Fig. 1. Schematic representation of Eqn 1 and 2, showing our conceptualization of a bird's energy balance. Birds gain energy during foraging and lose energy when traveling between food patches. The switch between these modes is instantaneous. (A) The general case where energy gain, E_n(t_p), and the power required for flight, P(t_t), are functions of time (Eqn 1). (B) The simplification used in this study where E_n and P are constant over time (Eqn 2). The total travel time is in both cases calculated by the sum t_t=_it_t(i) and the time spent foraging is calculated by t_p=_it_p(i). Note that P is given in positive values in Eqn 1 and 2, so that -P is used on the negative part of the vertical axis.