Mathematical modeling of a complex reality: An interdisciplinary journey from monotone systems to honey bee colony losses

Honey bees form highly complex biological societies. Honey bee colony losses recently reported and the consequent threat of a possible pollinator crisis are provoking justified concern. Attempts to assess the role of several stressors like viruses, parasites, pesticides or nutritional impairment, under field condition, have produced contrasting results. To explore the possible causes of this incongruity a mathematical model of honey bee health has been developed, starting from experimental observations and conceptual considerations. The resulting dynamical system is monotone and can lead to multi-stability, suggesting that individual bees exposed to the same stressors can end into different health conditions depending on minor differences in their initial states. For instance, the immune-suppressive capacity of a common virus can generate a bimodal distribution of the mortality which, embedded into a model of the hive, can favor in turn the collapse of the colony. The model analysis can thus explain the variability of results depending on field conditions and, at the same time, the difficulty of predicting the net effect of each single stress factor affecting bee health outside of the controlled lab environment. Overall, the study is a concrete example of a fruitful interdisciplinary collaboration among experimental and theoretical biology, dynamical systems, control theory and scientific computing, leading to a potential advance in the comprehension of nature, grounded on mathematical modeling.

The plenary lecture is part of the Presentation Days of the PhD course in Earth Science, Fluid-Dynamics, and Mathematics. Interactions and Methods of the University of Trieste held on 23–25 February 2021. If you want to attend, please write to .