Concomitant predation on parasites is highly variable but constrains the ways in which parasites contribute to food web structure

Summary Previous analyses of empirical food webs (the networks of who eats whom in a community) have revealed that parasites exert a strong influence over observed food web structure and alter many network properties such as connectance and degree distributions. It remains unclear, however, whether these community‐level effects are fully explained by differences in the ways that parasites and free‐living species interact within a food web. To rigorously quantify the interrelationship between food web structure, the types of species in a web and the distinct types of feeding links between them, we introduce a shared methodology to quantify the structural roles of both species and feeding links. Roles are quantified based on the frequencies with which a species (or link) appears in different food web motifs – the building blocks of networks. We hypothesized that different types of species (e.g. top predators, basal resources, parasites) and different types of links between species (e.g. classic predation, parasitism, concomitant predation on parasites along with their hosts) will show characteristic differences in their food web roles. We found that parasites do indeed have unique structural roles in food webs. Moreover, we demonstrate that different types of feeding links (e.g. parasitism, predation or concomitant predation) are distributed differently in a food web context. More than any other interaction type, concomitant predation appears to constrain the roles of parasites. In contrast, concomitant predation links themselves have more variable roles than any other type of interaction. Together, our results provide a novel perspective on how both species and feeding link composition shape the structure of an ecological community and vice versa.


S1. Additional References and Description of Food Webs
: Locations and original sources for food-web datasets. The Ythan web used is version 3 from Huxham, Beaney & Raffaelli (1996). Following Huxham, Beaney & Raffaelli (1996), species 100 in this web was removed as it is an animal with no recorded resources in the food web. This also resulted in the removal of one link 100 → 85 where species 100 appeared as a resource.
14 Table S2: Representation of each type of species across the different food webs. Type "free-living" refers to webs with free-living species only while type "par & con" refers to "parasite" and "concomitant" webs which include parasites and free-living species. S refers to the total species richness in each web.
→ P to the number of links describing predation among free-living species, parasitism, predation between parasites, target predation of free-living species on parasites, and concomitant predation on parasites, respectively. Note that neither F t − → P nor P → P links were observed in the Ythan web.

Site
Type   Figure S1: Three-species motifs with unique positions numbered.

S2. Quantifying Species' and Links' Roles
Interactions between species are a direct consequence of the motif structure of 16 a food web. Motifs are the set of 13 three-species subwebs describing all possible 17 interaction patterns of three species (Milo et al., 2002;Stouffer et al., 2007, Fig. S1). within its food web, The same process was used to determine the roles of links between species, giving a vector that describes the role − → f w sl for each link l in community s in web type w.

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As described in the main text, we quantified the distribution of species' and links' 32 roles by their role dispersion and role diversity (Fig. 2, main text). In order to 33 quantify role diversity, we first needed to identify subsets of species (or links) that 34 have statistically-similar motif-based roles; that is, clusters of species (or links) that 35 appear in the same motif positions more often than one would expect by chance.

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To perform a clustering of this nature, we followed a recently-proposed method 37 that is an extension of community detection algorithms for complex networks to as "modularity") that is high when nodes in the same cluster tend to occupy the 45 same positions with similar frequencies and low otherwise (Stouffer et al., 2012). 46 We used a stochastic and heuristic optimisation method known as simulated annealing (Kirkpatrick, Gelatt & Vecchi, 1983) to cluster nodes (species or links) 48 while maximising modularity (Sales-Pardo et al., 2007;Girvan & Newman, 2002).

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Since this procedure is not always guaranteed to find a global optimum, and since 50 we are most interested in the expected variety of clusters per group as a proxy 51 for role diversity, we performed this modularity maximisation 100 separate times 52 for roles of species and links in each community. As with dispersion, we included 53 the roles of free-living species from the "free-living" web as well as the roles of 54 parasites from both the "parasite" and "concomitant" webs. We then calculated 55 the weighted average number of clusters containing each type of species (or link) 56 across the 100 modularity-maximised clusterings following where M i is the modularity of a given clustering i, k e M k is the sum of mod-58 ularities over all k clusterings, and p i is the relative probability of obtaining a

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When comparing across different types of species, we found that trophic group was The first major axis of variation for species roles corresponded to a split between positions in motifs containing only one-way interactions and positions in motifs containing at least one two-way interaction. This axis separates the roles of parasites including concomitant predation from other types of roles (Fig. 3A). The second major axis was largely defined by positions representing the base of a three-species food chain (3) and a species with two predators which do not eat each other. These positions are most common in the roles of basal resources. (B) The first major axis of variation for link roles also corresponds to a split between positions in motifs that contain only one-way interactions and those in motifs containing at least one two-way interaction. Positions associated with two-way interactions were more frequent in the roles of concomitant predation links than in other role types (Fig. 3B). The second axis is largely determined by two positions representing mutual predation between species with a common prey or common predator. These positions are most common in the roles of links describing predation between parasites.

S5. Species roles
Dispersion 104 We determined the overall relationship between species-richness and role dispersion 105 using the model 106 σ gs = β 1 B g + β 2 I + g + β 3 T g + β 4 P g + β 5 P cg + β 6 N gs + β 6 P g N gs . (4) where σ gs is the dispersion of group g (B, I, T, P, or P c ) in community s 107 (e.g., Ythan), B g , I g , T g , P g , and P cg are dummy variables that equal 1 if g is the 108 corresponding group type (i.e., B g =1 if g represents the roles of basal resources),

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N gs is the number of species N in group g at community s, and P g N gs represents 110 the number of species N in group g at community s if g represents the roles of 111 parasites without concomitant predation links.

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We then removed the non-significant overall effect of species richness (Table   113 S4), leaving the model, which was used to compare the dispersions of B, I, T, and P c roles as well as 115 the slope of P role dispersion over species richness. We tested the effect of species richness on role diversity using the model, 119 δ gs = β 1 B g + β 2 I g + β 3 T g + β 4 P g + β 5 P cg + β 6 N gs ,

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where δ gs is the role diversity of trophic group g in community s and all other 120 symbols are as in the dispersion models above. Only P c roles had a diversity 121 significantly different from zero and there was no significant effect of species rich-122 ness. This model was also used in the Tukey's HSD test of mean diversities across 123 groups, as the reduced model used to establish the mean diversity of P c roles, 124 δ gs = β 0 + β 1 P cg + β 2 N gs , did not include intercepts for other role types (Table S5). We examined the effect of link richness on the dispersion of link roles using the 129 model, where σ ls is the dispersion of the roles of link type l in community s, F → F l ,

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We then used the reduced model, which includes an effect of link richness for P → P roles only, to calculate the 141 confidence intervals in Fig. 6 (main text). The best parameter estimates returned 142 by the two models were very similar (Table S6). Finally, we determined that there was no effect of link richness on link role diversity 146 using the model where N ls is the role diversity for link type l in community s and all other 148 symbols are as above. We then used the model to generate confidence intervals in Fig. S4. Although the estimated diversities 150 for each link type differed between models (Table S7), the standard errors on these 151 estimates were large, such that different types of links did not have significantly 152   Figure S4: Diversity of unique roles was not related to the number of links in a community for any link type. Diversity of unique roles did not differ across link types.