Route optimisation and solving Zermelo's navigation problem during long distance migration in cross flows

Abstract

The optimum path to follow when subjected to cross flows was first considered over 80 years ago by the German mathematician Ernst Zermelo, in the context of a boat being displaced by ocean currents, and has become known as the 'Zermelo navigation problem'. However, the ability of migrating animals to solve this problem has received limited consideration, even though wind and ocean currents cause the lateral displacement of flyers and swimmers, respectively, particularly during long-distance journeys of 1000s of kilometres. Here, we examine this problem by combining long-distance, open-ocean marine turtle movements (obtained via long-term GPS tracking of sea turtles moving 1000s of km), with a high resolution basin-wide physical ocean model to estimate ocean currents. We provide a robust mathematical framework to demonstrate that, while turtles eventually arrive at their target site, they do not follow the optimum (Zermelo's) route. Even though adult marine turtles regularly complete incredible long-distance migrations, these vertebrates primarily rely on course corrections when entering neritic waters during the final stages of migration. Our work introduces a new perspective in the analysis of wildlife tracking datasets, with different animal groups potentially exhibiting different levels of complexity in goal attainment during migration.

Commuting fruit bats beneficially modulate their flight in relation to wind

“…Yet, in this case, drift explained only 7% of the variation in bat sideways speed, and thus the magnitude of this effect was subtle, at most. We note that the pattern of overcompensation at the beginning of the flight trajectory and drift near the end of the track is predicted by the solution of Zermelo's navigational problem [2].…”

“…We consequently suggest that behavioural adjustments aiming to minimize the cost of transport under various wind conditions have independently evolved in various aerial animal taxa. This demonstrates a wide generalization in responding to external factors during movement (sensu [43]) despite different ecological contexts, taxony and medium (air or water [2]). The specific mechanisms involved may strongly depend on flight performance (the motion capacity sensu [43]), specifically on the airspeeds of the focal groups relative to prevailing wind speeds.…”

“…The trajectories of commuting aerial and aquatic animals depend not only on the animals' own movements but also on the motion of the medium in which they move [1,2]. Hence, the flow vector (i.e.…”

Navigating the flow: individual and continuum models for homing in flowing environments

“…This process formally connects data inputs for the IBM (e.g. ocean currents, tracking studies) to the macroscopic model and will allow formal testing of different hypotheses for navigation, through comparing simulation/ analytical predictions with empirical observations: for similar studies, see [44].…”

Is it possible to acoustically identify individuals within a population?

“…To acquire this knowledge, the locations and movements of animals should be tracked across reproductive seasons or even across many years (Doucette 2010;Lopes et al 2013;Hays et al 2014). In biological studies, individuals are usually physically marked and tracked using radio transmitters (Doucette 2010), satellite loggers (Kennedy et al 2014), geolocators (Bächler et al 2010), colored and numbered bands (Lopes et al 2013;Neubauer et al 2012), tags (Ale et al 2011), medical cautery units (Ekner et al 2011), tattoos or dyes (Nietfeld et al 1994).…”