Mathematical Modeling of Honeybee Populations in Heterogeneous Environments: Linking Disease, Parasite, Nutrition, and Behavior

蜜蜂（Apis mellifera）不仅对维持生物多样性至关重要，它为85%的植物物种授粉，而且是世界上最具经济价值的农作物授粉者，在美国，作为商业授粉者，每年的价值在150亿到200亿美元之间。不幸的是，最近蜜蜂数量的急剧下降被认为是一场全球危机。蜂群损失的主要原因是寄生性瓦螨（瓦螨破坏者Anderson和Trueman）。这项研究揭示了蜜蜂数量急剧下降的奥秘，并制定了减少蜂群损失的控制策略，为研究和教育带来了挑战和机遇。这项研究是流行病学、生命科学和应用数学的交叉领域，这使得研究人员能够通过本科生和/或研究生的共享研究项目为学生开发一个整合跨学科学习的模板。建模框架不仅为研究对蜂群系统的多因素影响提供了一个强大的系统，而且为探索行为、流行病学和营养生态学如何在复杂系统中共同进化提供了一个很好的机会。该研究可为养蜂人制定控制瓦螨和减少蜂群损失的新策略提供依据，并使土地管理者受益。这些方法和结果将通过可以提供给科学界的在线视频讲座和现场研讨会来传播。夏季研究项目将提供给本科生，特别是代表性不足的少数民族学生，提供第一手的研究经验。亚利桑那州立大学和卡尔海登蜜蜂研究中心之间的这项合作研究促进了一种理论实验合作的文化，旨在开发现实的、数学上可处理的模型，这些模型将通过使用现场数据进行验证和参数化。跨学科合作将使研究人员能够研究疾病、寄生、营养和行为在不断变化的环境中的综合影响，以及在时间和空间的多尺度上对蜂群死亡率的影响。严谨的数学将与广泛的现场和实验室数据相结合来研究：寄生蜂如何通过位于不同景观结构的其他蜂箱的觅食者迁移到蜂群中，可能影响不同阶段结构的蜜蜂-寄生蜂种群动态。2. 蜜蜂-寄生虫-病毒如何在季节性环境中与蜜蜂觅食行为相互作用导致蜂群损失。3. 在具有多层次空间成分的动态环境中，将疾病、寄生、营养和蜜蜂觅食行为联系起来的关键反馈机制如何影响蜂群的生长动态和生存。本文将利用元种群框架中的非线性非自治微分方程和基于个体的模型来模拟蜜蜂种群，其空间尺度从个体、群体到区域水平，时间尺度从秒、天到月。

The honeybee, Apis mellifera, is not only crucial in maintaining biodiversity by pollinating 85% of plant species but also is the most economically valuable pollinator of agricultural crops worldwide with value between $15 and $20 billion annually as commercial pollinators in the U.S. Unfortunately, the recent sharp declines in honeybee population have been considered a global crisis. The primary cause of colony losses is the parasitic Varroa mites (Varroa destructor Anderson and Trueman). The study to unfold the mystery of the dramatic decline in honeybee populations and for developing control strategies for Varroa that reduce colony losses presents both challenges and opportunities for research and education. This research lives at the intersection of epidemiology, life sciences and applied mathematics, which enables the investigators to develop a template integrating interdisciplinary learning for students through shared research projects at the undergraduate and/or graduate level. The modeling framework provides not only a powerful system for examining multifactorial impacts on the honeybee colony system but also a great opportunity to explore how behavior, epidemiology and nutritional ecology coevolve within complex systems in general. This research can provide a basis for new strategies for controlling Varroa and reducing colony losses for beekeepers, and benefit land managers. The methods and results will be disseminated through online video lectures and in-person workshops that can be made available to the scientific community. Summer research projects will be provided to undergraduate students, especially underrepresented minority students, with a first-hand research experience.This collaborative research between Arizona State University and Carl Hayden Bee Research Center fosters a culture of theory-experiment collaboration with aims to develop realistic and mathematically tractable models that will be validated and parameterized via using field data. The interdisciplinary collaboration will enable the investigators to study the integrated effects of disease, parasitism, nutrition and behavior in changing environments and the effects on honeybee colony mortality across multiscale in time and space. Rigorous mathematics will be integrated with extensive field and lab data to investigate: 1. How parasite migration into colonies via foragers from other hives located at different landscape structures could affect the honeybee-parasite population dynamics with stage structures. 2. How the honeybee-parasite-virus interactions with the honeybee foraging behavior in seasonal environments cause colony losses. 3. How the crucial feedback mechanisms linking disease, parasitism, nutrient and honeybee foraging behavior might be responsible for the colony growth dynamics and survival in a dynamical environment with multilevel spatial components. Nonlinear nonautonomous differential equations within metapopulation frameworks and individual based models will be used to model the honeybee population with spatial scales ranging from the individual, the colony, to the regional level and timescale spanning from seconds, days, to months.