seminar: kratsch & mchardy 2014 bioinformatics 30(17), i527-i533

RidgeRace: ridge regression for continuous ancestralcharacter estimation on phylogenetic trees

Presentation by Rosemary McCloskey

Christina Kratsch1 Alice C. McHardy1

1Department for Algorithmic Bioinformatics, Heinrich Heine University

November 6, 2014

Kratsch & McHardy RidgeRace November 6, 2014 1 / 13

Ancestral reconstruction

phylogeny: binary tree representingevolutionary relationships betweenorganisms

I leaves ⇔ observed/sampled taxaI internal nodes ⇔ common ancestors

ancestral reconstruction:estimation of characteristics of unseenancestral taxa

I discrete (eg. DNA sequence)I continuous (eg. body weight)

http://topicpages.ploscompbiol.org/wiki/Ancestral reconstruction

I leaves ⇔ observed/sampled taxa

I internal nodes ⇔ common ancestors

I discrete (eg. DNA sequence)

I continuous (eg. body weight)

RidgeRace

Existing ancestral reconstruction algorithms:

assume traits evolve along the tree according to a particular model(eg. Brownian motion)

assume fixed rates of evolution across some or all branches

use ancestral reconstruction only as a stepping stone to examinecorrelated traits

RidgeRace:

uses phylogenetic information only (no evolutionary model)

allows any rate on any branch

has ancestral reconstruction as its goal

RidgeRace

RidgeRace:

RidgeRace

RidgeRace:

RidgeRace

RidgeRace:

RidgeRace

RidgeRace:

RidgeRace

RidgeRace:

Methods

Observed phenotypes are sums ofcontributions of each ancestralbranch, plus the root.

y4 = g0 + ga + gb + gc

Branch contributions areproportional to branch lengths.

ga = laβa

Methods

Observed phenotypes are sums ofcontributions of each ancestralbranch, plus the root.

y4 = g0 + ga + gb + gc

Branch contributions areproportional to branch lengths.

ga = laβa

Methods

Combining all yi,~y = L~β,

where (defining l0 = 1),

Li,j =

{lj branch j is ancestral to sample i

0 otherwise.

Optimize β via ridge regression:

β̂ = arg min~β

(yi − (L~β)i)2 + λ

β2j .

λ is the regularization penalty :

penalizes large βj more than small (reduces complexity)

shrinks small βj even closer to zero (reduces noise)

Methods

Li,j =

0 otherwise.

β̂ = arg min~β

(yi − (L~β)i)2 + λ

β2j .

Methods

Li,j =

0 otherwise.

β̂ = arg min~β

(yi − (L~β)i)2 + λ

β2j .

Methods

Li,j =

0 otherwise.

β̂ = arg min~β

(yi − (L~β)i)2 + λ

β2j .

Methods

Li,j =

0 otherwise.

β̂ = arg min~β

(yi − (L~β)i)2 + λ

β2j .

Methods

Li,j =

0 otherwise.

β̂ = arg min~β

(yi − (L~β)i)2 + λ

β2j .

Methods

Calculate states at internal nodesfrom estimated β̂.

x3 = β0 + laβa + lbβb.

For all xi,

x̂ = L′β̂,

L′ij =

{lj j → i

0 otherwise.

Methods

Calculate states at internal nodesfrom estimated β̂.

x3 = β0 + laβa + lbβb.

For all xi,

x̂ = L′β̂,

L′ij =

{lj j → i

0 otherwise.

Simulations

random trees of size 30, 100, 200, 300, 400, 500

phenotypic evolution by Brownian motion with σ2 ∈ {0.5, 1, . . . , 5}ancestral reconstruction with generalized least squares (GLS),maximum likelihood (ML), and RidgeRace

RidgeRace comparable to other methods.

Simulations

phenotypic evolution by Brownian motion with σ2 ∈ {0.5, 1, . . . , 5}

ancestral reconstruction with generalized least squares (GLS),maximum likelihood (ML), and RidgeRace

Simulations

Ovarian cancer data

Hierarchical clustering of 325 ovarian cancer samples.

Reconstructed survival time; mapped mutations to ancestral nodes byparsimony.

Ovarian cancer data

Hierarchical clustering of 325 ovarian cancer samples.

Reconstructed survival time; mapped mutations to ancestral nodes byparsimony.

Good points

The good:

simple approach comparable inperformance to more complexmethods

ancestral reconstructionwithout assuming a particularmodel of evolution

Good points

The good:

Good points

The good:

Room for improvement

choice of real data was a bitodd (not ancestralreconstruction)

limitation is very limiting

The estimation of β might thus bebiased if the depth of single leafnodes is large compared with therest of the tree. We thereforerecommend RidgeRace for

approximately balanced trees.

Bush, Robin M., et al. “Effects of passage historyand sampling bias on phylogenetic reconstruction ofhuman influenza A evolution.” PNAS 97.13 (2000):6974-6980.

Thank you!

Brownian motion

At each time step ∆t, movementdrawn from a normal distributionwith mean 0 and variance σ2, thenlet ∆t→ 0.

seminar: kratsch & mchardy 2014 bioinformatics 30(17), i527-i533

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