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Background  The rapid accumulation of molecular sequence data, driven by novel wet-lab sequencing technologies, poses new challenges for large-scale maximum likelihood-based phylogenetic analyses on trees with more than 30,000 taxa and several genes. The three main computational challenges are: numerical stability, the scalability of search algorithms, and the high memory requirements for computing the likelihood.    Results  We introduce methods for solving these three key problems and provide respective proof-of-concept implementations in RAxML. The mechanisms presented here are not RAxML-specific and can thus be applied to any likelihood-based (Bayesian or maximum likelihood) tree inference program. We develop a new search strategy that can reduce the time required for tree inferences by more than 50% while yielding equally good trees (in the statistical sense) for well-chosen starting trees. We present an adaptation of the Subtree Equality Vector technique for phylogenomic datasets with missing data (already available in RAxML v728) that can reduce execution times  and  memory requirements by up to 50%. Finally, we discuss issues pertaining to the numerical stability of the Γ model of rate heterogeneity on very large trees and argue in favor of rate heterogeneity models that use a single rate or rate category for each site to resolve these problems.    Conclusions  We address three major issues pertaining to large scale tree reconstruction under maximum likelihood and propose respective solutions. Respective proof-of-concept/production-level implementations of our ideas are made available as open-source code.

Algorithms, data structures, and numerics for likelihood-based phylogenetic inference of huge trees