Review on mathematical modeling of honeybee population dynamics

Authors: CHEN, Y. - Arizona State University; DeGrandi-Hoffman, Gloria; RATTI, V. - Arizona State University; KANG, Y. - Arizona State University

Submitted to: Mathematical Biosciences and Engineering (MBE) Journal
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 10/11/2021
Publication Date: 11/4/2021
Citation: Chen, Y., Hoffman, G.D., Ratti, V., Kang, Y. 2021. Review on mathematical modeling of honeybee population dynamics. Mathematical Biosciences and Engineering (MBE) Journal. 18(6):9606-9650. https://doi.org/10.3934/mbe.2021471.
DOI: https://doi.org/10.3934/mbe.2021471

Interpretive Summary: Honeybees are a critical part of agricultural production and the stabilization of natural ecosystems. Unfortunately, honeybee populations have been declining globally due to parasites, diseases, poor nutrition, pesticides, and climate change. Mathematical models have provided insights on potential factors and important processes that can cause colony loss. Models also have supplied guidance for improving the survival rate of colonies. In this review, we present various mathematical models from different aspects: 1) simple bee-only models with features such as age distribution and division of labor, food collection, and nutrient absorption; 2) models of bees with other species such as parasites and/or pathogens; and 3) models of bees affected by pesticide exposure. We also provide a review of computational models such as VARROAPOP and BEEHAVE that describe honey bee population dynamics in environments that include weather factors and distance and quality of food to predict the effects on colony growth and survival. Finally, we assert that addressing the global crisis of honey bee losses will require the integrated approach mathematical models provide to evaluate the combination of factors that culminate in the collapse of a colony. Mathematical models are needed to identify mechanisms that can be difficult or costly to quantify in field and will be an essential component in developing strategies to improve colony health. To fully realize the potential of modelling to capture realistic dynamics of colonies will require collaborations between biologists and mathematicians so that models can be based on and validated with experimental data.

Technical Abstract: Honeybees have an irreplaceable position in agricultural production and the stabilization of natural ecosystems. Unfortunately, honeybee populations have been declining globally. Parasites, diseases, poor nutrition, pesticides, and climate changes contribute greatly to the global crisis of honeybee colony losses. Mathematical models have been used to provide useful insights on potential factors and important processes for improving the survival rate of colonies. In this review, we present various mathematical tractable models from different aspects: 1) simple bee-only models with features such as age segmentation, food collection, and nutrient absorption; 2) models of bees with other species such as parasites and/or pathogens; and 3) models of bees affected by pesticide exposure. We aim to review those mathematical models to emphasize the power of mathematical modeling in helping us understand honeybee population dynamics and the related ecological communities. We also provide a review of computational models such as VARROAPOP and BEEHAVE that describe the bee population dynamics in environments that include factors such as temperature, rainfall, light, distance and quality of food, and their effects on colony growth and survival. In addition, we propose a future outlook on important directions regarding mathematical modeling of honeybees. We particularly encourage collaborations between mathematicians and biologists so that mathematical models could be more useful through validation with experimental data.