A mechanistic partial integro-differential equations model for bumblebee foraging behaviour

Bumblebees provide valuable pollination services to crops around the world. Empirical evidence has suggested that the addition of wildflower adjacent to cultivated crops could increase its pollination services. However, a quantification of the location, quantity and type of the wildflowers needed to optimize the pollination services is unknown and a call for modellers has been made.Here we develop a partial integro-differential equation model to predict the spatial distribution of foraging bumblebees in dynamic heterogeneous landscapes. The foraging population is divided into two subpopulations engaged in intensive search mode (modelled by diffusion) and extensive search mode (modelled by advection) respectively. Our model considers the effects of resource-dependent transition rates between movement modes, resource depletion, central-place foraging behaviour and the effects of memory in the spatial distribution of foraging bees. We use our model to quantify the benefits that planting wildflowers adjacent to a crop can have on its pollination services and show that small plantations in specific locations can lead to an increase of crop's pollination services.