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Inferring Population Size History from Large Samples of Genome-Wide Molecular Data - An Approximate
Bayesian Computation Approach.
Simon Boitard, Willy Rodríguez, Flora Jay, Stefano Mona, Frederic Austerlitz
To cite this version:
Simon Boitard, Willy Rodríguez, Flora Jay, Stefano Mona, Frederic Austerlitz. Inferring Population Size History from Large Samples of Genome-Wide Molecular Data - An Approximate Bayesian Compu- tation Approach.. conférence Jaques Monod ”Coalescence des approches théoriques et expérimentales en génomique évolutive et biologie des systèmes”, 2016, Roscoff, France. �hal-01604024�
Inferring Population Size History from Large Samples of Genome-Wide Molecular Data -
An Approximate Bayesian Computation Approach
Simon Boitard
1, Willy Rodríguez
2, Flora Jay
3, Stefano Mona
4, Frédéric Austerlitz
5(1) GenPhySE, Castanet-Tolosan, France. (2) IMT, Toulouse, France. (3) LRI, Orsay, France. (4) ISYEB, Paris, France. (5) UMR 7206, Paris, France.
ABC E STIMATION APPROACH
• Model : Kingman’s coalescent with mutation and recombination, piecewise constant population size with 21 fixed time windows.
• Simulated data : 450,000 samples of n haploid genomes, one genome = 100 2Mb-long “contigs”. Population sizes log-uniformly distributed from 10 to 100,000, with correlation between consecu- tive windows.
• Summary statistics : Folded Allele Frequency Spectrum (AFS) and average Linkage Disequilibrium (LD) for 18 bins of physical dis- tance between SNP (from 300bp to 1.4Mbp).
• ABC analysis : 0.5% samples accepted, neuralnet regression (Blum and François, 2010) from abc R package (Csilléry et al, 2012).
P REDICTION ERROR ( RANDOM HISTORIES )
Estimation of demographic history improved by :
(i) combining LD and AFS statistics (ii) increasing sample size
0.00.20.40.60.81.0
generations before present (log scale)
population size prediction error
0 10 100 1,000 10,000 100,000
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● LD statistics
AFS statistics without the proportion of SNP AFS statistics
AFS and LD statistics
0.00.20.40.60.81.0
generations before present (log scale)
population size prediction error
0 10 100 1,000 10,000 100,000
n=10 n=15 n=20 n=25 n=50
E STIMATION FOR SPECIFIC HISTORIES
Recent demography recovered and credible intervals, in contrast to PSMC (Li and Durbin, 2011) and MSMC (Schiffels and Durbin, 2014).
ABC, n=50
years before present (log scale)
effective population size (log scale)
10 100 1,000 10,000 100,000
1001,00010,000100,000
domestication breed formation
PSMC : n=2
10 100 1,000 10,000 100,000
1001,00010,000100,000
domestication breed formation
MSMC : n=4
10 100 1,000 10,000 100,000
1001,00010,000100,000
domestication breed formation
generations before present (log scale)
effective population size (log scale)
true value
estimations for one replicate 90% CI for one replicate
0 10 100 1,000 10,000 100,000
1001,00010,000100,000
0 10 100 1,000 10,000 100,000
1001,00010,000100,000
0 10 100 1,000 10,000 100,000
1001,00010,000100,000
0 10 100 1,000 10,000 100,000
1001,00010,000100,000
0 10 100 1,000 10,000 100,000
1001,00010,000100,000
0 10 100 1,000 10,000 100,000
1001,00010,000100,000
C OMPLEMENTARITY OF AFS AND LD STATISTICS
Depending on the scenario, LD or AFS is more informative.
AFS statistics
generations before present (log scale)
effective population size (log scale)
0 10 100 1,000 10,000 100,000
1001,00010,000100,000
E[TMRCA]
LD statistics
0 10 100 1,000 10,000 100,000
1001,00010,000100,000
E[TMRCA]
AFS and LD statistics
0 10 100 1,000 10,000 100,000
1001,00010,000100,000
E[TMRCA]
0 10 100 1,000 10,000 100,000
1001,00010,000100,000
E[TMRCA]
0 10 100 1,000 10,000 100,000
1001,00010,000100,000
E[TMRCA]
0 10 100 1,000 10,000 100,000
1001,00010,000100,000
E[TMRCA]
0 10 100 1,000 10,000 100,000
1001,00010,000100,000
E[TMRCA]
0 10 100 1,000 10,000 100,000
1001,00010,000100,000
E[TMRCA]
0 10 100 1,000 10,000 100,000
1001,00010,000100,000
E[TMRCA]
A PPLICATION TO NGS DATA IN CATTLE
Use genotype LD because of phas- ing errors and common alleles be- cause of sequencing errors.
After domestication, contiuous de- cline and clustering of breed histo- ries by area of origin.
years before present (log scale)
effective population size (log scale)
0 10 100 1,000 10,000 100,000
1003001,0003,00010,00030,000100,000
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● haplotype LD, all SNP genotype LD, all SNP genotype LD, MAF 10%
genotype LD, MAF 20%
years before present (log scale)
effective population size (log scale)
10 100 1,000 10,000 100,000
1003001,0003,00010,00030,000100,000
domestication breed formation
BrownSwiss Fleckvieh Holstein SwedishRed
Charolais Limousin Hereford Jersey
C ONCLUSIONS
• Accurate estimation of population size history, including the re- cent past, through the use of large samples of genomes and the combination of AFS and LD information.
• Based on unphased data and robust to sequencing errors.
• Ref PLoS Genet 12(3): e1005877, source code at https://forge- dga.jouy.inra.fr/projects/popsizeabc/
• Perspectives : simulate longer genomes through the use of faster simulation software (msprime, Kelleher et al, 2016), decoupling of observed times and change times.
