Duality for Wright-Fisher diffusion bridges
speaker: Paul Jenkins (University of Warwick)abstract: There is a well known duality relationship between the neutral Wright-Fisher diffusion running forwards in time and its genealogical counterpart running backwards in time, the coalescent. In this talk I will extend this relationship to find a dual for Wright-Fisher diffusion bridges - that is, allele frequency trajectories conditioned on both start- and endpoint. To study the frequency of an allele at time t in a bridge starting at time 0 and ending at time T > t, the emerging genealogical structure is a coalescent running backwards from time t to 0 and another coalescent running forwards from time t to T. We can also extend this idea to incorporate natural selection, in which the genealogical processes are now branching and coalescing in two directions from time t. This is joint work with Bob Griffiths (Oxford) and Dario Spanò (Warwick).
timetable:
Mon 1 Apr, 15:30 - 16:30, Aula Dini
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