Ecological networks such as plant-pollinator systems vary systematically in space and time. This variability includes fluctuations in global network properties such as total number and intensity of interactions in the network, but also in the local properties of individual nodes, such as the number and intensity of species-level interactions. Fluctuations of local properties can significantly affect higher-order network features, e.g. robustness and nestedness. These fluctuations should therefore be controlled for in applications that rely on null models, including pattern detection, perturbation experiments and network reconstruction from limited observations. By contrast, most randomization methods used by ecologists treat node-level local properties as hard constraints that cannot fluctuate. Here we synthesise a set of methods based on the statistical mechanics of networks, which we illustrate with some practical examples. We illustrate how this approach can be used by experimental ecologists to study the statistical significance of network patterns and the rewiring of networks under simulated perturbations. Modelling species heterogeneity, while allowing for local fluctuations around a theoretically grounded notion of structural equilibrium, will offer a new generation of models and experiments to understand the assembly and resilience of ecological networks.
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