Time and energy constraints and the relationships between currencies in foraging theory

Measured foraging strategies often cluster around values that maximize the ratio of energy gained over energy spent while foraging (efficiency), rather than values that would maximize the long-term net rate of energy gain (rate). The reasons for this are not understood. This paper focuses on time and energy constraints while foraging to illustrate the relationship between efficiency and rate-maximizing strategies and develops models that provide a simple framework to analyze foraging strategies in two distinct foraging contexts. We assume that while capturing and ingesting food for their own use (which we term feeding), foragers behave so as to maximize the total net daily energetic gain. When gathering food for others or for storage (which we term provisioning), we assume that foragers behave so as to maximize the total daily delivery, subject to meeting their own energetic requirements. In feeding contexts, the behavior maximizing total net daily gain also maximizes efficiency when daily intake is limited by the assimilation capacity. In contrast, when time available to forage sets the limit to gross intake, the behavior maximizing total net daily gain also maximizes rate. In provisioning contexts, when daily delivery is constrained by the energy needed to power self-feeding, maximizing efficiency ensures the highest total daily delivery. When time needed to recoup energetic expenditure limits total delivery, a low self-feeding rate relative to the rate of energy expenditure favors efficient strategies. However, as the rate of self-feeding increases, foraging behavior deviates from efficiency maximization in the direction predicted by rate maximization. Experimental manipulations of the rate of self-feeding in provisioning contexts could be a powerful tool to explore the relationship between rate and efficiency-maximizing behavio