New Mathematics for Pollinator Decline: From Colony Dynamics to Sustainable Agroecosystems

Bees and other pollinators are essential to healthy ecosystems and food security, yet they are declining at alarming rates. A 2025 study found that over 22% of North American pollinator species now face an elevated risk of extinction, and United States beekeepers lost over 60% of their honeybee colonies in the past year alone, representing more than $600 million in economic losses, jeopardizing the sustainability of an industry critical to food production. Because pollinating insects contribute over $15 billion annually to North American agriculture, their continued decline poses a serious threat to food security, farm economies, and biodiversity. This project addresses pollinator declines by developing new mathematical and artificial-intelligence-based tools to predict how interacting threats (such as disease, pesticides, habitat loss, and other environmental pressures) combine to harm pollinator communities and to identify effective strategies for protecting them. Rather than studying these threats in isolation, the research links what happens inside a single colony to broader patterns across farming landscapes, combining mathematical rigor with artificial intelligence to address one of the most pressing ecological and agricultural challenges of our time. The project's tools and findings will be made freely available to researchers, growers, beekeepers, and other stakeholders. It will also train undergraduate and graduate students through integrated cross-disciplinary mentorship at the intersection of mathematics, biology, artificial intelligence, and sustainability, strengthening both scientific capacity and food system resilience. This project pioneers new mathematical theory and artificial intelligence-enhanced modeling frameworks that link colony-level mechanisms with ecosystem-scale processes, yielding predictive, adaptive tools for sustainable pollination management through an interdisciplinary collaboration between mathematicians and pollinator biologists. The research follows a coherent progression across three aims. The first develops mechanistic models of honeybee colony resilience and collapse, incorporating Allee effects to capture tipping-point behavior under coupled temperature-toxicity, pesticide, parasite, and disease stressors, grounded in long-term laboratory and field observations. The second extends these models to multi-species plant–pollinator–pathogen–pest–agrochemical networks using stochastic reaction-diffusion-taxis partial differential equations that account for spatial fragmentation, nonlinear feedback, and environmental variability. The third designs adaptive management strategies using Filippov optimal control for piecewise-smooth ecological systems, Approximate Bayesian Computation for parameter inference, and reinforcement learning and hybrid dynamical systems-AI methods for AI-enabled decision support. These approaches are calibrated and validated using 40-hive field experiments and 190-colony longitudinal datasets. The project advances foundational mathematics by developing persistence theory (in invariant domains) for nonautonomous delay systems with Allee effects, coexistence criteria for stochastic spatial systems, and optimal control under ecological uncertainty. Its artificial intelligence and machine-learning components—embedded across parameter learning, uncertainty quantification, and adaptive control—provides data-informed tools for evidence-based pollination management at colony and agroecosystem scales. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. NSF Award ID: 2602341 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Yun Kang | Institution: Arizona State University, SCOTTSDALE, AZ | Award Amount: $468,704 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2602341 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2602341.html