The assembly of local communities from regional pools is a multifaceted process that involves the confluence of interactions and environmental conditions at the local scale and biogeographic and evolutionary history at the regional scale. Understanding the relative influence of these factors on community structure has remained a challenge and mechanisms driving community assembly are often inferred from patterns of taxonomic, functional, and phylogenetic diversity. Moreover, community assembly is often viewed through the lens of competition and rarely includes trophic interactions or entire food webs. Here, we use motifs -subgraphs of nodes (e.g. species) and links (e.g. predation) whose abundance within a network deviates significantly as compared to a random network topology -to explore the assembly of food web networks found in the leaves of the northern pitcher plant Sarracenia purpurea. We compared counts of three-node motifs across a hierarchy of scales to a suite of null models to determine if motifs are over-, under-, or randomly represented. We then assessed if the pattern of representation of a motif in a given network matched that of the network it was assembled from. We found that motif representation in over 70% of site networks matched the continental network they were assembled from and over 75% of local networks matched the site networks they were assembled from for the majority of null models. This suggests that the same processes are shaping networks across scales. To generalize our results and effectively use a motif perspective to study community assembly, a theoretical framework detailing potential mechanisms for all possible combinations of motif representation is necessary.

BackgroundBiological networks provide great potential to understand how cells function. Network motifs, frequent topological patterns, are key structures through which biological networks operate. Finding motifs in biological networks remains to be computationally challenging task as the size of the motif and the underlying network grow. Often, different copies of a given motif topology in a network share nodes or edges. Counting such overlapping copies introduces significant problems in motif identification.ResultsIn this paper, we develop a scalable algorithm for finding network motifs. Unlike most of the existing studies, our algorithm counts independent copies of each motif topology. We introduce a set of small patterns and prove that we can construct any larger pattern by joining those patterns iteratively. By iteratively joining already identified motifs with those patterns, our algorithm avoids (i) constructing topologies which do not exist in the target network (ii) repeatedly counting the frequency of the motifs generated in subsequent iterations. Our experiments on real and synthetic networks demonstrate that our method is significantly faster and more accurate than the existing methods including SUBDUE and FSG.ConclusionsWe conclude that our method for finding network motifs is scalable and computationally feasible for large motif sizes and a broad range of networks with different sizes and densities. We proved that any motif with four or more edges can be constructed as a join of the small patterns.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-1271-7) contains supplementary material, which is available to authorized users.

Background Biological networks describes the mechanisms which govern cellular functions. Temporal networks show how these networks evolve over time. Studying the temporal progression of network topologies is of utmost importance since it uncovers how a network evolves and how it resists to external stimuli and internal variations. Two temporal networks have co-evolving subnetworks if the evolving topologies of these subnetworks remain similar to each other as the network topology evolves over a period of time. In this paper, we consider the problem of identifying co-evolving subnetworks given a pair of temporal networks, which aim to capture the evolution of molecules and their interactions over time. Although this problem shares some characteristics of the well-known network alignment problems, it differs from existing network alignment formulations as it seeks a mapping of the two network topologies that is invariant to temporal evolution of the given networks. This is a computationally challenging problem as it requires capturing not only similar topologies between two networks but also their similar evolution patterns. Results We present an efficient algorithm, Tempo , for solving identifying co-evolving subnetworks with two given temporal networks. We formally prove the correctness of our method. We experimentally demonstrate that Tempo scales efficiently with the size of network as well as the number of time points, and generates statistically significant alignments—even when evolution rates of given networks are high. Our results on a human aging dataset demonstrate that Tempo identifies novel genes contributing to the progression of Alzheimer’s, Huntington’s and Type II diabetes, while existing methods fail to do so. Conclusions Studying temporal networks in general and human aging specifically using Tempo enables us to identify age related genes from non age related genes successfully. More importantly, Tempo takes the network alignment problem one huge step forward by moving beyond the classical static network models.

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