Tree-valued stochastic processes

Classically, allelic frequencies in large populations are modelled as (real- or measure-valued) diffusion processes (see e.g. Etheridge, A. An introduction to superprocesses. American Mathematical Society, 2001). Much of their analysis is done using a backward, i.e., coalescent-based approach. We integrate these two approaches into a single stochastic process, taking values in genealogical trees. By now, we have constructed tree-valued processes under neutrality (Greven et al, 2010) and under selection (Depperschmidt et al. 2011). Topological foundations are laid in Greven et al. (2009) and Depperschmidt et al. (2011). In the selective case, our analysis gives for the first time approximations for the genealogical distances in a sample in equilibrium. In future work, we address the biologically important consequences of recombination on the evolution of genealogies.

Weitere Informationen: http://www.stochastik.uni-freiburg.de
Tel: 0761/203-5667
Email: peter.pfaffelhuber@stochastik.uni-freiburg.de

Projektbeginn: 2005
Projektende: (unbegrenzt)

Prof. Dr. Peter Pfaffelhuber

Albert-Ludwigs-Universität Freiburg
Abteilung für Mathematische Stochastik
Prof. Dr. Peter Pfaffelhuber
Ernst-Zermelo-Straße 1
79104 Freiburg

Telefon: 0761/203-5664
Fax: 0761/203-5661
Email: sekretariat@stochastik.uni-freiburg.de
http://www.stochastik.uni-freiburg.de/pfaffelhuber

• Depperschmidt A

• Greven A, Pfaffelhuber P, Winter A: Tree-valued resampling dynamics Martingale problems and applications Probab Theory Rel, 2013; 155: 789-838. : https://doi.org/10.1007/s00440-012-0413-8 (download: http://arxiv.org/abs/0806.2224)
• Depperschmidt A, Greven A, Pfaffelhuber P: Marked metric measure spaces Electron Commun Prob, 2011; 16: 174-188. : https://doi.org/10.1214/ECP.v16-1615 (download: https://projecteuclid.org/euclid.ecp/1465261973)
• Greven A, Pfaffelhuber P, Winter A: Convergence in distribution of random metric measure spaces: (Lambda-coalescent measure trees). Probab Theory Rel, 2009; 145 (1): 285-322. : http://dx.doi.org/10.1007/s00440-008-0169-3 (download: http://arxiv.org/abs/math/0609801)