Combining network theory and reaction–advection–diffusion modelling for predicting animal distribution in dynamic environments

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Abstract Movement is a key process driving animal distributions within heterogeneous landscapes. Graph (network) theory is increasingly used to understand and predict landscape functional connectivity, as network properties can provide crucial information regarding the resilience of a system to landscape disturbances, e.g. removal of habitat patches. The temporal dimension of movement patterns, however, is not generally included in network analysis, which can lead to a discrepancy between observed space use and landscape connectivity. Reaction–advection–diffusion models, when coupled with network analysis, could provide a powerful mechanistic framework based upon spatio‐temporal dimensions of animal movement, but this approach remains poorly developed for ecological studies. We developed a mechanistic space use model that considers both residency time in resource patches and movement amongst those patches within a spatial network. The framework involves two main steps: first, the network topology that best reflects functional connectivity for the study system is identified; second, a spatio‐temporal flow dynamic is implemented within the network using reaction–advection–diffusion modelling. To illustrate the approach, we used observations of radiocollared plains bison Bison bison bison that were travelling in a meadow network within a forest matrix. In the model application, we found that the graph best reflecting the functional connectivity of bison was a complex graph of ultra‐small world scale‐free network type. The reaction–advection–diffusion model involved the effect of meadow area and inter‐meadow distance on bison travels. Simulations showed that a simple graph or distance‐based graphs provided less accurate predictions of bison distribution, while also predicting different management actions to effectively impact bison space use. Our study demonstrates how reaction–advection–diffusion modelling, coupled with network theory, can provide a robust mechanistic framework for predicting animal distribution in dynamic environments. The modelling approach can be applied to a large range of systems that are subjected to rapid environmental changes due to habitat management or natural resource extraction, for example. Furthermore, our study demonstrates that management and conservation planning can strongly depend upon network structure, and that a faulty assessment of network topology can result in poor planning, with potential unexpected impacts on animal distributions.