[4] These mathematical results set the ME criterion free from the Occam's razor principle and confer it a solid theoretical and quantitative basis.
[4] To solve this drawback, Pauplin[9] proposed to replace OLS with a new particular branch length estimation model, known as balanced basic evolution (BME).
Le Sy Vinh and Arndt von Haeseler[11] have shown, by means of massive and systematic simulation experiments, that the accuracy of the ME criterion under the BME branch length estimation model is by far the highest in distance methods and not inferior to those of alternative criteria based e.g., on Maximum Likelihood or Bayesian Inference.
Moreover, as shown by Daniele Catanzaro, Martin Frohn and Raffaele Pesenti,[12] the minimum length phylogeny under the BME branch length estimation model can be interpreted as the (Pareto optimal) consensus tree between concurrent minimum entropy processes encoded by a forest of n phylogenies rooted on the n analyzed taxa.
[6] FastME, the "state-of-the-art",[5] starts with a rough tree then improves it using a set of topological moves such as Nearest Neighbor Interchanges (NNI).