Evolutionary dynamics permeates life and life-like systems. Mathematical methods can be used to study evolutionary processes, such as selection, mutation, and drift, and to make sense of many phenomena in life sciences. Stochastic analysis is an emerging tool to understand cancer dynamics, to guide personalized medicine, and to study important problems such as drug resistance.
In this talk, I will describe mathematical approaches to several evolutionary questions. How likely is a single mutant to take over a population of individuals? What is the speed of evolution, if things have to get worse before they can get better (aka, fitness valley crossing)? Can cell cooperation, hierarchical relationships between cells, spatial interactions, or randomness influence the speed or direction of evolution? Applications to biomedicine will be discussed.