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

蜜蜂为85%的植物授粉，不仅对维持生物多样性至关重要，而且是世界上最有经济价值的农作物授粉者，作为美国的商业授粉者，每年的价值在150亿至200亿美元之间。不幸的是，蜜蜂数量最近的急剧下降被认为是一场全球危机。种群损失的主要原因是寄生的瓦罗阿螨(瓦罗阿螨、破坏者、安德森和特鲁曼)。这项研究旨在揭开蜜蜂数量急剧下降的谜团，并为Varroa制定减少蜂群损失的控制策略，这既给研究和教育带来了挑战，也带来了机遇。这项研究是流行病学、生命科学和应用数学的交汇点，这使研究人员能够开发一个模板，通过在本科生和/或研究生层面共享研究项目来整合学生的跨学科学习。该模型框架不仅为研究蜂群系统的多因素影响提供了一个强大的系统，而且还提供了一个很好的机会来探索行为、流行病学和营养生态如何在复杂系统中共同进化。本研究可为防治蜂害、减少蜂群损失的新策略提供依据，并为土地管理者提供有益的参考。这些方法和成果将通过可向科学界提供的在线视频讲座和面对面讲习班传播。暑期研究项目将提供给有第一手研究经验的本科生，特别是未被充分代表的少数族裔学生。亚利桑那州立大学和卡尔·海登蜜蜂研究中心的这项合作研究培养了一种理论-实验合作的文化，旨在开发现实的、数学上易于处理的模型，这些模型将通过使用现场数据进行验证和参数化。这种跨学科的合作将使研究人员能够研究疾病、寄生虫、营养和行为在不断变化的环境中的综合影响，以及在多个时间和空间尺度上对蜜蜂群体死亡率的影响。严格的数学将结合大量的野外和实验室数据来研究：1.寄生虫如何通过位于不同景观结构的其他蜂巢的觅食进入蜂群，影响具有阶段结构的蜜蜂-寄生虫种群动态。2.蜜蜂-寄生虫-病毒与蜜蜂在季节性环境中觅食行为的相互作用如何造成蜂群损失。3.疾病、寄生、营养和蜜蜂觅食行为之间的关键反馈机制如何影响种群的生长动态和在多层次空间成分的动态环境中的生存。集合种群框架内的非线性非自治微分方程和基于个体的模型将被用来对蜜蜂种群进行建模，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.