A mathematical model of aggressive mimicry. (1st November 2018) - Kloock, Carl T; Getty, Thomas
Abstract : We present a mathematical model of aggressive mimicry systems in which predators lure prey by mimicking food items of those prey. We use this model to explore potential dynamics of mimicry systems where a bad outcome results in death. This leads to some counterintuitive expectations not found in earlier models of aggressive mimicry that have not included the potential for dupe death. Abstract: Aggressive mimicry is a widespread phenomenon in which predators use resemblance to objects in the environment to exploit organisms that make discrimination errors ("dupes"). Aggressive mimics harm dupes in several ways, including predation, parasitism (including brood parasitism), and infection. Previous models of aggressive mimicry have been built from models originally derived for protective mimicries where the risk of death to dupes was not considered. Some kinds of aggressive mimicry carry significant risk of death for the dupes. Death changes things in significant ways that may be better modeled using the techniques developed for understanding foraging under predation risk. We present a simple model of a common type of aggressive mimicry system in which mimics are predators and lure dupes by mimicry of a food resource. The model combines a simple model for foraging under risk of predation with signal detection theory. This modeling approach reveals 2 contrasting potential responses of dupes to mimics. Counterintuitively, dupes might be selected to become either more or less discriminating and risk averse as predators become more common or more memetic, depending on starting conditions relating to alternative resources available to the dupes. Implications of these divergent trajectories for aggressive mimicry systems are explored.