Optimal departure fat loads and stopover site use in avian migration: an analytical model

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Abstract
We develop an analytical model which determines optimal depature fat loads and stopover site use for time-minimizing bird migration with any number of sites, to identify conditions under which birds carry more fat than necessary to reach the next stopover site (overloads) or skip suitable stopover sites. The model is analysed with three sites: the wintering ground, one stopover site (both of which are characterized by their daily fattening rates), and the breeding ground. Overloads and skipping can occur if the sites decrease in quality in the direction of migration. Departure fat loads are usually either at the level necessary to reach the stopover site or at the level for a non-stop flight to the breeding ground; overloads are only deposited under rare circumstances. To model the effects of stochasticity in fat deposition we include explicit functions for the dependence of fitness on arrival time. If overloads are deposited, they are largest when the fitness function is concave, lowest when convex, and intermediate when linear.