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III. POPULATION HISTORY MODELLING
SPECIES
SUBPOPULATIONS
(DEMES)
POPULATIONS
MOLECULAR
ECOLOGY
6 April 2017
We are interested in genetic structure of a
population(s) and HOW HAS BEEN CREATED
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We are interested in genetic structure of a
population(s) and HOW HAS BEEN CREATED
We are interested in genetic structure of a
population(s) and HOW HAS BEEN CREATED
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SOURCE AREA
COLONIZED AREA
Historical data available
Genetic data available
Population history (& genetic data)
 Past evolutionary and demographic processes have left
traces in the genetic variation – analyzing them we
attempt to reconstruct evolutionary history of
populations
 Studying population history = modelling
– Selection of the most appropriate model (evolutionary
scenario)
– Estimation of parameters (e.g. time of events,
number of founders, duration of bottlenecks,
population size, mutation rate)
 Description of recent invasions (invasion genetics)
 Description of older history (phylogeography)
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Inferring population history – ABC modelling
 We have observed data (e.g. microsatellite genotypes)
 We know genetic variation and structure
 We would like to know which demographic processes and how and
when have created such an observed data = population
evolutionary history
 Why is ABC approach useful in modelling population history?
It allows to deal with much more complex
models with many parameters and a lot of
complex data (many samples, populations,
genetic loci, sequences)
and hence models much more realistic
 model choice and parameter estimation
 exact LIKELIHOOD function is intractable in complex
situations and can be bypassed (approximated) by a
SIMILARITY MEASURE between many simulated (under
various models) and a single real (observed) data
 data SIMULATION under various models
 COMPARISON of simulated and observed data – model
choice
 Acoording to the most supported model we can ESTIMATE
VALUES of its parameters – parameter estimation
Approximate Bayesian Computation
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Decreasing of dimensionality
SIMULATED DATASETS
OBSERVED
DATASET
VERSUS
VERSUS
SUMMARY
STATISTICS
Scenario 1
Scenario 2
Scenario 3
Observed data set
kolonizace3_PCA_1_2_5700
P.C.1 ( 60.0%)
543210-1-2-3-4-5-6
P.C.2(18.6%)
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
-2.5
-3
-3.5
-4
Comparison of simulated and real dataset to infer probability of various
models (evolutionary scenarios of population history)
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NEW APPROACH
Approximate Bayesian Computation (ABC)
Beaumont et al. 2002, Genetics
- estimations of parameters
- useful for model choice among various scenarios applied on the same data
- the likelihood criterion is replaced by a similarity criterion
between simulated & observed datasets
- measured by a distance between summary statistics computed on both
datasets
0 0 1 1 2 5 5 5 9
24
50 52
84 79
115
0
20
40
60
80
100
120
140
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
in genetics,
evolutionary biology
and ecology
“Approximate Bayesian Computation”
topic in Web of Science
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ABC approach used successfully for
description of recent invasion scenarios
 Estoup & Clegg 2003, Molecular Ecology: Zosterops lateralis, Pacific islands
 Estoup et al. 2004, Evolution: Bufo marinus, Australia
 Pascual et al. 2007, Molecular Ecology: Drosophila subobscura, invasion
over Atlantic ocean
 Lombaert et al. 2010, PLoS ONE: Harmonia axyridis, invasion through the
Atlantic and subsequently to the whole world
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Software
Sunnåker et al. 2013, PLOS Computational Biology
SOFTWARE
Bez GUI:
SimCoal – simulator + ABC regression – Anderson et al. 2005
msBayes – simulator + ABC regression – Hickerson et al. 2007
S GUI:
ONeSAMP – ABC rejection – jen jedna Wright-Fisher populace – Tallmon et al.
2004
popABC – ABC rejection – Lopes et al. 2009
abc – Csilléry et al. 2011, Methods in Ecology and Evolution
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no simple software solution => inaccessible to most
biologists
BUT NOW  Do It Yourself: DIYABC software
allows to infer populaton history using the ABC
approach
(Cornuet et al. 2008, 2010, 2014)
DIYABC
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Genetic data
 Sequences
 SNPs
 Genotypes
1. SIMULATION STEP:
a very large reference table is produced
and recorded
prior parameter distributions
scenario
mutation model
summary statistics (e.g. number of
alleles, expected heterozygosity,fst)
the most time-consuming step
based on the genealogical tree of
sampled genes and coalescent
theory
ABC works in 3 steps
Cornuet et al. 2008, Bioinformatics
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SOURCE REGION
COLONIZED
REGION
Historic background
Genetic data (microsatellites, SNPs)
SOURCE REGION Historic background
COLONIZED
REGION
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SOURCE REGION Historic background
COLONIZED
REGION
SOURCE REGION Historic background
Prior distribution of parameters describing the scenario:
Ty, Tz --- divergence times – establishment of Y and Z
populations
Uniform distribution(min 100, max 500 generations)
COLONIZED
REGION
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100 500
Ty
10 10000
X
0,0001 0,001
µ
Prior distribution of
parameters
describing the model
Evolutionary scenarios = models
SIMULATED DATASETS
Genetic data → summary statistics
scenario X Y Z Ty Tz µ mean number of alleles mean heterozygosity
2 3797 7013 9839 484 486 0.00083 8.4 13.2 11.3 0.7841 0.8669 0.8589
3 3648 1355 1206 453 209 0.00072 7.9 6.1 4 0.7894 0.6371 0.5465
1 6802 7945 3929 176 346 0.0003 8.8 11.4 7.1 0.7877 0.8367 0.7824
1 4715 9090 5767 290 301 0.00048 7.5 12.6 9.1 0.7842 0.8211 0.7919
3 134 2714 3804 406 342 0.00029 1.4 4.8 4.7 0.0651 0.5182 0.5906
1 9331 902 4882 305 197 0.00096 13.6 6.5 13 0.863 0.5471 0.8294
3 1912 1785 6813 385 124 0.00035 4.3 5.5 7.1 0.5924 0.6414 0.7134
1. SIMULATION STEP:
a very large reference table is produced
and recorded
2. REJECTION STEP:
only the simulated data closest to the
observed dataset are retained
based on Euclidian distances in
multidimensional space of summary
statistics
DIYABC works in 3 steps
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Scenario 1
Scenario 2
Scenario 3
Observed data set
kolonizace3_PCA_1_2_5700
P.C.1 ( 60.0%)
543210-1-2-3-4-5-6
P.C.2(18.6%)
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
-2.5
-3
-3.5
-4
Comparison of our observed dataset with simulated ones
and inferring posterior distributions of scenarios
SOURCE REGION
Now: posterior distributions will be estimated
according to the winning scenario
THE WINNER
COLONIZED
REGION
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1. SIMULATION STEP:
a very large reference table is produced
and recorded
2. REJECTION STEP:
only the simulated data closest to the
observed dataset are retained
3. ESTIMATION STEP:
Estimating posterior distributions of
parameters through a local linear
regression procedure
DIYABC works in 3 steps
Scenario 1
Observed data set
kolonizace3_PCA_1_2_5700
P.C.1 ( 60.0%)
43210-1-2-3-4-5
P.C.2(18.6%)
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
-2.5
-3
-3.5
-4
Posterior distributions of parameters are estimated
according to the most supported scenario
100 500
Ty
10 10000
X
0,0001 0,001
µ