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SUMMARY:The graph Moran process - John Lapinskas (University of Oxford)
DTSTART:20190307T143000Z
DTEND:20190307T153000Z
UID:TALK117172@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:The graph Moran process is an interacting particle system\, so
 mewhat similar to a randomised version of bootstrap percolation\, introduc
 ed in 2005 as a way to model the spread of mutations in evolutionary biolo
 gy. Individuals are modelled as vertices on a connected graph\, allowing o
 nly adjacent individuals to interact. Initially\, a single uniformly rando
 m vertex is a "mutant" and the remaining vertices are "non-mutants". The p
 rocess evolves as a Markov chain\, with vertices copying their states to t
 heir neighbours ("reproducing") at intervals. Mutants are either more or l
 ess likely to reproduce than non-mutants\, corresponding to a beneficial o
 r harmful initial mutation. Eventually\, the entire graph will be filled w
 ith either mutants ("fixation") or non-mutants ("extinction"). This framin
 g naturally lends itself to extremal questions\, such as: How high can fix
 ation probability be? How long can the process take to absorb? And how sma
 ll a "jump" can there be between the performance of harmful and beneficial
  mutations? In this talk\, I\nwill survey a number of recent advances on t
 hese questions and others.\n
LOCATION:MR12
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