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

Abstract

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.

Keywords: Eel; Energy consumption; Migration; Ocean current; Optimization; Swimming speed and depth.

Fig. 1

Comparison of Oceanic Flow Fields for Winter and Summer Scenarios at the shallowest and deepest depths used in this study. (a) Surface-level (0 m) flow field in the Winter Scenario; (b) Deep-sea (700 m) flow field in the Winter Scenario; (c) Surface-level (0 m) flow field in the Summer Scenario; (d) Deep-sea (700 m) flow field in the Summer Scenario. The Winter Scenario flow field is derived from the average monthly flow for January 2020, while the Summer Scenario is based on the average monthly flow for July 2020. The spawning area is indicated by ‘goal’. Please note that the color scale bars differ between the panels.

Fig. 2

Optimal migration path in the Winter Scenario at Various Depths. Panels (a1–a4) depict optimal migration paths at the surface (Depth = 0 m); panels (b1–b4) illustrate optimal migration paths at a moderate depth (Depth = 200 m); panels (c1–c4) present optimal migration paths in the deep sea (Depth = 600 m). The color along the optimal migration path indicates the migration time from the arbitrary start point to the spawning area (indicated by ‘goal’). At D = 0, the position of the Kuroshio current is marked with a black dashed line to visually represent the interaction between the migratory paths and the ocean currents.

Fig. 3

Statistical analysis across all established optimal migration paths to major habitats (Fig. S1, Supplementary Information) in the Winter Scenario. (a1) The variation of the Tortuosity Index ${\eta }_{\text{tort}}$ with respect to swimming speed U, indicating that higher speeds result in straighter optimal migration paths. (a2) The variation of ${\eta }_{\text{tort}}$ with respect to swimming depth D, showing that greater depths lead to straighter optimal migration paths. (b1) The variation of Swimming Distance $S_{\text{swim}}$ with respect to swimming speed, indicating that higher speeds may slightly reduce swimming distance. (b2) The variation of $S_{\text{swim}}$ with respect to time swimming depth, showing that greater depths lead to less swimming distance. (c1) The variation of optimal migration time with respect to swimming speed, indicating that higher speed significantly reduces migration time. (c2) The variation of optimal migration time with respect to swimming depth. (d1) The variation of fat consumption with respect to swimming speed. (d2) The variation of fat consumption with respect to swimming depth. In (d1) and (d2), two groups of results based on different fat consuming criterions are displayed, where “hydrodynamic measurement” group represents the results using Eq. (2), and “metabolic measurement” group represents the results using Eq. (3). For each panel, Pearson correlation coefficient (Pc) is displayed at upper-right corner. Linear regression analyses on all the data in Fig. 3 are provided in Supplementary Information, §S5.

Fig. 4.

20-year Standard deviation of ocean current vector field at various depths. (a) on each January 1 from 2001 to 2020, and (b) on each July 1 from 2001 to 2020.

Fig. 5

Monthly Standard deviation of ocean current vector field at various depths. (a) in January, 2020, and (b) in July, 2020.

Fig. 6

Water temperature at various depth. (a) Monthly average in January, 2020, and (b) monthly average in July 2020.