Ecological Network Metrics: Opportunities for Synthesis

Network ecology provides a systems basis for approaching ecological questions, such as factors that influence biological diversity, the role of particular species or particular traits in structuring ecosystems, and long-term ecological dynamics (e.g., stability). Whereas the introduction of network theory has enabled ecologists to quantify not only the degree, but also the architecture of ecological complexity, these advances have come at the cost of introducing new challenges, including new theoretical concepts and metrics, and increased data complexity and computational intensity. Synthesizing recent developments in the network ecology literature, we point to several potential solutions to these issues: integrating network metrics and their terminology across sub-disciplines; benchmarking new network algorithms and models to increase mechanistic understanding; and improving tools for sharing ecological network research, in particular “model” data provenance, to increase the reproducibility of network models and analyses. We propose that applying these solutions will aid in synthesizing ecological subdisciplines and allied fields by improving the accessibility of network methods and models.


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Interactions are at the heart of ecology and drive many of its key questions. What are From the perspective of the broader field of ecology, the proliferation of con-216 cepts, terms, and metrics is not a new issue (e.g., Ellison et al. 2005;Tansley 1935). 217 Ecologists have a long history of using network concepts and related models in mul-218 tiple subdomains (e.g., metapopulations, matrix population models, community co-219 occurrence models, ecosystems) without fully recognizing or capitalizing on the sim-220 ilarities of the underlying models. Each subdomain has constructed its own concepts 221 and methods (occasionally borrowing from other areas), and established its own jar-

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The OBO could provide a platform for harmonizing ecological network metrics, 239 terms, and concepts. Key obstacles to such harmonization include a requirement that 240 network ecologists work within a common framework, and the need for an individual 241 or leadership team to periodically curate the ontology based on new developments in 242 the field. In determining the best course of action, network ecologists could follow the 243 example of how similar OBO projects have been managed in the past. The FOODON 244 food role ontology project (http://www.obofoundry.org/ontology/foodon.html) 245 contains information about "materials in natural ecosystems and food webs as well 246 as human-centric categorization and handling of food." It could serve as an example 247 or even the basis of a ecological network metric ontology.

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Benchmarking: Trusting our models of mechanisms 249 Inferences about processes in ecological systems have relied in part on the application 250 of simulation models that generate matrices with predictable properties. As discussed 251 in the previous section, the proliferation of network metrics points to the need for 252 the investigation and comparison of how these metrics will behave in the context 253 of different modeling algorithms. Once a metric or algorithm has been chosen, it 254 is tempting apply them widely to empirical systems to detect patterns, but before 255 research proceeds, a process of "benchmarking" with artificial matrices that have 256 predefined amounts of structure and randomness should be used to examine the 257 behavior of the algorithms and the metrics that are applied to them.

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In addition to the random matrix approaches of null and ER models, there are 291 other, more complex algorithms that are used to generate structured matrices. Per-292 haps one of the best known in network theory is the Barabasi-Albert (BA, Barabási   293 and Albert 1999) model, which adds nodes and edges to a growing network with 294 a greater probability of adding edges to nodes with a higher degree. The BA algo-295 rithm is similar to ecological network algorithms that generate non-random structure, 296 because of either direct influence or similar processes operating in systems of inter-297 est. Some of these models include processes of "preferential attachment" in which 298 organisms tend to interact with the same, common species. Food-web modeling algo-299 rithms also have been developed that use a trait-based approach (e.g., Allesina and

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The statistical behavior of some models and metrics can be understood ana-304 lytically. For example, the networks generated by the BA algorithm display degree 305 distributions that approximate a power-law distribution, like many real-world "scale- is imperative for advancing the field.

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Sharing data and open-source code have become established in ecology, and net-328 work ecologists are now producing more network models and data (e.g., Fig. 1A).

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These include not only ecological interaction networks, but also an influx of other rele-  should reveal an increasing curve, and will indicate the signal-to-noise ratio below 935 which the test cannot distinguish the pattern from randomness. Alternatively, one 936 can begin with a purely random matrix but embed in it a non-random substructure, ness and connectance, but they discarded webs with unconnected nodes and subwebs 947 because these topologies were not observed in the empirical webs. A "stub recon-948 struction" algorithm builds a topology that is constrained to the observed number 949 of edges per node (Newman et al. 2001). Each node is assigned the correct number 950 of edges, and then nodes are successively and randomly paired to create a growing 951 network. However, this algorithm also generates multiple edges between the same 952 two nodes, which must be discarded or otherwise accounted for. Maslov and Sneppen for every node by swapping edges randomly between different pairs of nodes. This 955 algorithm is closely analogous to the swap algorithm used in species co-occurrence 956 analyses that preserves the row and column totals of the original matrix (Connor 957 and Simberloff 1979). The more constraints that are added to the algorithm, the 958 less likely it is that simple sampling processes can account for patterns in the data.

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However, some constraints, such as connectivity or matrix density, may inadvertently 960 "smuggle in" the very processes they are designed to detect. This can lead to the 961 so-called "Narcissus" effect (Colwell and Winkler 1984 Borrett (2013) General G Chain Length Number of edges between two nodes in a group Food-Web G Average Path Length The average number of times a unit of matter or energy travels from one compartment to another before exiting the ecosystem