Selection is one of the factors that most influence the shape of genealogical trees. Here we report results of simulations of the infinite-sites version of Moran's model of population genetics aiming at quantifying how the presence of selection affects the branching pattern (topology) of binary genealogical trees. In particular, we consider a scenario of purifying or negative selection in which all mutations are deleterious and each new mutation reduces the fitness of the individual by the same fraction. Analysis of five statistical measures of tree balance or symmetry borrowed from taxonomy indicates that the genealogical trees of samples of populations in which selection is actuating are in the average more asymmetric than neutral trees and that this effect is enhanced by increasing the sample size. However, a quantitative evaluation of the power of these balance measures to detect a tree topology significantly distinct from the neutral one indicates that they are not useful as tests of neutrality of mutations.
The nk model of fitness interactions is examined. This model has been used by previous authors to investigate the effects of fitness epistasis on substitution dynamics in molecular evolution, and to make broader claims about the importance of epistasis. To examine these claims, an infinite-allele approximation is introduced. In this limit, it is shown that the nk model is, at an appropriate level of description, formally identical to the non-epistatic House-of-Cards model—a well-studied model in theoretical population genetics. It is further shown that in many parameter regimes, the analytical results obtained from this infinite-allele approximation are very close to results from the full nk model (with a finite number of alleles per locus). The findings presented shed light on a number of previous results.