Whole-Colony Dynamic Energy Budget Model for Bumble Bees: Assessing the Impact of Wildflower Patches on Crop Pollination.

Bumble bees are important pollinators of many crops around the world. In recent decades, agricultural intensification has resulted in significant declines in bumble bee populations and the pollination services they provide. Empirical studies have shown that this trend can be reversed by enhancing the agricultural landscape, for example, by placing wildflower patches adjacent to crops. Despite the empirical evidence, the mechanisms behind these positive effects are not fully understood. Theoretical studies, in the form of mathematical or computational models, have proven useful in providing insights, but the complexity of the underlying system means that certain factors remain unexplored. In this work, we build a unique model coupling a whole-colony Dynamic Energy Budget (DEB) approach for population dynamics to a Maximum Entropy (MaxEnt) principle formulation for the spatial distribution of foraging bees. The use of a DEB to asses whole-colony energy budgets, and its coupling to a spacial model is novel. The use of MaxEnt to predict foraging spatial distributions is still in its early stages, and our work highlights its potential to advance and expand upon the traditional assumptions of the Ideal Free Distribution. We use the developed model to asses the possible benefits and drawbacks of planting wildflower nearby crops for crop pollination services. We answer questions of when should wildflowers bloom, how many should we plant, which type of wildflowers, and where should we place them.