Abstract
Table 2: Accuracy of the reconstructions as measured with the Generalized Quartet Distance (GQD). For each continent we report the average and the variance of the GQD over all the languages spread on the continent. The different columns correspond to the two different ways of constructing the distance matrix (LDN and LDND) and to the three distance-based algorithms considered. The last column labelled RANDOM reports the results for the null model considered. See the main text for details.
['[BOLD] GENERALIZED QUARTET DISTANCE', '[BOLD] GENERALIZED QUARTET DISTANCE  [BOLD] LDN', '[BOLD] GENERALIZED QUARTET DISTANCE  [BOLD] LDN', '[BOLD] GENERALIZED QUARTET DISTANCE  [BOLD] LDN', '[BOLD] GENERALIZED QUARTET DISTANCE  [BOLD] LDND', '[BOLD] GENERALIZED QUARTET DISTANCE  [BOLD] LDND', '[BOLD] GENERALIZED QUARTET DISTANCE  [BOLD] LDND', '[BOLD] GENERALIZED QUARTET DISTANCE']
To quantify the accuracy of the inferred trees, for each language family we computed the Generalized Robinson-Foulds score (GRF) and the Generalized Quartet Distance (GQD) of the inferred trees with the corresponding Ethnologue classifications. In particular we report, for each continent, the mean and the variance, across all the language families in that continent, of the values of the GRF and of the GQD between the inferred trees and the corresponding Ethnologue classifications, using both the LDN and the LDND distances. For each continent we considered all the language families present in the ASJP database. As already mentioned, the GRF and the GQD are two complementary measures of the disagreement between the inferred tree and the expert classification. The GRF quantifies the percentage of wrong edges in the inferred trees, while the GQD counts how many quartets in the Ethnologue tree are different butterflies than in the reconstructed tree. In both cases the performance of the different algorithms always look very similar, though in almost all cases the noise reduction made by FastSBiX corresponds to a slightly better ability in reconstructing the correct phylogenies. FastSBiX features indeed the lowest average scores and, in many cases, the lowest variances. The last column of the tables, named “RANDOM”, shows the error one would have for a randomly reconstructed tree. This information is useful to correctly appreciate the algorithmic ability of inferring the correct phylogenetic relationships. While in fact we correct the distance measures in order to avoid biases due to non binary classification, it is evident that it is easier to be consistent with a very coarse grained classification than with a finer one. In order to take into account this observation, we can compare the errors made by the reconstruction algorithms with the errors a completely randomly constructed tree (with the same leaves) would feature. over 10 realizations of the GRF and the GQD between a randomly reconstructed tree and the Ethnologue classification.