Predators learn during the process of prey hunting, forming search images and memories for the prey and updating their subsequent foraging decisions accordingly. When prey species form a mimicry ring sharing similar warning signals, predator memory are likely forms not only through direct associative learning but also through indirect learning via interspecific generalization. However, it remains unclear how such associative learning affects the evolutionary dynamics of warning signals in mimicry ring species.
 Here, we conduct a mathematical analysis to examine how predator associative learning affects the evolution of warning signals in prey species that form mimicry rings. First, we model the dynamics of predator memory and relate it to the predator’s predation rates. Second, we incorporate these processes into the signal evolution. We consider a mimicry ring consisting of two prey species: a model population with defensive traits and a mimic population with (or without) defensive traits. This setup incorporates both Müllerian and Batesian mimicry.
 When only one model population with a defensive trait exists, warning signals monotonically converge to a common signal. However, when mimic populations are introduced, signals in the mimicry ring may exhibit signal convergence, evolutionary tracking, or signal divergence. We identify parameter conditions associated with the above different evolutionary outcomes of signals, focusing particularly on the degree of initial signal inconsistency, the strength of indirect learning effects, and the sensitivity to predator memory, and examine the factors that most strongly influence evolutionary trajectories.
 In this talk, we present analysis showing that memory-mediated feedback on predation rates, driven by associative learning, can alter the evolutionary fate of mimicry systems, providing insight into the origin of signal diversity and stability in mimicry rings.