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Enhancing Searches for Optimal Trees Using SIESTA

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Book cover Comparative Genomics (RECOMB-CG 2017)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 10562))

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Abstract

Many supertree estimation and multi-locus species tree estimation methods compute trees by combining trees on subsets of the species set based on some NP-hard optimization criterion. A recent approach to computing large trees has been to constrain the search space by defining a set of “allowed bipartitions”, and then use dynamic programming to find provably optimal solutions in polynomial time. Several phylogenomic estimation methods, such as ASTRAL, the MDC algorithm in PhyloNet, and FastRFS, use this approach. We present SIESTA, a method that allows the dynamic programming method to return a data structure that compactly represents all the optimal trees in the search space. As a result, SIESTA provides multiple capabilities, including: (1) counting the number of optimal trees, (2) calculating consensus trees, (3) generating a random optimal tree, and (4) annotating branches in a given optimal tree by the proportion of optimal trees it appears in. SIESTA is available in open source form on github at https://github.com/pranjalv123/SIESTA.

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Acknowledgments

We thank the anonymous reviewers for their helpful criticisms on an earlier draft, which greatly improved the manuscript. We also thank Erin Molloy, Sarah Christensen, and Siavash Mirarab, for feedback on the initial results.

Funding. This study made use of the Illinois Campus Cluster, a computing resource that is operated by the Illinois Campus Cluster Program in conjunction with the National Center for Supercomputing Applications and which is supported by funds from the University of Illinois at Urbana-Champaign. This work was partially supported by U.S. National Science Foundation Graduate Research Fellowship Program under Grant Number DGE-1144245 to PV and U.S. National Science Foundation grant CCF-1535977 to TW.

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Illinois, Urbana, IL, 61801, USA

    Pranjal Vachaspati & Tandy Warnow

Authors
  1. Pranjal Vachaspati
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  2. Tandy Warnow
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Editor information

Editors and Affiliations

  1. University of Campinas, Campinas, São Paulo, Brazil

    Joao Meidanis

  2. Rice University, Houston, Texas, USA

    Luay Nakhleh

Supplementary Materials

Supplementary Materials

Table 1. We show the mean number of optimal trees for ASTRAL, averaged over 25 replicates of 50-taxon simulated datasets with 5 genes that vary in the level of missing data. AD12 is moderate ILS, AD31 is high ILS, and AD68 is very high ILS.
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Table 2. We show the mean number of optimal trees for ASTRAL, averaged over 10 replicates of 50-taxon simulated datasets with 10 genes that vary in the level of missing data. AD12 is moderate ILS, AD31 is high ILS, and AD68 is very high ILS.
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Table 3. We show the mean number of optimal trees for ASTRAL, averaged over 10 replicates of 50-taxon simulated datasets with 25 genes that vary in the level of missing data. AD12 is moderate ILS, AD31 is high ILS, and AD68 is very high ILS.
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Table 4. Number of optimal trees (in scientific notation) for ASTRAL, FastRFS-basic, and FastRFS-enhanced on SMIDgen simulated supertree data sets with varying numbers of taxa and genes, and differing scaffold factors. ASTRAL has several orders of magnitude fewer optimal trees than FastRFS-basic and FastRFS-enhanced.
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Fig. 7.
figure 7

The strict consensus of FastRFS trees is more accurate than FastRFS. We show Delta-error (change in mean topological error between FastRFS and the strict consensus of FastRFS trees) on simulated supertree datasets with 100, 500, and 1000 species; values below 0 indicate that the strict consensus FastRFS is more accurate (i.e., it has lower error) than FastRFS. The figure shows how the percentage of taxa in the scaffold source tree impact accuracy, averaged over 10 replicates for 1000-taxon data and 25 replicates for 100- and 500-taxon data. Error bars indicate the standard error; the topological error is the average of the FN and FP error rates.

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Fig. 8.
figure 8

Mean error rates for a single FastRFS tree and the strict consensus of all FastRFS trees on the supertree datasets with 100, 500, and 1000 species, compared to the number of optimal trees. We show FP rate and FN rates for each method; these are equal for default FastRFS (because it is always binary), but different for the strict consensus of the FastRFS trees. As the number of optimal trees increases, the decrease in the FP rate is larger than the increase in the FN rate for the strict consensus of the FastRFS trees, explaining why the average error for the strict consensus of the FastRFS trees is lower than for a single FastRFS tree (as shown in Fig. 7). Results for 193 replicates are shown on 1000-taxon data, results for 312 replicates are shown on 500-taxon data, and results for 104 replicates are shown on 100-taxon data.

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Fig. 9.
figure 9

The strict consensus of ASTRAL trees is more accurate than ASTRAL when gene trees are incomplete. We show Delta-error (change in mean topological error between FastRFS and the strict consensus of FastRFS trees) on simulated phylogenomic datasets with varying numbers of incomplete gene trees on 50-species datasets with three different ILS levels; values below 0 indicate that the strict consensus ASTRAL is more accurate (i.e., it has lower error) than ASTRAL. Note that there is a big advantage in computing the strict consensus tree of the optimal ASTRAL trees instead of a single ASTRAL tree under the highest amount of missing data, and that the advantage decreases as the amount of missing data decreases. We show results for 25 replicates. Error bars indicate the standard error; topological error is the average of the FN and FP error rates.

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Fig. 10.
figure 10

Mean change in error between the strict consensus of the ASTRAL trees compared to a single ASTRAL tree on the 50-taxon phylogenomic datasets with varying degrees of missing data and ILS, as a function of the number of optimal trees. Values below zero indicate that the strict consensus tree has better accuracy (lower error) than a single ASTRAL tree. We show the change in FP rates (blue, solid line) and in FN rates (red, dashed); the black line represents the baseline. This figure shows that the strict consensus has lower false positives than a single ASTRAL tree and higher false negatives, but also that the reduction in false positives is larger than the increase in false negatives. The figure also shows that the reduction in false positives increases with the number of optimal trees. (Color figure online)

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Vachaspati, P., Warnow, T. (2017). Enhancing Searches for Optimal Trees Using SIESTA. In: Meidanis, J., Nakhleh, L. (eds) Comparative Genomics. RECOMB-CG 2017. Lecture Notes in Computer Science(), vol 10562. Springer, Cham. https://doi.org/10.1007/978-3-319-67979-2_13

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  • DOI: https://doi.org/10.1007/978-3-319-67979-2_13

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  • Online ISBN: 978-3-319-67979-2

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