PS 32-190 - Saving time: A framework for quick estimates of optimal swim speed in fish applied to decision making during upstream migration

Abstract: Estimations of metabolic costs are valuable tools for ecologists to study optimal decision making in animals. Such evaluations require careful consideration of constraints, such as exhaustion and additional costs due to anaerobic activity, especially when evaluating decision making over long periods time. However, complex models of optimal decision making can become computationally expensive and slow to execute. Our goal was to develop a framework for estimating optimal fish swim speed based on a complex metabolic model, while limiting the time-consuming process of optimizing the function for swim speed; we then applied this framework to spatio-temporally explicit decision making during upstream migration. The metabolic model used here accounted for metabolic and swimming costs and recovery from exhaustion and due to anaerobic activity (in J/s). The costs were weighted against the difference between swim speed and water velocity (i.e., cost of travel [COT] in J/m). We used the optimize function in R to calculate optimal swim speed at a given velocity (thereby minimizing COT) as a baseline for our framework. The model indicated that optimal swim speed occurred in three stages: 1) relatively slow, aerobic movement; 2) movements at the maximum sustainable aerobic swim speed; and 3) very fast, unsustainable anaerobic swim speeds. Our framework parameterized the endpoints of these stages so that optimal swim speed could be calculated without further optimization using only water velocity as an input. We then tested this in a gridded, spatio-temporally explicit environment in which each cell (20 x 20 m) contained parameters such as temperature, water velocity, and depth that changed on daily ticks. Fish migrated nearly 9 km upstream from cell to cell based on simple rules. The ideal path between two endpoints was the one that minimized total energy costs (in J), which were calculated with the original metabolic function using our estimate for optimal swim speed and the distance traveled from one cell to another. The path with minimum total cost was determined using Dijkstra’s algorithm. This analysis yielded realistic paths through the environment and total costs for traversing the paths. This technique provides valuable predictions for A/B testing different flow and temperature regimes that can occur due to anthropogenic changes, including damming, bank stabilization of rivers, and global warming. The approach outlined here is general enough that it can be applied to many species. The computation time saved also facilitates analyses of relatively large environments over long time scales.