The efficiency of varying methods and degrees of time compensation for the solar azimuth

Daytime migrants are known to orientate using the position of the sun, compensating for its changing position throughout the day with a 'time-compensated sun compass'. This compass has been demonstrated in many migratory species, with various degrees of accuracy for the actual movement of the sun. Here, we present a model for differing levels of compensation for the solar ephemeris that shows that a high degree of efficiency, in terms of distance travelled, can be achieved without full time compensation. In our model, compensating for the sun's position had a diminishing return with an accuracy of 80% leading to only a 2% reduction in distance travelled. We compare various modes of time compensation-full, partial, time averaged and step-revealing their directional efficiency in terms of distance travelled under an autumn migration scenario. We find that the benefit of time compensation varies with latitude, with time averaging performing very well, especially at all high latitudes, but step compensation performing better at very low latitudes. Importantly, even rudimentary adjustment can dramatically increase the efficiency of migration, which suggests an easy pathway for the independent evolution of time compensation.