An economic model of the limits to foraging range in central place foragers with numerical solutions for bumblebees

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Abstract
Summary: 1. A model is described that evaluates the maximum economic foraging range in central place foragers by using optimality criteria to discriminate between foraging sites at different distances from the forager's central place. 2. The basic model can be varied to suit foragers that optimise either their rate of net energy uptake or their foraging efficiency. 3. The model requires specification of the time and energy budgets of travel and foraging, and of the rewards obtainable at potential foraging sites. 4. The specific case of bumblebees, whose foraging ranges are poorly known, is considered. 5. Numerical solutions of the model for parameter values that represent bumblebees and their forage predict economic foraging ranges exceeding several kilometres. The model demonstrates that economics alone can explain extensive flight ranges in bees.

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