Genealogical distances under low levels of selection

For a panmictic population of constant size evolving under neutrality, Kingmans 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. The difference to neutrality is [Formula] for genic selection with selection intensity and [Formula] for other modes of dominance.