Project Details
Projekt
The effect of natural selection on genealogies
Subject Area
Mathematics
Term
from 2015 to 2020
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 285170854
Natural selection shapes genealogies within a population in various ways. In our proposal, we suggest both, a general qualitative study of some aspects of genealogies under selection, and a quantitative treatment of specific relevant models. More precisely, we study models with unbounded selection (so there are arbitraryly beneficial and/or deleterious fitness classes) using Girsanov transforms and approximate dualities, and selection in fluctuating environment (where an allele can be beneficial or deleterious, depending on the environment) using a general result on stochastic averaging in the limit of fast environmental changes. For both models, we use the previously developed technique of treating genealogical trees as metric measure spaces, leading to tree-valued stochastic Markov processes. The qualitative work is dealing with a comparison of genealogical distances under neutrality and under selection. We conjecture that many ssituations including selection lead to shorter genealogical distances.
DFG Programme
Priority Programmes
Subproject of
SPP 1590:
Probabilistic Structures in Evolution
