1. Incorporating uncertainty in distance-matrix phylogenetics
Wally Gilks Leeds University
Tom Nye Newcastle University
Pietro Liò Cambridge University
Isaac Newton Institute
December 17, 2007

2. Distance-based methods
Larger trees
Faster algorithms
Less model-dependent
Genome-scale evolutionary rearrangements

3. Agglomerative distance methods
NJ (Saitou and Nei, 1987)
BioNJ (Gascuel, 1997)
Weighbor (Bruno et al, 2000)
MVR (Gascuel, 2000)
FastME (Desper and Gascuel, 2004)

4. Variance models Independent distances Correlated distances A
Ordinary Least Squares (OLS)
Weighted Least Squares (WLS)
NJ, Weighbor, FastME
Correlated distances
shared evolutionary paths (Chakraborty, 1977)
computed from shared sequences: BioNJ
induced by estimation process (we show)
Generalised Least Squares (GLS)
Hasegawa (1985), Bulmer (1991), MVR A
A B C

5. Two types of tree Ultrametric time tree Non-ultrametric
divergence tree
Time
(mya)
Divergence
= “true distance”
= integrated rate of evolution
= path length
Divergence
more evolution

6. Which tree type to assume?
Ultrametric tree makes stronger assumptions
Different methods for estimating each type
But both types are in principle correct!
Our method coherently integrates both types
Produces rooted tree, no need for outgroup

7. An agglomerative stage
time tree
divergence tree
Time
(mya)
Divergence E E C A C A D B D B

8. Divergence additivity
divergence tree
and for X = C,D,… E C A D B

9. Distances are estimated divergences
Regression model
divergence tree
mean zero
and for X = C,D,… E C A D B
parameters

10. Divergences are distorted timesA B C D E
Time
(mya)
time tree
parameter
mean zero
uncorrelated
Random effects model

11. Variance assumptions controls noise function of clade A structure
variance parameters
clade A size
shared node A
elapsed time
Chakraborty (1977)
Nei et al (1985)
Bulmer (1991)
controls distortion

12. Estimation Time tree and divergence tree are estimated simultaneously
by GLS (Hasegawa, 1985; Bulmer, 1991)
Choose most recent agglomeration always
Estimated divergences become the distances for the next stage
Variance formula accommodates estimation-induced correlations

13. Notes Can estimate variance parameters s2 and n
Computationally efficient algorithm
same time-complexity as BioNJ
we call it StatTree

14. Simulations 16 taxa, unbalanced topology, 100 simulations
Mean topological correctness
n=1%
n=5%
n=10%
s=5%
StatTree = 95%
BioNJ = 83%
StatTree = 89%
BioNJ = 81%
StatTree = 85%
BioNJ = 77%
s=10%
StatTree = 72%
BioNJ = 50%
StatTree = 71%
BioNJ = 48%
StatTree = 67%
BioNJ = 53%
s=20%
StatTree = 44%
BioNJ = 28%
StatTree = 45%
BioNJ = 26%
StatTree = 43%
16 taxa, unbalanced topology, 100 simulations