estimating the effective sample size of phylogenetic tree topologies from bayesian mcmc analyses
TRANSCRIPT
Es#ma#ng(the(Effec#ve(Sample(Size(
of(tree(topologies(from((
Bayesian(MCMC(analyses(
Rob(Lanfear(
ANU(&(NESCent(
(
@roblanfear(
(
1. Effec#ve(Sample(Size((ESS)(
2. ESS(for(tree(topologies,(in(principle(
3. ESS(for(tree(topologies,(in(prac#ce(
4. An(example(using(hox(genes(
(
1. Effec#ve(Sample(Size((ESS)(
(
-2
0
2
0 250 500 750 1000x
y
-10
0
10
0 250 500 750 1000x
yESS(=(544.6(
ESS(=(7.5(
ESS = n1+ 2 ρ
k=1
∞
∑k
ESS(>(200(
Drummond(AJ,(Ho(SYW,(Phillips(MJ,(Rambaut(A((2006)((
Relaxed(Phylogene#cs(and(Da#ng(with(Confidence.(PLoS(Biol(4(5):(e88.(
?(
ESS = n1+ 2 ρ
k=1
∞
∑k
(
(
(
2.(ESS(for(tree(topologies,(in(principle(
(
A( D(B( C( A( D(B( C(
ESS(=(544.6(
ESS(=(7.5(
-8
-4
0
4
8
0 2500 5000 7500 10000x
y
ESS(=(549.5(
0
1
2
3
0 1000 2000 3000 4000 5000x
y
Raw(data(
Distances(between(sequen#al(samples(
ESS(=(7.5(
0.0
0.2
0.4
0.6
0.8
0 4 8 12distance
density
gap1
5
10
-8
-4
0
4
8
0 2500 5000 7500 10000x
y
ESS(=(549.5(Raw(data(
-8
-4
0
4
8
0 2500 5000 7500 10000x
y
ESS(=(549.5(Raw(data(
-8
-4
0
4
8
0 2500 5000 7500 10000x
y
ESS(=(549.5(Raw(data(
-8
-4
0
4
8
0 2500 5000 7500 10000x
y
ESS(=(549.5(Raw(data(
(
3. ESS(for(tree(topologies,(in(prac#ce(
-8
-4
0
4
8
0 2500 5000 7500 10000x
y
ESS(=(549.5(Raw(data(
0.5
1.0
1.5
2.0
2.5
0 10 20 30 40 50Gap size
Med
ian
dist
ance
-8
-4
0
4
8
0 2500 5000 7500 10000x
y
ESS(=(549.5(Raw(data(
0.5
1.0
1.5
2.0
2.5
0 10 20 30 40 50Gap size
Med
ian
dist
ance
Median(distance(between(random(pairs(
-8
-4
0
4
8
0 2500 5000 7500 10000x
y
ESS(=(549.5(Raw(data(
0.5
1.0
1.5
2.0
2.5
0 10 20 30 40 50Gap size
Med
ian
dist
ance
Lower(CI(of(median((from(bootstrapping)(
Median(distance(between(random(pairs(
0.5
1.0
1.5
2.0
2.5
0 10 20 30 40 50Gap size
Med
ian
dist
ance
-8
-4
0
4
8
0 2500 5000 7500 10000x
y
ESS(=(549.5(Raw(data(
0.5
1.0
1.5
2.0
2.5
0 10 20 30 40 50Gap size
Med
ian
dist
ance
-8
-4
0
4
8
0 2500 5000 7500 10000x
y
ESS(=(549.5(Raw(data(
0.5
1.0
1.5
2.0
2.5
0 10 20 30 40 50Gap size
Med
ian
dist
ance
-8
-4
0
4
8
0 2500 5000 7500 10000x
y
ESS(=(549.5(Raw(data(
0.5
1.0
1.5
2.0
2.5
0 10 20 30 40 50Gap size
Med
ian
dist
ance
0.5
1.0
1.5
2.0
2.5
0 10 20 30 40 50Gap size
Med
ian
dist
ance
-8
-4
0
4
8
0 2500 5000 7500 10000x
y
ESS(=(549.5(Raw(data(
0.5
1.0
1.5
2.0
2.5
0 10 20 30 40 50Gap size
Med
ian
dist
ance
18(
0.5
1.0
1.5
2.0
2.5
0 10 20 30 40 50Gap size
Med
ian
dist
ance
-8
-4
0
4
8
0 2500 5000 7500 10000x
y
ESS(=(549.5(Raw(data(
0.5
1.0
1.5
2.0
2.5
0 10 20 30 40 50Gap size
Med
ian
dist
ance
18(
Approximate(ESS(=(10000/18(=(555.6((
-8
-4
0
4
8
0 2500 5000 7500 10000x
y
ESS(=(549.5(Raw(data(
0
20
40
-200 0 200 400Difference between approximate and actual ESS (N=500)
count
256(reps(>(true(ESS(
244(reps(<(true(ESS(
Sign(test:(p(=(0.6228(
(
4.(An(example(using(hox(genes(
Bfl_Xlox
Nvi_Lox5
Mmu_HoxA10
Bfl_Hox1
Nvi_Lox2
Mmu_HoxB9
Mmu_C
dx2
Bfl_Evx
A
Mmu_HoxA3
Bfl_Hox4
Ttr_eve
Bfl_Hox6
Nvi_scr
Csp_Xlox
Nvi_Lox4
Lan_scr
Nvi_Post2
Mmu_HoxB5
Alo_pb
Mmu_Gsh2
Nvi_Hox3
Mmu_Evx2
Hro_ev
e
Mmu_HoxA5
Mmu_HoxB1
Bfl_Gsx
Mmu_Xlox
Cva_Hox1
Mmu_HoxA6
Mmu_HoxB6
Mmu_HoxA1
Mmu_HoxA2Mmu_HoxB2
Csp_Gsx
Bfl_Hox8
Nvi_D
fdMmu_H
oxB4
Mmu_H
oxA4Htr_
Lox18
Csp_C
dx
Lan_Post2
Mmu_Gsh
1
Mmu_Evx1
Mmu_HoxB8
Hro_Lox5
Pst_Xlox
Mmu_HoxB7
Bfl_Hox3
Mmu_HoxA9
Bfl_Hox2
Nvi_C
dx
Cva_H
ox3
Mmu_HoxB3
Hme_Lox4
Mmu_HoxA7
Mmu_HoxC8
Bfl_Hox9
Nvi_Hox1
Nvi_Post
1
Bfl_Cdx
Mmu_HoxC10
Bfl_Hox7
Bfl_Hox5
Mmu_C
dx1
Cva_Hox2
Bfl_Hox10
Hro_Lox2
Lan_Po
st1
(
68(Hox(genes((
MCMC(run(using(MrBayes(
59K(samples(aeer(burnin(
10
20
30
40
0 100 200 300Gap size
Med
ian
dist
ance
Robinson'Foulds,distance,Approximate(ESS(=(746.9(
10
20
30
40
0 100 200 300Gap size
Med
ian
dist
ance
Robinson'Foulds,distance,Approximate(ESS(=(746.9(
0.4
0.6
0.8
1.0
0 100 200 300Gap size
Med
ian
dist
ance
Branch,Score,Difference,Approximate(ESS(=(694.1(
10
20
30
40
0 100 200 300Gap size
Med
ian
dist
ance
Robinson'Foulds,distance,Approximate(ESS(=(746.9(
0.4
0.6
0.8
1.0
0 100 200 300Gap size
Med
ian
dist
ance
Branch,Score,Difference,Approximate(ESS(=(694.1(
60
80
100
0 100 200 300Gap size
Med
ian
dist
ance
Path,Difference,Approximate(ESS(=(880.6((
Thanks(to(Dan(Warren(
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Code(available(at((
github.com/danlwarren/RWTY(
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Slides(will(be(on(SlideShare(
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Comments?([email protected](