An increase in search time S1 will likely make prey2:
As S1 increases, the predator must wait longer to encounter the preferred prey 1. The expected rate from rejecting prey 2 and continuing to search therefore declines, making the immediate lower-profitability item more acceptable. This is the central diet-breadth prediction of optimal foraging theory: scarcity of the highest-ranked prey broadens the optimal diet, whereas abundance permits specialization. The profitability E2/h2 of prey 2 need not change; what changes is its value relative to the opportunity cost of continued searching. An increase in search time consequently shifts the acceptan
Ref: Ecology: From Individuals to Ecosystems, Begon et al., 5th Ed., Ch. 10