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 animals use of information on its interacting counterparts. Here, we present a theoretical model that captures the basic features of an animals associative learning, which may involve generalization, for a simplest case of warning signals. Specifically, we derive formulae for the average level of associative memory as functions of a few parameters that reflect the population density of prey, predators efficiency of prey detection, and the properties of predators associative learning, including generalization and memory decay. This average level of associative memory is of central importance in determining preys fitness and, thus, the evolution of warning signals (i.e. aposematism). The derived formula also shows that another species with similar signal enhances the fitness of an aposematic species of concern as long as their signal is similar enough for generalization to occur. The model developed here can be extended to more complicated cases and the basic idea can be applied to modeling other interactions involving associative learning with generalization.