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Statistical criteria have long been the standard for selecting the best model for phylogenetic reconstruction and downstream statistical inference. Although model selection is regarded as a fundamental step in phylogenetics, existing methods for this task consume computational resources for long processing time, they are not always feasible, and sometimes depend on preliminary assumptions which do not hold for sequence data. Moreover, although these methods are dedicated to revealing the processes that underlie the sequence data, they do not always produce the most accurate trees. Notably, phylogeny reconstruction consists of two related tasks, topology reconstruction and branch-length estimation. It was previously shown that in many cases the most complex model, GTR+I+G, leads to topologies that are as accurate as using existing model selection criteria, but overestimates branch lengths. Here …