Multiscale models for movement in oriented environments and their application to hilltopping in butterflies

Hilltopping butterflies direct their movement in response to topography, facilitating mating encounters via accumulation at summits. In this paper, we take hilltopping as a case study to explore the impact of complex orienteering cues on population dynamics. The modelling employs a standard multiscale framework, in which an individual's movement path is described as a stochastic 'velocity-jump' process and scaling applied to generate a macroscopic model capable of simulating large populations in landscapes. In this manner, the terms and parameters of the macroscopic model directly relate to statistical inputs of the individual-level model (mean speeds, turning rates and turning distributions). Applied to hilltopping in butterflies, we demonstrate how hilltopping acts to aggregate populations at summits, optimising mating for low-density species. However, for abundant populations, hilltopping is not only less effective but also possibly disadvantageous, with hilltopping males recording a lower mating rate than their non-hilltopping competitors.