Optimal central place foraging flights in relation to wind

Many flying animals, like birds feeding their young, make commuting flights between a central place and foraging areas in the surroundings. Such central place foraging (CPF) represents a special case of foraging theory. We use simple geometry and trigonometry to analyse CPF flight performance (a round-trip cycle of outward flight from the central place and inward flight back along the reverse track) in relation to wind. In addition to considering the situation of a constant and uniform wind field, we take into account two factors that are likely to apply in many CPF situations under natural conditions: (a) that animals carry a load that will increase the energy expenditure during the inward flight and (b) that they may fly at different altitudes during out- and inward flights in the wind gradient above the ground or sea surface. Four main predictions emerge: (1) efficiency of CPF flights will be reduced with increasing wind speed, and foraging at the longest ranges is expected under low wind speeds. (2) A preference for CPF flights in crosswinds is expected in a constant and uniform wind field. (3) Carrying a load during the inward flight makes it optimal to fly with a small component of following winds during this flight while the outward flight will have a corresponding component of opposed winds. (4) With a steep wind gradient (e.g. over rough terrain) providing much shelter from wind at the lowest altitudes, predicted behaviour may change from crosswind preference to a preference for flights along the head/tailwind axis (at low altitude into headwinds and high altitude in tailwinds). Detailed tests of predictions for CPF flights in relation to wind will be important for understanding constraints and adaptations in animal responses to wind and for evaluating consequences of changing wind regimes in animal movement ecology.