Fluctuating ecological networks: A synthesis of maximum-entropy approaches for pattern detection and process inference

1. Ecological networks such as plant–pollinator systems and food webs vary in space and time. This variability includes fluctuations in global properties such as the total number and intensity of interactions in the network but also in the number and intensity of local (i.e. node level) species interactions. 2. Fluctuations of species' properties can significantly affect higher-order network features, for example, robustness and nestedness, and should therefore be taken into account in null models for pattern detection and hypothesis testing. 3. In ecological research, classical null models treat node-level properties as ‘hard’ constraints that cannot fluctuate. Here, we review and synthesize a set of maximum-entropy methods that allow for fluctuating (‘soft’) constraints, offering a new addition to the classical toolkit of the ecologist. We illustrate the methods with some practical examples, pointing to currently available open-source computer codes. We clarify how this approach can be used by experimental ecologists to detect non-random patterns with null models that not only rewire, but also redistribute interaction strengths by allowing fluctuations in the enforced constraints. 4. Explicit modelling of interspecific heterogeneity through local (i.e. species level) fluctuations of topological and quantitative constraints offers a statistically robust and expanded (e.g. including weighted links) set of tools to understand the assembly and resilience of ecological networks