Genealogies of time Genealogies of time structured data, an structured data, an

application on cave bear application on cave bear ancient DNAancient DNA

Frantz Frantz DepaulisDepaulis

Ludovic Ludovic OrlandoOrlando

Catherine Catherine HannïHannï

UMR 5534        Centre de Génétique Moléculaire et Cellulaire

        Université Claude Bernard, Lyon I

UMR 7625        Laboratoire d’écologie

Paris 6/ENS

Outline of the presentationOutline of the presentation

1 Introduction: Gene genealogiesIntroduction: Gene genealogies2 ResultsResults

2 .1 Simulation exploratory results.1 Simulation exploratory results2 .2 Cave bear application.2 Cave bear application

3 ConclusionsConclusions

Wright Fisher Neutral modelWright Fisher Neutral modelAssumptionsAssumptions Selective neutrality (Selective neutrality (NNe e s s <<1)<<1) Demography Demography

- Isolated panmictic Population, - Isolated panmictic Population,

- Constant size - Constant size NN

- Poisson Distribution of offspring - Poisson Distribution of offspring PP (1) (1)

- Same sampling time- Same sampling time

Mutational, sequence data: Mutational, sequence data: infinite site model (ISM) infinite site model (ISM)

- No recombination- No recombination

- Independent mutations- Independent mutations

- Constant mutation rate - Constant mutation rate µµ

Along the sequenceAlong the sequence

Across time Across time

- Each mutation affects a new nucleotide site- Each mutation affects a new nucleotide site

-Coalescence-

Genealogy of a gene sampleGenealogy of a gene sample

gene sample

ancestral lineage

coalescence= common ancestor

Most recent common ancestor (MRCA)

-Coalescence-

CoalescentCoalescent

a b c d e f

Most recent common ancestor of the

sample(MRCA)

sample of “genes” /

of individual

s

Common ancestor

(CA)

neutral mutati

ons

TC

C

G

CG

A

A

-Coalescence-

ConstructiConstructing ng

coalescentcoalescents, s,

a b cd e f1°)Ages of the nodes

t3

p=1/2NExp( p )

t1

t2

t4

t5:

additional assumption: n << N

p = (n (n -1)/2) /2N

-Coalescence-

neutral mutati

ons G

TC

C

G

CA

3°) uniform distribution of

mutations

gene sample

Topologyof the tree

2°)

CA

C

G

CG

T T

neutral distribution of sequence polymorphis

m

A AA

A

a b cd e f

MRCA

common ancestor (CA)

t1

t2

t3

t4

t5:

100 000 times

ConstructiConstructing-ng-

deconstrucdeconstructing ting

coalescentscoalescents

-Coalescence-

T

A

C

C

G

CG

CC

GA A

C

T T

G

A

AT

A

A

C

G

T

C

CT

CA A

T

T

G

A

T

C

T

A

C

C

G

CG

C

TG

G G

CC

C

G

AA

A

A

T

Haplotype tests: simulationsHaplotype tests: simulations

parameters‡ : S =8 n =6

K = 6K = 5K = 4

10 000

simulations

haplotype number K {haplotyp

e diversity

H = 1- fi2 H = 0.83H = 0.78H = 0.72

CC

A

T

{

Depaulis and Veuille MBE 1998‡ Hudson 1993

...

0.20.30.40.50.60.70.80.9

H

density

observed H : P = 0.03 *

Distribution of simulated

H

0.1

-Coalescence-

GCGCGCGAACCCATT outgroup 121531416121423 frequencies

Alignment of polymorphic Alignment of polymorphic sites: sites: frequencies of mutationsfrequencies of mutations

GCCCGCGAATCCATTGCGTGCGATCCGATTGCGTACAATCCCGTCGTGTACAATCTCGACGTGTACAATCTCGACGCGTGGAATCCCGTTCCGCGCGGTCCCATT

n =7

S =15C

T

→

T

C

C

-Coalescence-

0

1

2

3

4

5

6

7

1 2 3 4 5 6

unfolded

0

1

2

3

4

5

6

7

1 2 3 4 5 6

unfoldedfolded

Frequency spectrum of Frequency spectrum of mutations & neutrality mutations & neutrality

teststests

fi : number

of occurrences in a sample

Number of

polymorphic sites

== 00(Tajima Genetics 1989)

sityheterozygo estimator

(1975) sWatterson'

S

i

ii

nn

fnf

1 )1(

)(2

1

1

1

ˆn

i

W

i

S

)ˆˆ(

ˆˆ

W

W

SED

=4Ne

)ˆˆ(

ˆˆ*

e

e

SED

e

H=-H(Fay and Wu Genetics 2000)

state derived the

ofty homozygosi

S

i

iH nn

f

1

2

)1(

2

(Fu and Li Genetics 1993)

-Coalescence-

Mitochondria, correlation LD/distance Mitochondria, correlation LD/distance recombination or mutational effects?recombination or mutational effects?

distance d

r 2 = ↘(d )

Pearson’s

statistic tested by

permutations of

sites

Awadalla et al. (Science 1999)

Time structured data & Time structured data & genealogiesgenealogies

- Parasites during disease evolution (virus…)

- Microbial experimental evolution

- Ancient DNA

Issue:

- To what extent the analyses are affected by time structure?

- How to correct for this?

-Coalescence-

n =2n =5

Algorithm for time Algorithm for time structured coalescentstructured coalescent

a b c

d e f

n =3

n =3

n =2

t 1

n =4

The exponential law is The exponential law is memoryless !memoryless !

n1 =3

- Simulations-

Age structure effect on gene Age structure effect on gene genealogies genealogies

Contemporaneous sample Limited time

structure

Two subsets

with large time

spacingExcess of rare variants Deficit of LD

Deficit of rare variants Excess of LDDifferentiation

t 1

n1 =4

- Simulations-

Pearson

10

S/S0

Effect of subset Effect of subset size on statistical size on statistical

tests : tests : meanmean t1 =0.2 Ne generations

Dt: Tajima's (1989) D; D*fl Fu and Li (1993)'s D*; Hfl Fay and Wu's (2000) H; ZnS Kelly (1997)'s ZnS; K and H Depaulis and Veuille (1998)'s haplotype tests (K is scaled to its expected maximal value S+1 corresponding to ); Pearson: Pearson correlation coefficient between pairwise allelic correlation and distance between mutations; Fst Hudson et al's (1992) Fst.

nn11

n =40, S =20

- Simulations-

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0.2 0.4 0.6 0.8 n1/n

Mean

Dt D*fl Hfw ZnS K Hpi/pi0 Fst

Effect of subset size on Effect of subset size on statistical tests : statistical tests : significance rate significance rate

Empty symbols: deficit of the statistics; Filled symbols: excess of the statistics. Dt: Tajima's (1989) D; D*fl Fu and Li (1993)'s D*; Hfl Fay and Wu's (2000) H; ZnS Kelly (1997)'s ZnS; K and H Depaulis and Veuille (1998)'s haplotype tests; Pearson: Pearson correlation coefficient between pairwise allelic correlation and distance between mutation tested by permutations according to Awaddala et al. (1999); Fst Hudson et al's (1992) Fst tested by permutations

t1 =0.2 Ne generations nn11

n =40, S =20

- Simulations-

0

0.05

0.1

0.15

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1n1/n

significance rate

Dt_inf D*fl_inf Hfw_inf ZnS_inf K_sup H_sup Fst

Effect of a half Effect of a half subset age on subset age on

statistical tests: statistical tests: mean mean

Dt: Tajima's (1989) D; D*fl Fu and Li (1993)'s D*; Hfl Fay and Wu's (2000) H; ZnS Kelly (1997)'s ZnS; K and H Depaulis and Veuille (1998)'s haplotype tests (K is scaled to its expected maximal value S+1 corresponding to ); Pearson: Pearson correlation coefficient between pairwise allelic correlation and distance between mutations; Fst Hudson et al's (1992) Fst.

t 1

nn11==nn/2/2

- Simulations-

-1

-0.5

0

0.5

1

1.5

2

2.5

3

0.001 0.01 0.1 1 10t1 in 2Ne generations

Mean

Dt D*fl Hfw K H ZnS Pearson Fst Pi/Theta0 S/S0

Effect of a half subset Effect of a half subset age on statistical tests: age on statistical tests:

significance ratessignificance rates

Empty symbols: deficit of the statistics; Filled symbols: excess of the statistics. Dt: Tajima's (1989) D; D*fl Fu and Li (1993)'s D*; Hfl Fay and Wu's (2000) H; ZnS Kelly (1997)'s ZnS; K and H Depaulis and Veuille (1998)'s haplotype tests; Pearson: Pearson correlation coefficient between pairwise allelic correlation and distance between mutation tested by permutations according to Awaddala et al. (1999); Fst Hudson et al's (1992) Fst tested by permutations

t 1

nn11==nn/2/2

- Simulations-

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.001 0.01 0.1 1 10t1 in 2Ne generations

Significance rate

Dt_inf Dt_sup D*fl_inf D*fl_sup ZnS_inf K_sup H_sup Fst

Cave bear: Cave bear: Ursus spelaeusUrsus spelaeus(12-300kYA)(12-300kYA)

- Application-

Sampling sitesSampling sites- Application-

Alignment of Alignment of polymorphic sites:polymorphic sites: D-loop D-loop of cave bear of cave bear

REF TTGTCAACTT TCGAATTGAA GTREF TTGTCAACTT TCGAATTGAA GT#NOASC3500_40-45 ..A....T.C ..A....... ..#NOASC3500_40-45 ..A....T.C ..A....... ..#NOASC3800_40-45 ..A....T.C ..A....... ..#NOASC3800_40-45 ..A....T.C ..A....... ..#NOASC85F16_40-45 .......... .......... ..#NOASC85F16_40-45 .......... .......... ..#NOASC95456_40-45 ..A....T.C ..A....... ..#NOASC95456_40-45 ..A....T.C ..A....... ..#NOASC92386_40-45 ..A....T.C ..A....... ..#NOASC92386_40-45 ..A....T.C ..A....... ..#NOASC92413_40-45 C.A....T.C ..A....... ..#NOASC92413_40-45 C.A....T.C ..A....... ..#NOASC92152_40-45 C.A....T.C ..A....... A.#NOASC92152_40-45 C.A....T.C ..A....... A.#NOASC5300_50-60 ..A....T.C ..A....... ..#NOASC5300_50-60 ..A....T.C ..A....... ..#NOASC11600_80 .......... .......... ..#NOASC11600_80 .......... .......... ..#NOASC12500_80 .......... .......... ..#NOASC12500_80 .......... .......... ..#NOASC13800_80 .......... .......... ..#NOASC13800_80 .......... .......... ..#NOASC100801_80 .......... .......... ..#NOASC100801_80 .......... .......... ..#NOASC12400_80 ..A....T.C ..A....... ..#NOASC12400_80 ..A....T.C ..A....... ..#NOASC11800_80 .CA....T.C ..A.G..... ..#NOASC11800_80 .CA....T.C ..A.G..... ..#NOASC11700_80 C.A....T.C ..A....... A.#NOASC11700_80 C.A....T.C ..A....... A.#NOASC84E16_90-130 C.A....T.C ..A....... ..#NOASC84E16_90-130 C.A....T.C ..A....... ..#NOASC84G19_90-130 C.A....T.C ..A....... ..#NOASC84G19_90-130 C.A....T.C ..A....... ..#NOASCbrC5-02_90-130 C.A....T.C ..A....... ..#NOASCbrC5-02_90-130 C.A....T.C ..A....... ..#NOASC15400_90-130 C.A....T.C ..A......G ..#NOASC15400_90-130 C.A....T.C ..A......G ..#NOASC15700_90-130 ....T.G.C. .TA..C..G. ..#NOASC15700_90-130 ....T.G.C. .TA..C..G. ..#NOATAB2_40 .......... .......... ..#NOATAB2_40 .......... .......... ..#NOAGrotteMerve_? .......... .T........ ..#NOAGrotteMerve_? .......... .T........ ..#NOAAZE_80-130 .......... .......... .C#NOAAZE_80-130 .......... .......... .C#NOAGigny189F3_? ..A....T.C ..A....... ..#NOAGigny189F3_? ..A....T.C ..A....... ..#NOAJAL104_? C.A....T.C ..A....... ..#NOAJAL104_? C.A....T.C ..A....... ..#NOATAB15_25-35 ..A......C ..A....... ..#NOATAB15_25-35 ..A......C ..A....... ..#NOAGailenreuth_? ..A......C ..A....... ..#NOAGailenreuth_? ..A......C ..A....... ..#NOA47910_30 ..A....T.C ..A....A.. ..#NOA47910_30 ..A....T.C ..A....A.. ..#NOAHohleFels_? ..A....T.C ..A..C.... ..#NOAHohleFels_? ..A....T.C ..A..C.... ..#NOACLA_35 ..A....T.C C.A....... ..#NOACLA_35 ..A....T.C C.A....... ..#NOACLB_35 ..A....T.C C.A....... ..#NOACLB_35 ..A....T.C C.A....... ..#NOAChiemsee_35 ..A..G.... ..A...C... ..#NOAChiemsee_35 ..A..G.... ..A...C... ..#NOARamesch1_? ..A..G.... ..A...C... ..#NOARamesch1_? ..A..G.... ..A...C... ..#NOARamesch2_? ..A..G.... ..A...C... ..#NOARamesch2_? ..A..G.... ..A...C... ..#NOAGeissenklt1_? ...CT..... .T.G.C.... ..#NOAGeissenklt1_? ...CT..... .T.G.C.... ..#NOAGeissenklt2_? ...CT..... .T.G.C.... ..#NOAGeissenklt2_? ...CT..... .T.G.C.... ..#NOANixloch_? ...CT..... .T...C.... ..#NOANixloch_? ...CT..... .T...C.... ..

--------------------------------------------- --------------------------------------------- Alp barrierAlp barrier#SOAPoto_? ...CT..... .T...C.... ..#SOAPoto_? ...CT..... .T...C.... ..#SOAVind1_? ...CT..... .T...C.... ..#SOAVind1_? ...CT..... .T...C.... ..#SOAVind2_? ...CT..... .T...C.... ..#SOAVind2_? ...CT..... .T...C.... ..#SOAConturi_? .......T.. .......... ..#SOAConturi_? .......T.. .......... ..

n n =41 =41 S S =22=22

(Loreille et al. 2001) (Orlando et al. 2002) (Hofreiter et al. 2002)(Kühn et al. 2001)

Ne= 13 000

- Application-

Neutrality tests, Belgium Neutrality tests, Belgium cavecave

a permutation test

- Application-

Statistic Dt D*fl Hfw K H ZnS Pearson

Observed -0.82 -1.55 -1.32 7 0.79 0.24 -0.39 (2.8*)a

(P value %) (21.0) (5.3) (18.4) (16.4) (37.7) (43.7) (2.8*)

Mean 0.06 -0.05 0.30 8.3 0.79 0.26 0.00

CI [-1.42;1.51] [-1.89;1.18] [-4.46;2.62] [5;11] [0.64;0.88] [0.10;0.55] [-0.25;0.20]

No time

structure

% rejected (4.9;5.5) (5.2;2.8) (5.4;4.8) (1.7;3.9) (4.9;4.6) (5.5;5.1) (5.0;/)

(P value %) (30.0) (8.8) (17.2) (8.6) (31.2) (31.7) (2.7*)

Mean -0.30 -0.38 0.39 9.1 0.80 0.22 0.00

CI [-1.56;1.26] [-1.89;0.84] [-4.04;2.56] [6;12] [0.66;0.89] [0.08;0.47] [-0.29;0.23]

Average

time

structure

% rejected (7.8;3.0) (8.2;1.0) (4.2;3.7) (0.8;9.5) (3.3;7.8) (11.5;2.9) (4.9;/)

(P value %) (30.0) (8.6) (17.4) (7.9) (30.9) (31.9) (2.8*)

Mean -0.33 -0.42 0.37 9.1 0.80 0.22 0.00

CI [-1.59;1.18] [-1.89;0.84] [-4.20;2.54] [6;12] [0.66;0.89] [0.08;0.48] [-0.29;0.24]

Scladina

n=20

S=15

Uncertainty

in time

structure % rejected (9.3;2.8) (9.3;0.8) (4.5;3.6) (0.7;9.8) (3.7;7.5) (11.6;2.8) (4.8;/)

Neutrality tests, dated Neutrality tests, dated subsamplesubsample

a permutation test

- Application-

Statistic Dt D*fl Hfw K H ZnS Pearson

Observed -1.21 -2.28 -0.69 12 0.86 0.14 -0.27 (11.4) a

(P value %) (10.5) (0.6**) (25.7) (16.5) (32.1) (24.3) (11.5)

Mean -0.09 -0.08 0.29 10.3 0.82 0.23 0.00

CI [-1.49;1.50] [-1.98;1.32] [-5.66;3.18] [7;14] [0.69;0.90] [0.09;0.48] [-0.19;0.16]

No time

structure

% rejected (5.0;5.2) (3.6;1.4) (5.3;4.7) (4.0;2.8) (5.3;4.7) (5.7;5.0) (4.7;/)

(P value %) (17.7) (1.7*) (24.3) (38.2) (42.6) (41.8) (11.2)

Mean -0.42 -0.59 0.35 11.8 0.84 0.18 0.00

CI [-1.69;1.11] [-2.28;0.72] [-5.34;2.98] [8;15] [0.71;0.91] [0.07;0.39] [-0.23;0.20]

Average

time structure

% rejected (9.3;2.1) (6.9;0.3) (4.7;2.6) (1.2;11.1) (3.4;9.5) (13.7;2.4) (4.9;/)

(P value %) (18.5) (1.9*) (23.4) (39.9) (43.2) (41.1) (11.9)

Mean -0.44 -0.61 0.37 11.8 0.84 0.18 0.00

CI [-1.70;1.09] [-2.28;0.72] [-5.23;2.99] [8;16] [0.71;0.91] [0.07;0.40] [-0.24;0.19]

all dated

n=27,

S=20

Uncertainty

in time

structure

% rejected (9.3;2.4) (7.0;0.2) (4.6;2.7) (1.2;11.7) (3.5;9.7) (14.1;2.5) (5.4;/)

Neutrality tests, total Neutrality tests, total samplesample

a permutation test

- Application-

Statistic Dt D*fl Hfw K H ZnS Pearson Fst

Observed -0.45 -0.88 1.35 17 0.91 0.10 -0.09 (22.0) a 0.32 (0.4**) a

(P value %) (37.1) (14.7) (47.1) (1.7*) (3.7*) (18.1) (21.5) (0.4**)

Mean -0.09 -0.09 0.30 12.3 0.83 0.19 0.00 -0.03

CI [-1.44;1.52] [-1.85;1.38] [-5.84;3.15] [8;16] [0.70;0.90] [0.07;0.41] [-0.20;0.17] [-0.38;0.27]

No time

structure

% rejected (4.5;5.3) (4.1;1.1) (4.8;4.7) (3.0;4.3) (4.8;4.9) (5.5;4.6) (4.8;/) (/;4.6)

(P value %) (45.5) (35.6) (45.6) (7.8) (5.5) (36.6) (21.8) (1.3*)

Mean -0.45 -0.74 0.32 13.9 0.84 0.15 0.00 -0.01

CI [-1.71;1.10] [-2.49;0.73] [-5.38;2.93] [9;18] [0.71;0.91] [0.05;0.34] [-0.23;0.20] [-0.40;0.38]

Average

time

structure

% rejected (10.2;2.2) (10.7;0.1) (4.2;2.4) (0.8;16.1) (4.3;7.9) (15.2;2.2) (4.9;/) (/;8.9)

(P value %) (42.1) (40.7) (44.9) (10.3) (6.2) (39.2) (21.8) (1.7*)

Mean -0.54 -0.90 0.26 14.3 0.84 0.14 0.00 -0.01

CI [-1.76;0.96] [-2.81;0.73] [-5.70;2.90] [10;18] [0.71;0.91] [0.05;0.32] [-0.24;0.21] [-0.40;0.41]

n=41,

S=22

Uncertainty

in time

structure

% rejected (12.2;1.4) (14.2;0.1) (4.5;2.3) (0.5;19.8) (4.0;7.9) (16.7;2.1) (4.7;/) (/;9.7)

LD as a function of distanceLD as a function of distance- Application-

R2 = 0.4174

0.01

0.1

1

0 10 20 30 40 50 60 70

distance (nt)

r 2

Can substantially bias the resultsCan substantially bias the results– Even if within 10% of the age of the MRCAEven if within 10% of the age of the MRCA

bottom of the tree with more branchesbottom of the tree with more branches

non random subset of mutations (rare ones)non random subset of mutations (rare ones)

– small: long external branches, excess of rare small: long external branches, excess of rare variants (negative D, deficit of LD)variants (negative D, deficit of LD)

– great: a long internal branch apparent great: a long internal branch apparent differentiation excess of intermediate differentiation excess of intermediate frequency variants (positive D, excess of LD) frequency variants (positive D, excess of LD) if equilibratedif equilibrated

Time structure , Time structure , ConclusionConclusion

AcknowledgementsAcknowledgements

CNRSCNRS Nick BartonNick Barton