# Disjoint Tree Mergers for Large-Scale Maximum Likelihood Tree Estimation
## 4 Discussion
### Comparison of the Three ML Codes  
The running time comparison shows RAxML to be clearly the most computationally intensive, followed by IQ-TREE, and then by FastTree, which is, by far, the fastest method. Therefore, we begin by comparing FastTree to the other methods (Figure 3). On two conditions (i.e., RNASim1000 and RNASim10k datasets), FastTree ties for best among these methods (Tables 3 and 6). However, on the datasets with fragmentary sequences (1000M1-HF) or with heterotachy (Cox1-HET), FastTree is clearly less accurate than both  
Figure 3: Comparing the GTM pipeline to ML methods for running time. Here, we show the runtime (hours) of computing the trees using three different ML methods and a GTM pipeline. For the 1000M1-HF, RNASim1000, and Cox1-HET datasetes, the GTM pipeline uses IQ-TREE starting tree, IQ-TREE constraint trees, and IQ-TREE guide tree. For the RNASim10k and RNASim50k datasets, the GTM pipeline uses FastTree starting tree, IQ-TREE constraint trees, and FastTree guide tree. All of the ML methods were given true alignments and allowed to run to completion except for RAxML, which was limited to 24 h on the 1000M1-HF, RNASim1000, and Cox1-HET datasets, and limited to 168 h on the RNASim10k and RNASim50k datasets. On the RNASim50k datasets, the IQ-TREE failed to return a tree and RAxML returned a tree with an error rate of 100%, and so results for RAxML and IQ-TREE are not shown for that condition.  
RAxML and IQ-TREE (Tables 4 and 5). Hence, FastTree, although, by far, the fastest of these methods, is less robust to these challenging conditions.  
A comparison between RAxML and IQ-TREE is also interesting. RAxML and IQ-TREE have nearly identical accuracy on RNASim1000, and there is only a small advantage to RAxML on the Cox1-HET datasets (Tables 3 and 4). However, RAxML is much more accurate than IQ-TREE on the 1000M1-HF dataset, and it is much less accurate on the RNASim10k dataset (Tables 5 and 6). Hence, the relative performance of RAxML and IQ-TREE depends on the dataset properties, with size and sequence length heterogeneity distinguishing the two methods.  
This study shows that very large datasets present specific challenges to ML heuristics. On the RNASim10K dataset, all of the tested methods were able to return reasonably accurate trees within the limitations on running time and available memory, but the same did not hold for the RNASim50K dataset (Tables 6 and 7). This trend suggests that algorithmic strategies for ML heuristics that have been successful on smaller datasets (with at most 1000 or so sequences) may be counterproductive on ultra-large datasets. Specifically, when the sequence dataset is ultra-large, with many thousands (or tens of thousands) of sequences, methods, such as RAxML and IQ-TREE, which make a significant effort to produce good likelihood scores through numeric parameter optimization may not be competitive (in terms of topological accuracy) with methods (such as FastTree) that do not make as serious an effort to optimize the numeric parameters and, instead, focus on exploring more model tree topologies.