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.
P. Jagers, O. Nerman, and Z. Ta\"ıb. Selected Proceedings of the Sheffield Symposium on Applied Probability (Sheffield, 1989), volume 18 of IMS Lecture Notes Monogr. Ser., page 118--126. Hayward, CA, Inst. Math. Statist., (1991)