1. Xuhua Xia xxia@uottawa.ca http://dambe.bio.uottawa.ca
How to date
Xuhua Xia

2. Objectives Two major objectives of molecular phylogenetics
Branching patterns (speciation or gene duplication events)
Dating of the speciation or gene duplication events
Classification of methods
Criteria used
Maximum likelihood (ML) method (e.g., PAML)
Bayesian methods (e.g., BEAST)
Least-squares (LS) method based on distance-based matrices (e.g., DAMBE)
Hard- or soft-bound
Global or local clock
Data needed
A topology
A set of aligned sequences OR a distance matrix satisfying the molecular clock hypothesis (either globally or locally)
Calibration points
One or more from fossil record
From sampling time for rapidly evolving species (e.g., RNA viruses)
Slide 2

3. Rationale
Given two species i and j, we can compute the evolutionary distance between them (dij which is the number of substitutions per site), but how do we know the time (t) that these two species have diverged from their common ancestor?
Knowing dij alone does not give us time. We also need to know the rate of change (r, which is equivalent to speed).
If we know that a runner runs at a constant speed of 10 km/hr and that he has covered a distance of 20 km, then he has run 2 hours ( = 20km/(10 km/hr)
If we know that r is 0.02 substitutions/myr, and dij = 0.04 substitutions, then the two species have diverged from each other 2 myr (or 1 million each from their common ancestor).
Estimation: r (rate) and T (time).
Slide 3

4. The LS method in linear regression
Y = a + b x X Y
R(Residual) 3
11.5
a+b*3 – 11.5 2
7.5
a+b*2 – 7.5 1 5
a+b*1 – 5 4 14
a+b*4 – 14
RSS = 0 means a perfect fit of the linear model to the data. A large RSS means a poor fit.
Slide 4

5. The rational of the LS method4 2 1 3 4
Sp1
Sp2 d12
Sp3 d13 d23
Sp4 d14 d24 d34
Slide 5

6. Multiple calibration points4 2 1 3 4
Sp1
Sp2 d12
Sp3 d13 d23
Sp4 d14 d24 d34
Slide 6

7. Slide 7

8. a) b) gibbon sumatran orangutan gorilla
20.655±1.221
3.104±0.273
orangutan
14±0
gorilla
Hard calibration point = 14 million years
7.079±0.527
bonobo
1.754±0.184 a)
chimpanzee
7±0
Hard calibration point = 7 million years
human
gibbon
sumatran
20.903±1.503
3.206±0.280
orangutan
14.757±0.217
gorilla
Soft calibration point = 14 million years
bonobo
7.258±0.530 b)
1.818±0.180
Soft calibration point = 7 million years
chimpanzee
5.487±0.434
human

9. Dating with local clocks
OTU1
OTU2 7
OTU
OTU a) b) 6
OTU4
T1 = 10 3
OTU3 3
t2 = 5
2 r2
OTU2
RSS = 0
r0 = 0.6, r1 = 3, r2 = 1.2 2
t3 =
5 r1
OTU1 c)
OTU4
T1 = 10
OTU3
t2 =
OTU2
RSS =
r =
t3 =
OTU1

10. Method comparison
RY07
BEAST
Slide 10

11. calibration time = 10 Myr
Pan
7.890±1.308
Homo
calibration time = 35 Myr
9.450±1.522
Gorilla
12.988±2.053
32.564±4.103
Pongo
56.059±5.436
Macaca
Callithrix
Daubentonia
Cheirogaleus
26.761±3.528
Mirza
calibration time = 77 Myr
7.9±1.4
M.ravelobensis
M.tavaratra
21.639±2.906
78.210±1.871
M.berthae
49.231±4.101
2.2±0.4
M.myoxinus
5.3±0.9
2.3±0.4
M.rufus1
37.682±3.785
4.617±0.808
M.rufus2
9.7±1.3
4.348±0.845
M.sambiranensis
M.griseorufus
7.089±1.119
M.murinus
66.992±5.038
Lepilemur
36.351±2.849
Propithecus
Hapalemur
26.049±2.955
9.608±1.533
Lemur
14.668±1.861
Eulemur
18.125±2.285
Varecia
Loris
46.073±5.575
Galago

12. calibration time = 77 my calibration time = 35 my
Galago
[ , ]
Loris
Varecia
[ , ]
Eulemur
[ , ]
Lemur
[ , ]
[6.8351, ]
Hapalemur
Propithecus
[25.534, ]
[53.26,79.827]
Lepilemur
M.murinus
[4.8645,8.6395]
M.griseorufus
calibration time = 77 my
[7.3,11.7]
M.sambiranensis
[2.7447,4.8025]
M.rufus2
[ , ]
[3.3,5.3]
M.rufus1
[3.7,6.0]
[1.6314,2.9896]
[ ,21.595]
M.myoxinus
[ , ]
[1.3,2.6]
[68.927, ]
M.berthae
M.tavaratra
An alternative way of presenting variation of the estimated time is by a confidence interval.
[5.7784,9.3783]
M.ravelobensis
[ ,29.488]
Mirza
Cheirogaleus
Daubentonia
Callithrix
[ , ]
Macaca
[ , ]
Pongo
[ , ]
calibration time = 35 my
calibration time = 10 my
Gorilla
[8.059, ]
Homo
[5.5629,9.3534]
Pan

14. Rationale of Tip-Dating
t1=?
t2=?
t3=?
t4=?
t5=?
15 yr
25 yr
30 yr
20 yr
10 yr 40 50 30 40 20
RSS=(d12/r+15-2*t1)2+(d13/r+10-2*t3)2+(d14/r+20-2*t3)2
+(d15/r+30-2*t5)2+(d16/r+25-2*t5)2+(d23/r *t3)2
+(d24/r *t3)2+(d25/r *t5)2+(d26/r *t5)2
+(d34/r *t2)2+(d35/r *t5)2+(d36/r *t5)2
+(d45/r *t5)2+(d46/r *t5)2+(d56/r *t4)2
r = 0.01
Slide 14

15. Final dated tree s6@1965 1950 s5@1960 1940 s4@1970 1960 s3@1980 1950
Slide 15

16. Dates with standard deviation
1,902.81±8.42
1,875.51±13.38
1,817.23±16.71
1,791.98±21.08
1,792.77±22.00
1,770.96±24.30
1,766.78±25.64
Slide 16

17. Dating and cospeciationH1 H2 H3 H4 H5 H6 H7 H8 H9
H10
H11
H12
H13
H14
P14
P13
P12
P11
P10 P9 P8 P7 P6 P5 P4 P3 P2
Slide 17 P1

18. Dating and cospeciationH1 H2 H3 H4 H5 H6 H7 H8 H9
H10
H11
H12
H13
H14 P1 P2 P3 P4 P5 P6 P7 P8 P9
P10
P11
P12
P13
P14
Coincidental cophylogeny

21. Dating gene duplication
S6B
S5B
S4B
S3B
S1B
S2B
Dating gene duplication events:
1. The gene duplication event occurred at T0.
2. Two approaches are used to approximate T0.
If the duplicated genes, or their third codon positions, conform to molecular clock, then estimate T0 (next slide)
If duplicated genes do not conform to molecular clock, then use genes that do conform to molecular clock to estimate T1, which underestimates T0.
S11A
S12A
S10A
S9A
S8A
S7A
S6A
S5A
S4A
S3A
S1A
S2A T2 T0 T1

22. Estimating T0
Ti and Ti' can be estimated with either nonsynonymous substitutions or synonymous substitutions, designated Ti.N and Ti.N', and Ti.S and Ti.S'
Ideally, both paralogous genes conform to molecular clock and Ti = Ti', i = :
Ti.N  Ti.N', and Ti.S  Ti.S': Rare.
Ti.N  Ti.N', and Ti.S  Ti.S': Very rare
Ti.N  Ti.N', and Ti.S  Ti.S': Common
Ti.N  Ti.N', and Ti.S  Ti.S': Most common.
S6B
S5B
S4B
S3B
S1B
S2B T3 T2 T4 T1 T5 T0
T3'
S2A
T2'
S1A
T4'
S3A
T1'
S4A
T5'
S5A
S6A
S7A
S8A
S9A
S10A
S12A
S11A

23. Dating gene duplication
S2B
The loss of the paralogous lineage leading to S5B and S6B (or S5A and S6A) leads to an underestimate of the gene duplication time, shifting from Node M to Node N.
Failing to sample the lineage leading to S5B and S6B has the same effect.
S11A
S12A
S10A
S9A
S8A
S7A
S6A
S5A
S4A
S3A
S1A
S2A
S1B N
S3B M
S4B
S5B
S6B

24. Application: HIV transmission in NA
Hypothesis 1 (Advocated by Haiti scientists): Some North Americans went to Africa and contracted HIV-1. They took advantage of the sex tourists in Haiti in 1960s and transmitted HIV-1 to Haitian women.
Hypothesis 2: Haitians contracted HIV-1 earlier than the sex tourism in 1960s. Some North Americans went there to take advantage of the sex tourism, contracted HIV-1, and brought the disease to North America
Differences in predictions in both HIV-1 topology and time of divergence.
Slide 24
Xuhua Xia