Multiscale Multistage Ecological and Evolutionary Modeling with Applications to Social Insect Colonies

Social insect colonies, such as bees, ants, wasps are excellent systems for which to model organizational challenges in complex adaptive societies. Social insect biologists face the challenge of integrating both the individual and colony levels of a given organization. This research aims to develop and study ecological and evolutionary models that not only adequately integrate the different levels of interaction in a colony but also capture the complexity of the internal dynamics within social groups, as well as their evolutionary outcomes.

The project serves as an ideal vehicle for interdisciplinary research and education at the intersection of applied mathematics and life sciences. The methods and theories developed in this research may be applied to many domains outside of biology, including epidemiology (for example in the ongoing Covid-19 pandemic), optimization theory, the immune system and robotics.

The research continues to develop a template integrating interdisciplinary learning and teaching for students from applied mathematics and life sciences through shared research projects at both the undergraduate and/or graduate levels. The funding will also support graduate students in applied mathematics during summer studies. Summer research projects provide underrepresented, minority undergraduate students with first-hand research experience.

Lectures and simple projects related to this research will be given to high school sophomores, juniors and seniors who are participating in The SCience and ENgineering Experience (SCENE) at ASU where SCENE provides cutting-edge science research experience to the participating high school students.

This collaborative research between Applied Mathematics and Biology at Arizona State University fosters a culture of theory-experiment collaboration which aims to develop novel and sophisticated modeling approaches to understand the interface between social dynamical processes and multilevel selections. This interdisciplinary collaboration will (a). integrate across ecological scales and stages; (b). incorporate selection and thus evolutionary effects; and (c). incorporate directly measurable parameters, including metabolic costs, efficiency of energy flow, individual mass and group size.

The new analytical techniques and theories will be developed and added to current dynamical theory and evolutionary game theory. The proposed integrated multiscale models will address central themes in Behavior Ecology and Sociobiology, including: 1. How do social groups balance the benefits of information flow against the costs of pathogens that spread via the same mechanisms that foster communication? 2.

How does hierarchy formation of complex social groups, scale relative to environmental conditions and constraints? 3. How do patterns of social interactions at different colony stages influence fitness and how are they shaped by selection? Rigorous mathematics will be integrated with extensive field and laboratory data to study complex adaptive systems of social insect societies in the evolutionary settings with multistage structures in both individual and colony levels.

Nonlinear, non-autonomous differential equations as well as spatial stochastic processes, combined with available empirical data, will be used to model ecological and evolutionary dynamics at different ecological scales and stages.

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.