Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

A duality relation for type distributions on partitions in the Moran model with recombination
Mareike Esser

Last modified: 2014-04-01


Building on the talk by Sebastian Probst, we reconsider the Moran model with recombination, together with the ancestral process for the partitions of the set of sites, $\{1,\ldots,n\}$. We present a formal duality relation between the type distribution process forward in time and the partitioning process backward in time, where the joint probabilities of types at tuples of loci play the role of the duality function.
We prove this via the representation of the duality function in terms of recombinators, and with the help of various tools from discrete mathematics, in particular, the Moebius inversion principle.


Moran model; recombination; type distributions; duality