Evolving genealogies under recombination

• Applicant: Professor Dr. Peter Pfaffelhuber
• Subject Area: Mathematics
• Term: from 2012 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 221847528

The Kingman coalescent is a prominent example of a random tree, arising in the field of population genetics as the genealogy of a large population under neutral evolution. The ancestral recombination graph (ARG) extends this random tree to become a random graph, which encodes the correlated genealogies at several loci along a recombining chromosome. However, the coalescent as well as the a ARG only account for a single point in time. We extend this static picture and study the evolution of the ARG along the evolution of the population. Our project1extends recent work of Greven et al. and Depperschmidt et al., who study the evolving genealogy at a single locus (i.e. without recombination) in neutral as well as selective cases, respectively. We construct the evolving genealogy under recombination using well-posed martingale problems, and study its properties under neutrality as well as under selection. Special emphasis is given on a continuum of recombining loci and properties of the map ℓ→ genealogy at locus ℓ. Moreover, at least if selection is weak, our approach allows to compute properties of the genealogical trees along a recombining chromosome. In addition, we use the evolving genealogy under recombination to investigate the model for a bacterial population where the recombination rate depends on the similarity of the recombining genetic material.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1590: Probabilistic Structures in Evolution