Title: Evolutionary dynamics on small networks
Evolutionary dynamics can be strongly affected by spatial structure. A popular way to model such spatial structure are networks, where each node represents an individual and offspring can be placed to other sites via the links. How does such a network affect the probability of a new mutation to take over the entire population? And how does it alter the time this process is expected to take? Of particular interest are structures that increase the probability that advantageous mutations take over. Such amplifiers are surprisingly abundant among all networks. Looking at all undirected networks up to a certain size also reveals general properties of such amplifiers and allows to identify particular structures for further analysis. These approaches reveal general properties of networks that are often surprising and counter-intuitive and shed new light on the evolution of populations with complex spatial structure.