Peter Keller abstract
Peter Keller, School of Maths, UoE
Time Symmetries in biological models -- a Markov Chain approach
Many models of biological processes contain certain distributional symmetries. The best known is probably the fixation time symmetry both in the Moran and the Wright-Fisher Model of population genetics. Similar symmetries appear in other contexts as for example for Molecular Motors.
As these models are all Markov Chains in either discrete or continuous time, we use the algebraic properties of Markov Chains to address the problem of detection of time symmetries.
A helpful concept is the introduction of a generalized detailed balance equation together with some symmetry conditions of the transition graph, that express as a duality or intertwining relation of the infinitesimal generator with itself.