same food web using Bayesian group modeling, we found that plants from the same habitats tend to be grouped, a result that is logical because habitat types have distinct spatial distributions in the Serengeti. Therefore, the structure at the producer level may partially reflect the flow of energy and nutrition supplying the food web from different spatial locations, with herbivores integrating spatially-segregated groups of plants, and carnivores integrating spatially-widespread herbivores. What most strongly distinguishes our results from those of Baskerville et al. (2011) is the aggregation of herbivores. Baskerville et al. (2011) identified a group of “small herbivores” that included Hippopotamus amphibius, a large mammal, and a miscellaneous group that included herbivores ranging from small (e.g., Madoqua kirkii) to large size (e.g., Loxodonta africana). At the level of herbivores, the aggregation of species on the basis of EAJS differentiated two large mammals, Loxodonta africana and H. amphibius, that have no predator because of their body size. It also identified a group (Group 7) that contained species with small body sizes that are subject to predators. The grouping of carnivores also was related to the weights of the herbivores that they

P. Gao, J.A. Kupfer / Ecological Informatics 30 (2015) 110–118

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0.4 AJS

Silhouette index

0.35 EAJS

0.3 0.25

0.2 0.15 0.1 0.05 0 2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Number of Clusters Fig. 4. Silhouette index of 2 to 20 groups of species in a Serengeti food web based on Additive Jaccard Similarity (AJS) and Extended Additive Jaccard Similarity (EAJS).

prey upon. Therefore, the aggregation of species on the basis of EAJS provided a stronger and clearer pattern associated with animal weights. Capturing the complexity of food webs is essential to understanding how energy and materials flow through and cycle within ecosystems via feeding relationships (Gall et al., 2015) and to assessing the robustness of ecosystems to species extinction (Calizza et al., 2015), climate change (Camacho et al., 2015; Seifert et al., 2015) and anthropogenic impacts (Chen et al., 2011; Chen et al., 2015). In addition to patterns related to the habitat structure of plants and animal body mass, the clustering of species by EAJS may provide valuable information to maintain the ecosystem stability and functioning and suggest the channels through which energy and materials flow in the Serengeti ecosystem. The clustering based on EAJS identifies the groups of producers that support the carnivores and omnivores that comprise Groups 1–3 (Fig. 2). Species in Group 3 (with one exception) rely solely on producers in Group 13. Groups 1 and 2 are ultimately supported by plants in various producer groups, but they have different primary producer groups providing food sources. Group 2 relies primarily on plants in Group 13. In contrast, the four species that serve as prey of Caracal caracal in Group 1 (especially Procavia capensis in Group 5) eat not only plants in Group 13, but also many of the plants in Group 16. Although the amount of energy passing through each feeding link is not available, our classification identifies the importance of plants in Group 13, which are the sole producers supporting the four carnivores and omnivores in Group 3 and the primary producers supporting Group 2. Groups 2 and 3 contain 8 out 9 carnivores and omnivores in the Serengeti ecosystem. 6. Conclusion In this study, we developed a novel trophic similarity measure, Extended Additive Jaccard Similarity (EAJS), that considers not only the similarity of shared predators and prey at adjacent trophic levels but at all the trophic levels. Aggregation of species for the Serengeti ecosystem based on EAJS was compared to the groups of species derived on the basis of the more widely used Additive Jaccard Similarity (AJS). Compared to groups identified on the basis of AJS values, those derived using EAJS had greater within-group similarity in terms of species' trophic relationships and greater discrimination vs. those in other groups. Groups derived from EAJS values also better reflected ecological factors known to structure food webs, including habitat type (especially for plants) and body mass (especially for animals). The advantage of EAJS lies in the fact that it considers species feeding relations in food webs in a broad scale (i.e., not limited to adjacent trophic levels). Our approach provides a means for revealing the patterns of trophic relations among species in food webs and exploring known and unknown factors shaping food web structure.

Acknowledgments This work was supported by a Dean's Dissertation Fellowship from the College of Arts and Sciences at the University of South Carolina to the lead author.

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