The Free Lunch is not over yet—systematic exploration of numerical thresholds in maximum likelihood phylogenetic inference

Maximum likelihood (ML) is a widely used phylogenetic inference method. ML implementations heavily rely on numerical optimization routines that use internal numerical thresholds to determine convergence. We systematically analyze the impact of these threshold settings on the log-likelihood and runtimes for ML tree inferences with RAxML-NG, IQ-TREE, and FastTree on empirical datasets. We provide empirical evidence that we can substantially accelerate tree inferences with RAxML-NG and IQ-TREE by changing the default values of two such numerical thresholds. At the same time, altering these settings does not significantly impact the quality of the inferred trees. We further show that increasing both thresholds accelerates the RAxML-NG bootstrap without influencing the resulting support values. For RAxML-NG, increasing the likelihood thresholds ϵLnL and ϵbrlen to 10 and 103, respectively, results in an average tree inference speedup of 1.9 ± 0.6 on Data collection 1, 1.8 ± 1.1 on Data collection 2, and 1.9 ± 0.8 on Data collection 2 for the RAxML-NG bootstrap compared to the runtime under the current default setting. Increasing the likelihood threshold ϵLnL to 10 in IQ-TREE results in an average tree inference speedup of 1.3 ± 0.4 on Data collection 1 and 1.3 ± 0.9 on Data collection 2.