The behavior of the treeness test was examined for evolutionary independence (Cavalli-Sforza and Piazza, 1975) using evolutionary histories from simulated and real [gene frequencies of Italian native cattle breeds] data. For each set of characters, the treeness statistic (T) was evaluated for the 945 topologies possible with 6 populations or a random sample of them. The resulting distributions were analyzed. All the distributions studied show common features. Generally, a small fraction (< 6%) of all topologies gave T values compatible with the phylogenetic hypothesis. This fraction became smaller as the number of characters increased. The T values obtained for the simulated and reconstructed trees are always found at the far left tail of the distribution.