I congratulate the authors for this very interesting study. In particular, their evaluation on several relevant data sets.

I would like to bring the attention to the authors and readership that a very similar problem and methodological solution has been proposed by me and colleagues at

Costa et. al 2008, Inferring Differentiation Pathways from Gene Expression. Bioinformatics, v 24, p. i156-i164, 2008, http://bioinformatics.oxf....

There, we proposed a statistical model called dependence trees to infer the order of events in developmental processes. These models can be combined in mixtures to perform this inference on a gene module approach. Similarly to this proposal, the inference of the dependence trees is based on the Minimum Spanning Tree algorithm.