Deciphering Reticulate Evolution UsingPhylogenetic Reconciliation

Mukul S. Bansal

Department of Computer Science and Engineering,University of Connecticut,

USA

The Phylogenetic Networks WorkshopJuly 27, 2015

Supertrees or Supernetworks?

Gene Family Evolution

ProblemHow did any given gene family evolve?

I Gene families evolve inside species trees.I Affected by evolutionary events such as gene duplication,

horizontal gene transfer, and gene loss.

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Species Tree S

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Evolution of Gene Family G

Duplication

Loss

Transfer

Gene Tree on G

Definition: DTL Reconciliation

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Species Tree S

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G with evolutionary history

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Definition: DTL Reconciliation

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Species Tree S

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Gene Tree on G

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G with evolutionary history

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Input: A gene tree for that gene family, and a trusted rootedspecies tree.Output: An evolutionary history of that gene family showinghorizontal gene transfers, gene duplications, losses, and speciationevents.

DTL Reconciliation Problem Formulation

Parsimony formulation:

I Costs are assigned to duplications, transfers, and losses.

I Goal: Find the reconciliation that minimizes the total cost.

I Easy to compute cost for a given reconciliation.

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Costs: L=1, Δ=2, Θ=3

2 + 3 + 2x1 = 7

1Δ, 1Θ, 2L

Different reconciliation could have different cost.

Applications of DTL Reconciliation

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Species Tree S

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Gene Tree on G

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I Understanding how gene families evolve.

I Dating gene birth.

I Inferring orthologs/paralogs/xenologs.

I Gene tree error-correction.

I Whole genome species tree construction.

I Constructing species phylogenetic networks.

Applications of DTL Reconciliation

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Species Tree S

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Gene Tree on G

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I Understanding how gene families evolve.

I Dating gene birth.

I Inferring orthologs/paralogs/xenologs.

I Gene tree error-correction.

I Whole genome species tree construction.

I Constructing species phylogenetic networks.

Background: Computing Optimal DTL Reconciliations

For undated species tree:I Best time-consistent reconciliation: NP-hard (Tofigh et al.,

2011; Ovadia et al., 2011)I If time-consistency not enforced: O(mn)-time algorithm

(Bansal et al., 2012)

For dated species trees:I Best time-consistent reconciliation: O(mn2)-time algorithm

(Doyon et al., 2010)

DTLI model:I Considers ILS at unresolved species tree nodes (Stolzer et al.,

2012)

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Species Tree S

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Gene Tree G

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Background: Handling Multiple Optima

I There can be many optimal DTL reconciliations.

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Gene Tree Size

Number of Optimal Solutions by Gene Tree Size

I Enumeration: Exponential in input size (Tofigh. et al., 2011; Chenet al., 2012)

I Uniform random sampling and aggregation: O(mn2)-time (Bansalet al., 2013)

I Compact representation in reconciliation graph: O(mn3)-time(Scornavacca et al., 2013)

I Median reconciliation (Nguyen et al., 2013)

Background: Gene Tree Error-Correction

Gene tree construction is highly error-prone. Garbage in, garbageout.

I First-attempts: Mowgli-NNI (Nguyen et al., 2012), AnGST(David and Alm, 2011)

I New methods: TreeFix-DTL (Bansal et al., 2015), ALE(szollosi et al. 2013) ), TERA (Scornavacca et al., 2015))

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Background: Event Cost Assignment

Fundamental questions:

I What are the “best” event costs to use?

I How do reconciliations vary as we change event costs?

Algorithm to partition event cost space into equivalence regionsbased on pareto-optimality of event counts: O(m5n logm)-time(Libeskind-Hadas et al., 2014)

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Constructing Phylogenetic Networks

I Microbial phylogenetic networks are distinct fromhybridization networks.

Problem formulationInput: A collection of gene families (sequence alignments) and areference species tree.Output: Species tree augmented with horizontal edges(representing transfer events), and labels for each vertical andhorizontal edge specifying the genes that traveled through it.

Gene Trees

Species Tree

Genes ...

Genes ...

Genes ... Genes ...

Genes ...

Constructing Phylogenetic Networks

Advantages of using a reference species tree:

I Improved complexity and scalability.

I Inferred network does not depend on reference tree.

I Customizable and easily interpretable network view.

Basic implementation:

1. Infer gene trees.

2. Use DTL reconciliation to reconcile individual gene trees withreference tree.

3. Aggregate transfers inferred for gene trees onto species tree;e.g., NOTUNG.

Challenges due to reconciliation uncertainty

I Multiple optima, gene tree error, and event cost assignmentconfound reconciliation accuracy.

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Challenges due to reconciliation uncertainty

I Multiple optima, gene tree error, and event cost assignmentconfound reconciliation accuracy.

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Duplications Transfers Losses

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Possible Solution

Proposal: Distinguish between highly-supported andweakly-supported events across multiple optima, multiple eventcosts, and gene tree topologies.

I Easy to do for multiple optima and event costs based ondeveloped algorithms.

I No such algorithms for gene tree error.

Goal: Develop algorithms to generate alternative gene treetopologies and study variability of reconciliation across them.

Optimal Gene Tree Resolution (OGTR)

Input: A non-binary gene tree GN , a species tree S , and eventcosts.Output: Find a binary resolution GB of GN such that, the mostparsimonious DTL reconciliation of GB and S has smallestreconciliation cost.

I Provides rigorous framework for uniformly sampling from allcandidate gene trees.

I Non-binary gene tree obtained by collapsing weak edges.I Fundamental question for DTL reconciliation.

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OGTR is NP-hard

I OGTR is NP-hard for both undated and dated species trees(Kordi and Bansal, 2015).

I Surprising since problem is linear-time solvable underduplication-loss model (Zheng and Zhang, 2014).

Key Ideas:

I Reduction from minimum 3 set cover problem.

I Subtrees in species tree correspond to sets

I Subtrees in unresolved gene tree correspond to elements ofthe universe.

I Structure of gadget forces root of each subtree (element) tomap to a “set” in which that element occurs.

I Using more sets for the mapping results in higherreconciliation cost.

OGTR is NP-Hard

A Fixed-Parameter Algorithm for OGTR

I DP algorithms for binary gene trees can be extended to workwith non-binary gene trees.

I Consider all possible resolutions at each non-binary gene treenode and fill DP-table for subproblem with best score over allresolutions.

I Gives O(2k · k! · ln + mn) and O(2k · k! · ln + mn2)-timealgorithms for dated and undated species trees, respectively

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A Fixed-Parameter Algorithm for OGTR

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Uniform Sampling of Optimal Resolutions

I DP framework allows for sampling optimal resolutionsuniformly at random.

I Samples can be combined with event cost and multipleoptima analyses to assess robustness of individual events andmappings.

I Enables identification of highly- and weakly-supported eventsand mappings for network construction.

Future Directions: Assigning Weakly-Supported Events

1. Leverage high-support events to improve assignment of allother events:

I Use highly-supported events to infer highways of transfers.I Improve assignment of other events based on inferred

highways.

2. Use gene tree and species tree branch lengths to choosebetween alternative scenarios for low-support events.

Thank You!

Questions!