Stop early to travel fast: modelling risk-averse scheduling among nocturnally migrating birds

Many migrating birds divide their journeys into nocturnal flights interspersed by stopovers where they build up energy reserves (fuel) for subsequent flights. Given the difficulty in monitoring fuel loads of individual migrants over long distances, theoretical models are often used to interpret observed relations between departure fuel loads (DFLs) and fuel deposition rates (FDRs) in the context of time-minimised migration. Models applicable to nocturnal migration have hitherto considered only the departure decision, i.e. ignored interim stopover possibilities before fuel loads are depleted. This results in 'risk-prone' migratory schedules in terms of choice of stopover. In this study we assess 'risk-averse' behaviour, whereby nocturnal migrants minimise migration time by adjusting not only DFLs to experienced and expected FDRs, but also stopping fuel loads (SFLs), below which they stop to refuel at high-quality sites. We developed analytical formulae to solve for maximal risk-prone and risk-averse migration speeds in modelled environments comprised of two stopover qualities (high- and low-quality), and a constant probability of encountering a high-quality site (encounter probability). Risk-aversion was beneficial to migration speeds in over 99% of the modelled environments, with median ratios of risk-averse to risk-prone migration speeds ranging from 1.5 to 2.8. Among modelled environments, this benefit increased with increasing FDRs at high-quality sites, and was highest with low probabilities of encountering high-quality sites. Time-minimising risk-averse DFLs at low-quality sites were minimal in nearly all modelled environments, and whenever encounter probabilities were low, risk-averse SFLs typically indicated that migrants should stop immediately on encountering high-quality sites. Modelled fuel loads in environments with high and low encounter probabilities resembled observed fuel loads of migratory populations with ubiquitous and scarce food availability, respectively. This study demonstrates the benefits of risk-averse exploitation of variable resources, presents a new approach to model time-minimised migration in heterogeneous environments and emphasises the importance of premium stopover sites to nocturnally migrating birds.