Pathways: An Algorithm for Modeling Multiple Swimming Paths between Habitats and Their Energetic Costs in a 2D Flow Field

Based on a 2D velocity field on a structured grid, the Pathways algorithm analyzes potential swimming paths of fish between a starting point and defined target habitats (Holzapfel et al., 2026). The hydraulic inputs required for the algorithm include node numbers, the x and y coordinates of the calculation nodes, the x and y components of the flow velocity vector, and the water depth across the entire computational grid. Pathways models potential fish paths by allowing movement from the center of one cell to the centers of its four neighboring cells, as well as across the diagonals. To provide additional movement options, eight additional directions were incorporated into the code. These additional directions allow movement between the centers of two neighboring cells to the center of the next cell. Different swimming modes are implemented in the Pathways algorithm, and the swimming mode used to calculate the energy costs for dispersal from the starting patch depends on flow velocity, flow direction, and the modeled fish length (l). The fish length l must be provided as a model parameter. Threshold values that determine the transition between different swimming modes are variables in the code, allowing for flexibility and adaptability to different hydrodynamic and biological scenarios. The available paths for fish movement between habitats in a river section are evaluated based on the energy required for swimming, which is calculated as the time integral of the power P needed to swim at a relative velocity Ur through a fluid velocity field u. ********************************************************************************************************************************************************************************** Holzapfel, P., Wildt, D., Schmalfuss, L., Pasternack, G., Hauer, C. (2026). Quantifying connectivity between functional fish habitats: A novel energy-based approach assessing multiple pathways. Ecological Modeling, 515, 111515. https://doi.org/10.1016/j.ecolmodel.2026.111515