Discriminability and the Sigmoid Functional Response: How Optimal Foragers Could Stabilize Model-Mimic Complexes

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Abstract
Cryptic and mimetic prey species have evolved characteristics that contravene the ability of predators to detect them and discriminate their value before initiating attack. Traditonal optimal diet theory has not considered model-mimic complexes. Analyses of predation on mimicry systems have not been prescriptive of optimal behavior, have assumed perfect mimicry, and/or have not considered the presence of alternative prey. In this analysis, features of optimal signal detection theory are incorporated into traditional optimal diet theory to synthesize a more general theoretical framework that permits predictions on the basis of constrained predator perceptual abilities. Predictions include frequency dependent partial preference for prey types defined by profitability, but notfor types defined by appearance. Frequency-dependent partial preferences can create or enhance sigmoid functional responses, which can, in turn, stabilize randomly mixed model-mimic complexes.

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