# Improved Duplication-Transfer-Loss Reconciliation with
## 4 Results
### Biological Data  
We also applied RANGER-DTLx to a real biological dataset of over 4500 gene trees from 100 broadly sampled, predominantly microbial, species [5]. Specifically, this dataset consisted of 4547 TreeFix-DTL-corrected gene trees [30] rooted using the OptRoot method implemented in RANGER-DTL 2.0 [17]. We partitioned this dataset into three subsets based on the number of taxa present in the gene trees: less than 50 taxa, between 50-100 taxa, and more than 100 taxa. These subsets represent 76.4% (3474), 16.8% (765), and 6.8% (308) of the total number of gene trees, respectively. We measured the impact, in practice, of allowing for \(\mathbb{TL}\) and \(\mathbb{TX}\) events by (i) counting the number of gene trees for which the cost of an optimal reconciliation decreases when \(\mathbb{TL}\) and \(\mathbb{TX}\) are allowed, and (ii) counting the number of gene trees for which the cost of an optimal reconciliation does not decrease but for which there exist optimal reconciliations that invoke \(\mathbb{TL}\) or \(\mathbb{TX}\) events. We found that only 28 gene trees showed a reduction in reconciliation cost when reconciled using RANGER-DTLx with a \(\mathbb{TX}\) cost of 4 as compared to using RANGER-DTL. This number increases to 76 when a smaller \(\mathbb{TX}\) cost of 3 is used. However, as Table 6 shows, 50.7% of the gene trees, and nearly all of the gene trees with at least 50 leaves, had more optimal reconciliations even when using RANGER-DTLx with the higher \(\mathbb{TX}\) cost of 4. This is a result of some (but not all) of the co-optimal reconciliations invoking \(\mathbb{TL}\) and/or \(\mathbb{TX}\) events. These results suggest that while \(\mathbb{TL}\) and \(\mathbb{TX}\) events clearly lead to more parsimonious reconciliations in some cases for many gene trees it may be difficult to confidently infer if \(\mathbb{TL}\) and \(\mathbb{TX}\) events have in fact occurred. Runtime analysisWe also compared the runtimes of ecceTERA (undated version), RANGER-DTL, and RANGER-DTLx. Average runtimes for these methods on the three subsets of the biological dataset are shown in Table 7. As the table shoes, RANGER-DTL and ecceTERA are both extremely efficient, averaging a runtime of smaller than 1 s on all three subsets. As expected, given the increased complexity of the model, RANGER-DTLx takes longer than \begin{table}
\begin{tabular}{c c c} \hline \hline
**Dataset Size** & **Total \# Gene Trees** & **Gene Trees with Additional Co-Optimal Solutions** \\ \hline \(<\)50 taxa & 3474 & 1350 (38.9\%) \\
50–100 taxa & 765 & 667 (87.2\%) \\ \(>\)100 taxa & 308 & 292 (94.8\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Number of biological dataset gene trees that result in additional co-optimal reconciliations invoking \(\mathbb{TL}\) and/or \(\mathbb{TX}\) events. These results are based on event costs of 1, 2, 3, 4, and 4, for losses, duplications, transfers, \(\mathbb{TL}\), and \(\mathbb{TX}\), respectively. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Dataset-1**} & \multicolumn{2}{c}{**Dataset-2**} \\ \hline \# TX **Considered** & **Exact Matches** & **Average Distance** & **\# TX** **Considered** & **Exact Matches** & **Average Distance** \\ \hline RANGER-DTLx Cost 4 & 14 & 3 (21.4\%) & 1.71 & 34 & 13 (38.2\%) & 2.17 \\ RANGER-DTLx Cost 3 & 857 & 473 (55.2\%) & 1.52 & 1475 & 689 (46.7\%) & 2.03 \\ ecceTERA & 926 & 23 (2.5\%) & 4.90 & 1554 & 36 (2.8\%) & 6.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Accuracy of placing unsampled species donors on the species tree. All \(\mathbb{TX}\) events inferred by each method, regardless of support, for which the recipient species was identified correctly were used for this analysis. The inferred unsampled donor is considered an exact match if the location of the donor lineage on the species tree is the same as the true location of the donor. Numbers for TX events considered and exact matches are aggregated across all 500 gene tree/species tree pairs in each dataset.