Dynamic energy budget model for a bumble bee colony: Predicting the spatial distribution and dynamics of colonies across multiple seasons

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, however, by enhancing the agricultural landscape with natural habitat, such as adding wildflower patches adjacent to crops. Despite the empirical evidence, the mechanisms behind these positive effects are not fully understood, and the specific characteristics of the enhanced natural habitat that would maximize benefits are unclear at this time. Theoretical studies, in the form of mathematical models, have proven useful in elucidating the underlying mechanisms and determining the optimal natural habitat configurations. Existing models, however, generally focus only on particular aspects of bumble bee behaviour; some models are accurate at describing population dynamics, while others are accurate at describing their spatial distribution. In this work, we build a unique model coupling population dynamics, using a whole-colony Dynamic Energy Budget (DEB) approach, to a spatial distribution model based on the maximum energy principle. This coupling gives valuable new insights into the effects of spatial arrangements on population dynamics, and vice-versa. With our model, we answer questions such as when, how much, or what type of wildflower patches should be planted to maximize crop pollination services and minimize bee decline. We find that planting wildflowers that bloom before and after crop bloom is crucial to achieve high pollination services and preserving wild pollinator populations. We also find that small quantities of natural habitat are needed when the crop is nutritionally rich, but higher quantities are most beneficial when the crop is nutritionally deficient.