Mathematical Modeling of Social Insect Colonies as Complex Adaptive Systems

This research focuses on the intricate dynamical systems of eusocial insects, particularly ants, and honey bees, known for their highly organized colonies and cooperative behaviors. Research on eusocial insects contributes to understanding of animal and social behavior and promises to help agriculture and have huge economic impacts. Collaborating closely with ecologists, I construct diverse mathematical models tailored to different environmental contexts. These models encompass individual stochastic (Agent-based model), Ordinary Differential Equation (ODE), non-autonomous, and Delay Differential Equation (DDE) models, rigorously validated with experimental data and statistical methods. Employing dynamical theory, bifurcation analysis, and numerical simulations, I gain deeper insights into the adaptive behaviors exhibited by these insects at both colony and individual levels. Our investigation addresses pivotal questions: 1) What mechanisms underlie spatial heterogeneity within social insect colonies, influencing the spread of information and pathogens through their intricate social networks?2) How can I develop accurate mathematical models incorporating age structures, particularly for species like honeybees, utilizing delayed differential equations? 3) What is the influence of seasonality on honeybee population dynamics in the presence of parasites, as explored through non-autonomous equations? 4) How do pesticides impact honeybee population dynamics, considering delayed equations and seasonality? Key findings highlight:1) The spatial distribution within colonies significantly shapes contact dynamics, thereby influencing the dissemination of information and the allocation of tasks. 2) Accurate modeling of honeybee populations necessitates the incorporation of age structure, as well as careful consideration of seasonal variations. 3) Seasonal fluctuations in egg-laying rates exert varying effects on the survival of honeybee colonies. 4) Pesticides wield a substantial influence on adult bee mortality rates and the consumption ratios of pollen. This research not only unveils the intricate interplay between intrinsic and environmental factors affecting social insects but also provides broader insights into social behavior and the potential ramifications of climate change.