From bird flocks to fish schools, animal groups exhibit a
remarkable ability to manage challenging tasks that individuals could not
manage on their own. Despite
limitations on individual-level sensing, computation, and actuation, and with
no centralized instruction, animal groups make decisions quickly, accurately,
robustly and adaptively in an uncertain, changing environment. I will describe recent analytically tractable
models and methods for studying the mechanisms of collective migration and collective
decision-making in animal groups. A
focus is on bifurcation analyses, which systematically elucidate the dependence
of performance of the collective dynamics on parameters that model the system
and the environment.