A complex adaptive system (CAS) is a system that is complex in that it is a dynamic network of interactions, but the behavior of the ensemble may not be predictable according to the behavior of the components. Social insect colonies are excellent examples of complex adaptive. Mathematical models are powerful tools that can provide us quantitative approaches to elucidate complicated ecological and evolutionary processes on the numerous spatial, temporal and hierarchical scales at which CAS such as social insect colonies operate. In this talk, I will review some of our recent collaborative work with biologists regarding important and interesting questions of social insect colonies such as:

1. How do task organization and work performance scale with colony size and metabolism?

2. How does environment impact task allocation? And

3. How may climate and parasite impact honeybee population dynamics.