Niche and neutral processes leave distinct structural imprints on indirect interactions in mutualistic networks

Indirect interactions are central to ecological and evolutionary dynamics in pollination communities, yet we have little understanding about the processes determining patterns of indirect interactions, such as those between pollinators through shared flowering plants. Instead, research has concentrated on the processes responsible for direct interactions and whole-network structures. This is partly due to a lack of appropriate tools for characterising indirect interaction structures, because traditional network metrics discard much of this information. The recent development of tools for counting motifs (subnetworks depicting interactions between a small number of species) in bipartite networks enable detailed analysis of indirect interaction patterns. Here we generate plant-hummingbird pollination networks based on three major assembly processes – neutral effects (species interacting in proportion to abundance), morphological matching and phenological overlap – and evaluate the motifs associated with each one. We find that different processes produce networks with significantly different patterns of indirect interactions. Neutral effects tend to produce densely-connected motifs, with short indirect interaction chains, and motifs where many specialists interact indirectly through a single generalist. Conversely, niche-based processes (morphology and phenology) produced motifs with a core of interacting generalists, supported by peripheral specialists. These results have important implications for understanding the processes determining indirect interaction structures.


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Species in a community are often influenced by other species they do not interact with directly 55 (Strauss, 1991;Wootton, 1994Wootton, , 2002. Such indirect interactions are a fundamental component 56 of communities, governing ecological and evolutionary processes as much as, or more than,     For each of these sets of abundance, morphology and phenology data, we generated matrices  Neutrality was simulated using an abundance matrix, A. Elements of A were the product of 117 each species' relative abundance. Thus, element aij represents the interaction probability 118 between plant species i and hummingbird species j and is equal to the product of the relative 119 abundances of i and j. This matrix therefore represents neutrality: the likelihood of species 120 interacting randomly in proportion to their abundance. 121 We create two morphological match matrices, corresponding to two different methods in the hummingbird bill length (Weinstein & Graham, 2017). This approach relaxes the assumption 132 that a hummingbird is equally likely to interact with all flowers that have a floral corolla equal 133 to or shorter than its bill, and makes morphological match a continuous, rather than binary, 134 quantity. If the difference between floral corolla depth and hummingbird bill length was 0, the 135 difference was set to the minimum non-zero difference between corolla depth and bill length 136 in the web to prevent errors when dividing by zero values.

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Elements of the phenological overlap matrix, P, were calculated using matrix multiplication  For each assembly process, and for each dataset, we generated 1000 binary interaction matrices 144 from the probability matrix using the 'mgen' function in the 'bipartite' R package (Dormann,145 Frund, Bluthgen, & Gruber, 2009). In total there were 96,000 binary matrices (1000 generated 146 matrices ´ four assembly processes ´ 24 sets of abundance, morphology and phenology data).

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Generated matrices had the same connectance as their corresponding empirical matrices.

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Characterising indirect interactions using motifs 149 We next characterised the different patterns of indirect interactions for each network and  Macro-scale metrics, such as modularity, nestedness and connectance, summarise the structure of the whole 174 network. Micro-scale metrics, such as d´, degree or dependencies, characterise the structure of a single node.

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Motifs sit between these two extremes, at the meso-scale, capturing local-scale patterns of indirect interactions 176 between species. The 'meso-scale' level shows the five types of motif that make up the macro-scale network.

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Note that the network itself is a four-species motif and so, for this example, we only consider motifs with fewer 178 than four species (two-and three-species motifs). Importantly, motifs do not discard information about macro-  pathways than the main set of core-peripheral motifs, and thus slightly stronger indirect effects.

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As the generalists in these motifs might be able to buffer changes in each other's abundances, 231 it is likely that the generalists have a stronger effect on the specialist, than vice versa (Simmons,232 Cirtwill, et al., 2019). The specialist species' generalist partner has high levels of redundancy 233 in its interactions and thus may be a reliable partner for the specialist. However, asymmetric 234 complete motifs are likely less effective than core-peripheral motifs at curbing the spread of     Statistical analysis 295 We used an ANOVA framework to assess statistical differences between the frequencies of 296 motifs in networks generated using different assembly processes. First, a MANOVA was used 297 with frequencies of all 16 motifs as dependent variables and assembly process as the 298 independent variable to determine whether there was an overall effect of assembly process on 299 motif frequency distribution. Then, to identify how assembly processes affect specific 300 dependent variables, we conducted univariate ANOVAs for each motif. For this, pairwise 301 comparisons between assembly processes were calculated using the 'multcomp' R package 302 (Hothorn, Bretz, & Westfall, 2008). Adjusted p-values were used to account for multiple 303 comparisons, using the 'single-step' method in 'multcomp'. with more occurrences of core-peripheral motifs (motifs 5, 10 and 14) (Figures 1b, 3 and 4). 311 Furthermore, some differences were observed between morphological matching and 312 phenological overlap matrices: phenological overlap matrices had significantly higher 313 frequencies of motif 9 (a core-peripheral motif) than morphological matching, but significantly 314 lower frequencies of motif 14 (another core-peripheral motif; Figures 1b, 3 and 4).  asymmetric complete motifs 6, 11, 12 and 16) (Figures 3 and 4). Conversely, networks 344 produced assuming niche-based processes -those determined by morphology or phenology -345 contain more core-peripheral motifs, that comprise a core of interacting generalists, supported 346 by peripheral specialists (core-peripheral motifs 5, 10, 14) (Figures 3 and 4).  This has important implications for whole-network dynamics, as it suggests that under neutral 379 processes, the average length of the interaction chain between any two species will be lower,

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While there were few differences between different niche-based processes, networks based on 408 phenological overlap had significantly higher frequencies of motif 9 (a core-peripheral motif 409 with two generalists interacting) and significantly lower frequencies of motif 14 (a core-410 peripheral motif with three generalists interacting) than morphological matching models. This