Speaker
Description
George Berry, Christoph Hauert
We investigate an extension to the Moran process which adds ecological aspects through variable population sizes. For the original Moran process, birth and death events are correlated to maintain a constant population size. Here we decouple the two events and derive the stochastic differential equation that represents the dynamics in a well-mixed population and captures its behaviour as the population size becomes arbitrarily large. In evolutionary graph theory, two key determinants of the evolution processes are fixation probabilities and fixation times. While those are preserved for a large class of structures, some structures have been identified that act as ‘amplifiers’ of selection which suppress random drift and others that are ‘suppressors’ of selection which promote random drift. However, these features are crucially dependent on the sequence of events, such as birth-death vs death-birth – a seemingly small change with significant consequences. In our extension of the Moran process this distinction is no longer necessary or possible. Furthermore, ‘fixation’ means that only one trait remains, but ecological fluctuations will continue. We report the fixation probabilities and times for the well-mixed population, circulation graphs as well as amplifiers and suppressors, and compare them to the original Moran process.
