Abstract
For a panmictic population of constant size evolving under neutrality, Kingman’s coalescent describes the genealogy of a population sample in equilibrium. However, for genealogical trees under selection, not even expectations for most basic quantities like height and length of the resulting random tree are known. Here, we give an analytic expression for the distribution of the total tree length of a sample of size n under low levels of selection in a two-alleles model. We can prove that trees are shorter than under neutrality under genic selection and if the beneficial mutant has dominance h<1∕2, but longer for h>1∕2. The difference from neutrality is O(α2) for genic selection with selection intensity α and O(α) for other modes of dominance.
Highlights
Understanding population genetic models, e.g. the Wright-Fisher or the Moran model, can be achieved in various ways
Starting with Kingman (1982) and Hudson (1983), genealogical trees started to play a big role in the understanding of the models as well as of DNA data from a population sample
The disadvantage of these splitting events is that they make this genealogical structure far more complicated to study than the coalescent for neutral evolution
Summary
Understanding population genetic models, e.g. the Wright-Fisher or the Moran model, can be achieved in various ways. Starting with Kingman (1982) and Hudson (1983), genealogical trees started to play a big role in the understanding of the models as well as of DNA data from a population sample. Genealogies under selection have long been an interesting object to study Starting with Krone and Neuhauser (1997) and Neuhauser and Krone (1997), genealogical trees under selection could be described using the Ancestral Selection Graph (ASG). In addition to coalescence events, which indicate joint ancestry of ancestral lines, selective events affect the genealogy in the following way: First, going backward in time, splitting events indicate possible ancestry.
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