Capera-Aragones Pau, Mariño Joany, Hurford Amy, Tyson Rebecca C, Foxall Eric
Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel.
CMPS Department (Mathematics), University of British Columbia Okanagan, Kelowna, Canada.
Bull Math Biol. 2025 May 21;87(6):83. doi: 10.1007/s11538-025-01448-8.
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.
大黄蜂是全球许多农作物的重要传粉者。近几十年来，农业集约化导致大黄蜂种群数量及其提供的授粉服务大幅下降。实证研究表明，通过改善农业景观，例如在作物附近种植野花斑块，可以扭转这一趋势。尽管有实证依据，但这些积极影响背后的机制尚未完全明了。以数学或计算模型形式开展的理论研究已证明有助于提供见解，但基础系统的复杂性意味着某些因素仍未得到探索。在这项工作中，我们构建了一个独特的模型，将用于种群动态的全蜂群动态能量收支（DEB）方法与用于觅食蜜蜂空间分布的最大熵（MaxEnt）原理公式相结合。使用DEB来评估全蜂群能量收支，并将其与空间模型相结合是新颖的。使用MaxEnt来预测觅食空间分布仍处于早期阶段，我们的工作凸显了其在推进和拓展理想自由分布传统假设方面的潜力。我们使用所开发的模型来评估在作物附近种植野花以提供作物授粉服务可能带来的利弊。我们回答诸如野花应何时开花、应种植多少、种植何种野花以及应将它们种植在何处等问题。
