Modeling associative learning with generalization for a case of warning signals

Animals' associative learning plays a crucial role in many intraspecific or interspecific interactions, involving an animal's use of information on it s interacting counterparts. Here, we present a theoretical model that captu res the basic features of an animal's associative learning, which may invol ve generalization, for a simplest case of warning signals. Specifically: we derive formulae for the average level of associative memory as functions o f a few parameters that reflect the population density of prey, predator's efficiency of prey detection, and the properties of predator's associative learning, including generalization and memory decay. This average level of associative memory is of central importance in determining prey's fitness a nd, thus, the evolution of warning signals (i.e. aposematism). The derived formula also shows that another species with similar signal enhances the fi tness of an aposematic species of concern as long as their signal is simila r enough for generalization to occur. The model developed here can be exten ded to more complicated cases and the basic idea can be applied to modeling other interactions involving associative learning with generalization.