A probabilistic parsimonious model for species tree reconstruction

Leonardo de Oliveira MartinsDavid Posada

● leomrtns@uvigo.es

● dposada@uvigo.es

with invaluable help from Klaus Schliep and Diego Mallo

What do we want

● To account for uncertainty in gene tree and species tree estimation ← some gene families may be more informative, or maybe we don't have signal at all

● To estimate species trees given arbitrary gene families ←can contain paralogous, missing data, etc.

● To allow for several sources of disagreement ← real data seldomly can be explained by just one biological phenomenon

● Fast computation ← improvement provided by slower, fully probabilistic methods may be elusive, and they can benefit from our output nonetheless

Outline

Model of gene family evolution

Parsimonious estimation of disagreement

* reconciliation

* distance between trees

Hierarchical Bayesian model

Examples

* comparing many trees

* simulation

* TreeFam data set

D1

D2

G1S

G2

Model for the evolution of gene families

.

.

.

Dn

Gn

D1

G1S

Model for the evolution of gene families

distance between G and S

P(G

/S)

Our assumption:

We just need to consider the

simplest explanation for the

difference between the gene

and species trees

● we may use several such simple explanations

D1

G1S

Model for the evolution of gene families

distance between G and S

P(G

/S)

Our assumption:

We just need to consider the

simplest explanation for the

difference between the gene

and species trees

● we may use several such simple explanations

● work with unrooted gene trees

● penalize gene trees very different from species tree

Outline

Model of gene family evolution

Parsimonious estimation of disagreement

* reconciliation

* distance between trees

Hierarchical Bayesian model

Examples

* comparing many trees

* simulation

* TreeFam data set

Quantifying the disagreement

gene tree species tree

reconciliation

assuming deepcoal:

assuming duplosses:

1 deepcoal

1 dup3 losses

assuming HGT:

1 event

Quantifying the disagreement

gene tree species tree

reconciliation

assuming deepcoal:

assuming duplosses:

1 deepcoal

1 dup3 losses

Stochastic error/nonparametric

assuming HGT:

1 event

Outline

Model of gene family evolution

Parsimonious estimation of disagreement

* reconciliation

* distance between trees

Hierarchical Bayesian model

Examples

* comparing many trees

* simulation

* TreeFam data set

Quantifying the disagreement – other measures

mul-tree version: Chaudhary R, Burleigh JG, Fernández-Baca D (2013) Inferring Species Trees from Incongruent Multi-Copy Gene Trees Using the Robinson-Foulds Distance. arXiv:1210.2665

de Oliveira Martins et al. (2008) Phylogenetic Detection of Recombination with a Bayesian Prior on the Distance between Trees. PLoS ONE 3(7): e2651.

Quantifying the disagreement – other measures

see also: Whidden et al. (2013) Supertrees based on the subtree prune-and-regraft distance. PeerJ PrePrints 1:e18v1

Quantifying the disagreement – other measures

Hdist similar to: Nye TMW, Liò P, Gilks WR (2006) A novel algorithm and web-based tool for comparing two alternative phylogenetic trees. Bioinformatics 22: 117-119

Quantifying the disagreement – other measures

Now we have estimates for these

assuming deepcoal:

assuming duplosses:

1 deepcoal

1 dup3 losses

Stochastic error/nonparametric

assuming HGT:

1 event

Now we have estimates for these

assuming deepcoal:

assuming duplosses:

1 deepcoal

1 dup3 losses

Stochastic error/nonparametric

assuming HGT:

1 event

Gene tree parsimony

Now we have estimates for these

assuming deepcoal:

assuming duplosses:

1 deepcoal

1 dup3 losses

Stochastic error/nonparametric

assuming HGT:

1 event

Gene tree parsimony

Gene tree parsimony

Now we have estimates for these

assuming deepcoal:

assuming duplosses:

1 deepcoal

1 dup3 losses

Stochastic error/nonparametric

assuming HGT:

1 event

Gene tree parsimony

Gene tree parsimony

(approximate) dSPR

Now we have estimates for these

assuming deepcoal:

assuming duplosses:

1 deepcoal

1 dup3 losses

Stochastic error/nonparametric

assuming HGT:

1 event

Gene tree parsimony

Gene tree parsimony

(approximate) dSPR

RF, Hdist

Considering several measures of disagreement:

Thus we can incorporate e.g. duplications and losses while accounting for HGT and

random errors

Easy to include other distances in the future

Considering several measures of disagreement:

Problem: the normalization constant

E.g.: Rodrigue N, Kleinman CL, Philippe H, Lartillot N (2009) Computational Methods for Evaluating Phylogenetic Models of Coding Sequence Evolution with Dependence between Codons. Mol Biol Evol 26: 1663-1676.

Solution: importance sampling estimate of Z(.)

Ref.: Bryant D, Steel M (2009) Computing the Distribution of a Tree Metric. TCBB: 420 – 426

Thus we can incorporate e.g. duplications and losses while accounting for HGT and

random errors

Easy to include other distances in the future

Outline

Model of gene family evolution

Parsimonious estimation of disagreement

* reconciliation

* distance between trees

Hierarchical Bayesian model

Examples

* comparing many trees

* simulation

* TreeFam data set

G1 S

Gn

.

.

.

Distribution of gene trees: probabilistic model

D1

Dn

Q1

Qn

G1 S

Gn

λdup1

λdupn

λdupprior

.

.

.

Distribution of gene trees: probabilistic model

D1

Dn

Q1

Qn

G1 S

Gn

λdup1

λdupn

λdupprior

.

.

.

.

.

.

λloss1

λlossn

λlossprior

λspr1

λsprn

λsprprior...

Distribution of gene trees: probabilistic model

D1

Dn

Q1

Qn

G1 S

Gn

λdup1

λdupn

λdupprior

.

.

.

.

.

.

λloss1

λlossn

λlossprior

λspr1

λsprn

λsprprior...

ImportanceSampling

So we can use complex, state-of-the-art software

for phylogenetic inference

Distribution of gene trees: probabilistic model

G1 S

Gn

λdup1

λdupn

λdupprior

.

.

.

.

.

.

λloss1

λlossn

λlossprior

λspr1

λsprn

λsprprior...

Input

ImportanceSampling

So we can use complex, state-of-the-art software

for phylogenetic inference

Distribution of gene trees: probabilistic model

G1 S

Gn

λdup1

λdupn

λdupprior

.

.

.

.

.

.

λloss1

λlossn

λlossprior

λspr1

λsprn

λsprprior...

Output

ImportanceSampling

So we can use complex, state-of-the-art software

for phylogenetic inference

Distribution of gene trees: probabilistic model

G1 S

Gn

λdup1

λdupn

λdupprior

.

.

.

.

.

.

λloss1

λlossn

λlossprior

λspr1

λsprn

λsprprior...

Output

ImportanceSampling

So we can use complex, state-of-the-art software

for phylogenetic inference

Distribution of gene trees: probabilistic model

We should not rely on single estimates of gene

phylogenies

E.g.: Boussau B, Szollosi GJ, Duret L, Gouy M, Tannier E, Daubin V. (2012) Genome-scale coestimation of species and gene trees. Genome research 23: 323-330.

Outline

Model of gene family evolution

Parsimonious estimation of disagreement

* reconciliation

* distance between trees

Hierarchical Bayesian model

Examples

* comparing many trees

* simulation

* TreeFam data set

Example: distances between gene families

● 567 single-copy gene trees for 23 species

Data from.: Salichos L, Rokas A (2013) Inferring ancient divergences requires genes with strong phylogenetic signals. Nature 497: 327–331

● Analysis under a model where only RF, Hdist and dSPR are considered

● Not interested in data set per se (unreliable)

● Use it just as a didactical tool about how the model works

● 567 single-copy gene trees for 23 species

Data from.: Salichos L, Rokas A (2013) Inferring ancient divergences requires genes with strong phylogenetic signals. Nature 497: 327–331

● Analysis under a model where only RF, Hdist and dSPR are considered

Example: distances between gene families

RF Hdist SPR

● Not interested in data set per se (unreliable)

● Use it just as a didactical tool about how the model works

Example: distances between gene families

RF Hdist SPR

Posterior samples

Example: distances between gene families

RF Hdist SPR

Posterior samplesbest estimate

Example: distances between gene families

RF Hdist SPR

Outline

Model of gene family evolution

Parsimonious estimation of disagreement

* reconciliation

* distance between trees

Hierarchical Bayesian model

Examples

* comparing many trees

* simulation

* TreeFam data set

Analysis of simulated data sets

Idea from: Rasmussen MD, Kellis M (2012) Unified modeling of gene duplication, loss, and coalescence using a locus tree. Genome Res. 22: 755-765

We use gene trees only, and simulate tree inference error

● Fully probabilistic simulation of gene trees by Diego Mallo and

David Posada

● Birth and death of new loci, conditioned on a multispecies

coalescent, followed by sequence evolution

Analysis of simulated data sets – results

Analysis of simulated data sets – results

Analysis of simulated data sets – results

Outline

Model of gene family evolution

Parsimonious estimation of disagreement

* reconciliation

* distance between trees

Hierarchical Bayesian model

Examples

* comparing many trees

* simulation

* TreeFam data set

Single copy genes from Drosophila (TreeFam)● 4591 informative, single-copy gene families

● (TreeFam database has 14250 informative gene families)

Single copy genes from Drosophila (TreeFam)● 4591 informative, single-copy gene families

● (TreeFam database has 14250 informative gene families)

Estimated species tree:

Single copy genes from Drosophila (TreeFam)● 4591 informative, single-copy gene families

● Root location uncertain

Estimated species tree:

Single copy genes from Drosophila (TreeFam)● 4591 informative, single-copy gene families

● Root location uncertain

● Only one unrooted topology

Large gene families from Drosophila (TreeFam)● 43 gene families with 102~295 tips

Large gene families from Drosophila (TreeFam)

best species tree:

● 43 gene families with 102~295 tips

~100%

To recap, our model can

● Account for uncertainty in gene tree and species tree estimation ← some gene families may be more informative, or maybe we don't have signal at all

● Estimate species trees given arbitrary gene families ← can contain paralogous, missing data, etc.

● Allow for several sources of disagreement ← real data seldomly can be explained by just one biological phenomenon

● Be fast ← improvement provided by slower, fully probabilistic methods may be elusive, and they can benefit from our output nonetheless

The larger, the better – specially for rooting the species tree

Do not assume gene trees are known – embrace ignorance!

Different gene families may be product of distinct processes

It's parallelized, and all distances can be calculated very fast.

Thank you!

Check out http://darwin.uvigo.es for announcements, code, slides...