The calculated voyage: benchmarking optimal strategies and consumptions in the Japanese eel's spawning migration

Eels migrate along largely unknown routes to their spawning ground. By coupling Zermelo's navigation solution and data from the Japan Coastal Ocean Predictability Experiment 2 (JCOPE2M), we simulated a range of seasonal scenarios, swimming speeds, and swimming depths to predict paths that minimize migration duration and energy cost. Our simulations predict a trade-off between migration duration and energy cost. Given that eels do not refuel during their migration, our simulations suggest eels should travel at speeds of 0.4-0.6 body-length per second to retain enough energy reserves for reproduction. For real eels without full information of the ocean currents, they cannot optimize their migration in strong surface currents, thus when swimming at slow swimming speeds, they should swim at depths of 200 m or greater. Eels swimming near the surface are also influenced by seasonal factors, however, migrating at greater depths mitigates these effects. While greater depths present more favorable flow conditions, water temperature may become increasingly unfavorable, dropping near or below 5 °C. Our results serve as a benchmark, demonstrating the complex interplay between swimming speed, depth, seasonal factors, migration time, and energy consumption, to comprehend the migratory behaviors of Japanese eels and other migratory fish.