Math-Bio: Modeling evolution in dynamic populations: the decoupled Moran Process

Join us for the next Math-Bio seminar on Wednesday, October 9th, at 2:00 pm in the PIMS lounge (ESB 4133). George Berry, a PhD student at UBC, will present his work on "Modeling Evolution in Dynamic Populations: The Decoupled Moran Process." Learn about evolutionary dynamics and its impact on fixation probabilities and times in variable population sizes. PIMS tea to follow at 3:00 pm. Can't attend in person? Join us on Zoom!

Zoom information:

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https://ubc.zoom.us/j/64671573478?pwd=J1kiOTYqD0TukMjoVRpTWfBbqSr5TM.1

Meeting ID: 646 7157 3478
Passcode: 979571

The Moran process models the evolutionary dynamics between two competing types in a population, traditionally assuming a fixed population size. We investigate an extension to this 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. Our analysis explores the impact of this decoupling on two key determinants of the evolutionary process: fixation probabilities and fixation times. In evolutionary graph theory, these statistics depend significantly on the population structure, such that structures have been identified that act as ‘amplifiers’ of selection while others are ‘suppressors’ of selection. 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. We determine the fixation probabilities and times for the well-mixed population, regular graphs as well as amplifiers and suppressors, and compare them to the original Moran process.