A dynamical model of sexual harassment in damselflies and its implications for female-limited polymorphism

Female-limited polymorphism is a widespread phenomenon in damselflies. Typically, one female morph resembles the male (the andromorph), while the alternative morph(s) does not (the gynomorph(s)). Contemporary explanations for the phenomenon vary, but they generally assume that the polymorphism has a risen as a consequence of frequency-dependent selection on females to avoid excessive male harassment. Here, we quantitatively characterise two hypotheses, the learned-mate recognition hypothesis (LMR) and the male mimicry (MM) hypothesis. The LMR proposes that males learn more quickly to attack the more commonly encountered female morph in the population, so that rarer female phenotypes are harassed relatively less. By contrast, the MM proposes that when andromorphs are initially rare compared to males, then they are harassed less than gynomorphs, due to their morphological similarity to males. We present a parameterised dynamical model of the mating system as a way of quantifying the rate of male harassment of females. We then use this information in a multi-generational model that includes selection via the differential harassment of morphs and genetic drift, as well as between-year variability in damselfly density and sex ratio. The proportions of andromorphs at selective equilibria were analytically identified. While both the LMR and the MM versions of the model predict no consistent change in the equilibrium proportion of andromorphic females with increasing damselfly density, only the MM predicts that the equilibrium proportion of andromorphs should increase with sex ratio. Under low harassment rates (e.g. low population densities and/or low male search rates) selection is absent and female morph frequencies are free to drift. The potential applications of this form of dynamical model for other systems involving sexual harassment are discussed.