HAL Id: hal-02802676
https://hal.inrae.fr/hal-02802676
Submitted on 5 Jun 2020
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Inferring the ancestral dynamics of population size from
genome wide molecular data - an ABC approach
Simon Boitard
To cite this version:
Simon Boitard. Inferring the ancestral dynamics of population size from genome wide molecular data -
an ABC approach. Stochastic models in ecology, evolution and genetics (SMEEG), Dec 2013, Angers,
France. �hal-02802676�
Inferring the ancestral dynamics of population size from
genome wide molecular data - an ABC approach
Simon Boitard
UMR 7205 OSEB (EPHE - MNHN - CNRS), Paris.
UMR 1313 GABI (INRA - AgroParisTech), Jouy en Josas
Motivation
Genome wide sequence data contains rich information about population
size history, cf PSMC (Li and Durbin, 2011).
Pairwise Sequentially Markovian Coalescent (PSMC)
Markov chain for T 2 based on the Sequentially Markovian Coalescent
(SMC), transitions depend on N(t).
Estimation through an Hidden Markov Model (HMM).
Limited to one individual (n = 2) → not efficient for recent times.
Development of an ABC approach
Several estimation methods (Drummond et al, 2012; MacLeod et al,
2013; Sheehan et al, 2013), but limited to n = 2 or small genomic
regions.
ABC could take advantage of both genome wide data and large n.
Little assumptions required concerning the underlying model.
Application to farm animal species
Many genome sequences now available (pig, cattle, sheep, chicken),
and a huge amount of animals with dense genotyping data.
Several bottlenecks expected along their history :
Last glaciation : -25 000 – -60 000 years
Domestication : -10 000 years.
Creation of modern breeds and intensive selection : -200 years.
Here 25 unrelated animals (n = 50) from the Holstein cattle breed
(www.1000bullgenomes.com)
Outline
1 Methods
2 Results
Simulations
Application to Holstein data
3 Conclusions and perspectives
Outline
1 Methods
2 Results
Simulations
Application to Holstein data
3 Conclusions and perspectives
Principles of ABC (Approximate Bayesian Computation)
To estimate the parameters θ of a model from a dataset D, we
approximate the posterior probability P(θ|D) by the quantity P(θ|S),
for a set S of (meaningfull!) summary statistics.
We estimate P(θ|S) by simulations, with the following procedure :
1 Compute S = f (D)
2 For i from 1 to I:
1 Sample parameter θ i from the prior distribution of θ.
2 Simulate dataset D i from the model with parameter θ i .
3 Compute S i = f (D i ).
4 Select the simulation if dist(S i , S) < .
3 Estimate the posterior distribution of θ from the selected θ i values, by
simple counting or other approaches (regression).
Model
Coalescent with mutation and recombinaison, n = 50 haplotypes.
No structure.
Piecewise constant effective population size.
Intervals are defined from a previous PSMC analysis ...
2.5 3.0 3.5 4.0 4.5 5.0 5.5
5000 10000 15000 20000 25000 30000 35000
log10(générations)
Ne
... as well as breeding history
0 1 2 3 4 5 6
5000 10000 15000 20000 25000 30000 35000
log10(générations)
Ne
Prior distributions
Per generation per bp mutation rate : µ = 2.5e − 8.
Per generation per bp recombination rate : r ∼ U (0.2e − 8, 1e − 8).
Population size :
log(N 0 ) ∼ U (1, 5).
log(N i +1 ) = log(N i ) + α, α ∼ U (−1, 1).
1 ≤ log(N i ) ≤ 5.
Summary statistics - Allele Frequency Spectrum (AFS)
Frequency of polymorphic sites over the genome.
Frequency of sites with i copies of the minor allele, for i from 1 to
n/2.
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● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
5 10 15 20
0.02 0.04 0.06 0.08 0.10 0.12 0.14
minor allele count
frequency
Variance of these frequencies over the genome.
Methods
Summary statistics - Linkage Disequilibrium (LD)
Correlation between allelic data at two polymorphic sites.
LD at distance d related to population size at time t = 2c(d ) 1 .
Summary statistics - Linkage Disequilibrium (LD)
Correlation between allelic data at two polymorphic sites.
Mean and variance of LD for several distances between sites.
LD at distance d related to population size at time t = 2c(d ) 1 .
Implementation
Simulations :
Haplotype data simulated with ms. One sample = 50 independent
2MB segments.
500 000 simulated samples, ≈ 40h on a cluster with 500 jobs in parallel
(4 min per sample on average).
Holstein data :
Several pre-processing steps required to obtain haplotype data
(sequencing, alignment, genotype calling, haplotype estimation).
Haplotype data processed with the same Python program.
Final statistical analysis with the R package abc.
Outline
1 Methods
2 Results
Simulations
Application to Holstein data
3 Conclusions and perspectives
Outline
1 Methods
2 Results
Simulations
Application to Holstein data
3 Conclusions and perspectives
Cross validation
0.00 0.05 0.10 0.15 0.20 0.25
générations
erreur
0 10 40 200 400 800 1200 2000 5000 2E4
rejection 0.02 median
rejection 0.01 median
rejection 0.005 median
rejection 0.002 median
rejection 0.001 median
ridge 0.02 median
ridge 0.01 median
ridge 0.005 median
ridge 0.002 median
ridge 0.001 median
Estimation error
P
i (θ i − ˆ θ i ) 2
I ∗Var (θ i ) based on 100 CV replicates.
Influence of AFS and LD statistics - Cross Validation
0.00 0.05 0.10 0.15 0.20 0.25 0.30
generations
error
0 10 40 200 400 800 1200 2000 5000 2E4
all stat
AFS
LD
Influence of AFS and LD statistics - Cross Validation
0.00 0.05 0.10 0.15 0.20 0.25 0.30
generations
error
0 10 40 200 400 800 1200 2000 5000 2E4
all stat
no VAR_AFS
no VAR_LD
Influence of AFS and LD statistics - PLS regression
−1.0 −0.5 0.0 0.5 1.0
−1.0 −0.5 0.0 0.5 1.0
Comp 1
Comp 2
AFS_1 AFS_2
AFS_3
AFS_4
AFS_5
AFS_6
AFS_7 AFS_8
AFS_9
AFS_10 AFS_11 AFS_12 AFS_13
AFS_14
AFS_15
AFS_16
AFS_17
AFS_18
AFS_19 AFS_20
AFS_21
AFS_22
AFS_23
AFS_24
AFS_25
V_AFS_1
V_AFS_2
V_AFS_3
V_AFS_4
V_AFS_5
V_AFS_6
V_AFS_7
V_AFS_8
V_AFS_9
V_AFS_10
V_AFS_11
V_AFS_12
V_AFS_13
V_AFS_14
V_AFS_15
V_AFS_16 V_AFS_17
V_AFS_18
V_AFS_19
V_AFS_20
V_AFS_21
V_AFS_22
V_AFS_23 V_AFS_24
V_AFS_25 LD_2000
LD_417
LD_167
LD_83
LD_50
LD_31
LD_14
LD_4
LD_1
V_LD_2000
V_LD_417
V_LD_167
V_LD_83
V_LD_50
V_LD_31
V_LD_14
V_LD_4
V_LD_1
SNPf
r
N10 N0
N200 N40 N400
N800
N1200
N2000
N5000
N20000
Outline
1 Methods
2 Results
Simulations
Application to Holstein data
3 Conclusions and perspectives
Prior check
−10 0 10 20
−5 0 5 10 15 20
PC 1
PC 2
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