Phasing and recombination tutorial¶

In this tutorial you will extract information about the genotype phases and the recombination rate starting from VCF files.

How to make this notebook work¶

In this notebook we will use both the command line bash commands and R to setup the file folders.
Having to shift between two languages, you need to choose a kernel every time we shift from one language to another. A kernel contains a programming language and the necessary packages to run the course material. To choose a kernel, go on the menu on the top of the page and select Kernel --> Change Kernel, and then select the preferred one. We will shift between two kernels, and along the code in this notebook you will see a picture telling you to change kernel. The two pictures are below:

Bash Shift to the Bash kernel

Shift to the popgen course kernel

You can run the code in each cell by clicking on the run cell sign in the toolbar, or simply by pressing Shift+Enter. When the code is done running, a small green check sign will appear on the left side.
You need to run the cells in sequential order to execute the analysis. Please do not run a cell until the one above is done running, and do not skip any cells
The code goes along with textual descriptions to help you understand what happens. Please try not to focus on understanding the code itself in too much detail - but rather try to focus on the explanations and on the output of the commands
You can create new code cells by pressing + in the Menu bar above or by pressing B after you select a cell.

Learning outcomes¶

At the end of this tutorial you will be able to

Create phased data and discuss the results through the genome viewer
Estimate and analyze recombination maps
Plot recombination maps in R and compare different populations

Setting up folders¶

Here we setup a link to the Data folder and create the Results folder

Bash Choose the Bash kernel

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ln -s ../../Data
mkdir -p Results
ln -s ../../Data
mkdir -p Results

Inferring the genotype phase (AKA Phasing)¶

During base calling, we identified the two bases at each position in each diploid individual. However, we do not know which base goes on which of the two chromosomes. That means that we do not know if the two haploid chromosomes look like the left or right example below:

-----A-----C------         -----T-----C------ 
-----T-----G------    or   -----A-----G------

To do that we use the program Beagle, which applies a clustering algorithm to call the genotype phase.

We put the jointly called bases for Africans, West Eurasians, and East Asians in these three files:

Africa (9 individuals): Data/vcf/Allvariants_africa.vcf
West Eurasia (10 individuals): Data/vcf/Allvariants_westeurasia.vcf
Eash Asia (8 individuals): Data/vcf/Allvariants_eastasia.vcf

In this exercise we will just use the Africans and the West Eurasians.

Running Beagle¶

For additional information see the Beagle 4.1 manual

To obtain phased data, Beagle needs a genetic map. Genetic maps for widely used organisms (humans, mice, yeast, ...) are already available online. You can find the genetic map for chr2 (hg19 assembly) here: Data/genetic_map/plink.chr2.GRCh37.map.

We run Beagle on the african vcf file. Beagle is written in java language in a file with extension .jar, so we call it using java -jar.

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java -jar Data/software/beagle.08Jun17.d8b.jar \
        gt=Data/vcf/Allvariants_africa.vcf \
        map=Data/genetic_map/plink.chr2.GRCh37.map \
        out=Results/Allvariants_africa_phased
java -jar Data/software/beagle.08Jun17.d8b.jar \
        gt=Data/vcf/Allvariants_africa.vcf \
        map=Data/genetic_map/plink.chr2.GRCh37.map \
        out=Results/Allvariants_africa_phased

beagle.08Jun17.d8b.jar (version 4.1)
Copyright (C) 2014-2015 Brian L. Browning
Enter "java -jar beagle.08Jun17.d8b.jar" for a summary of command line arguments.
Start time: 10:51 AM CET on 05 Jan 2023

Command line: java -Xmx11904m -jar beagle.jar
  gt=Data/vcf/Allvariants_africa.vcf
  map=Data/genetic_map/plink.chr2.GRCh37.map
  out=Results/Allvariants_africa_phased

reference samples:       0
target samples:         10

Window 1 [ 2:135000277-144999565 ]
target markers:      49868

Starting burn-in iterations

Window=1 Iteration=1
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 3      max edges/level: 9
mean edges/node:  1.527  mean count/edge: 7

Window=1 Iteration=2
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 4      max edges/level: 11
mean edges/node:  1.380  mean count/edge: 5

Window=1 Iteration=3
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 4      max edges/level: 10
mean edges/node:  1.309  mean count/edge: 5

Window=1 Iteration=4
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 4      max edges/level: 10
mean edges/node:  1.270  mean count/edge: 5

Window=1 Iteration=5
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 3      max edges/level: 10
mean edges/node:  1.277  mean count/edge: 7

Window=1 Iteration=6
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 4      max edges/level: 10
mean edges/node:  1.236  mean count/edge: 5

Window=1 Iteration=7
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 4      max edges/level: 11
mean edges/node:  1.215  mean count/edge: 5

Window=1 Iteration=8
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 4      max edges/level: 11
mean edges/node:  1.202  mean count/edge: 5

Window=1 Iteration=9
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 4      max edges/level: 10
mean edges/node:  1.190  mean count/edge: 5

Window=1 Iteration=10
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 4      max edges/level: 11
mean edges/node:  1.182  mean count/edge: 5

Starting phasing iterations

Window=1 Iteration=11
Time for building model:         1 second
Time for sampling (singles):     1 second
DAG statistics
mean edges/level: 5      max edges/level: 11
mean edges/node:  1.129  mean count/edge: 4

Window=1 Iteration=12
Time for building model:         1 second
Time for sampling (singles):     1 second
DAG statistics
mean edges/level: 5      max edges/level: 11
mean edges/node:  1.134  mean count/edge: 4

Window=1 Iteration=13
Time for building model:         0 seconds
Time for sampling (singles):     1 second
DAG statistics
mean edges/level: 5      max edges/level: 12
mean edges/node:  1.115  mean count/edge: 4

Window=1 Iteration=14
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 6      max edges/level: 12
mean edges/node:  1.107  mean count/edge: 3

Window=1 Iteration=15
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 6      max edges/level: 12
mean edges/node:  1.101  mean count/edge: 3

Number of markers:               49868
Total time for building model: 7 seconds
Total time for sampling:       6 seconds
Total run time:                15 seconds

End time: 10:52 AM CET on 05 Jan 2023
beagle.08Jun17.d8b.jar (version 4.1) finished

We run the same command for the west eurasian vsc file:

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java -jar Data/software/beagle.08Jun17.d8b.jar \
        gt=Data/vcf/Allvariants_westeurasia.vcf \
        map=Data/genetic_map/plink.chr2.GRCh37.map \
        out=Results/Allvariants_westeurasia_phased
java -jar Data/software/beagle.08Jun17.d8b.jar \
        gt=Data/vcf/Allvariants_westeurasia.vcf \
        map=Data/genetic_map/plink.chr2.GRCh37.map \
        out=Results/Allvariants_westeurasia_phased

beagle.08Jun17.d8b.jar (version 4.1)
Copyright (C) 2014-2015 Brian L. Browning
Enter "java -jar beagle.08Jun17.d8b.jar" for a summary of command line arguments.
Start time: 10:52 AM CET on 05 Jan 2023

Command line: java -Xmx11904m -jar beagle.jar
  gt=Data/vcf/Allvariants_westeurasia.vcf
  map=Data/genetic_map/plink.chr2.GRCh37.map
  out=Results/Allvariants_westeurasia_phased

reference samples:       0
target samples:         10

Window 1 [ 2:135000277-144999565 ]
target markers:      49868

Starting burn-in iterations

Window=1 Iteration=1
Time for building model:         1 second
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 3      max edges/level: 9
mean edges/node:  1.226  mean count/edge: 7

Window=1 Iteration=2
Time for building model:         1 second
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 4      max edges/level: 10
mean edges/node:  1.182  mean count/edge: 5

Window=1 Iteration=3
Time for building model:         1 second
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 4      max edges/level: 10
mean edges/node:  1.140  mean count/edge: 5

Window=1 Iteration=4
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 4      max edges/level: 11
mean edges/node:  1.114  mean count/edge: 5

Window=1 Iteration=5
Time for building model:         1 second
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 4      max edges/level: 10
mean edges/node:  1.100  mean count/edge: 5

Window=1 Iteration=6
Time for building model:         1 second
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 4      max edges/level: 11
mean edges/node:  1.092  mean count/edge: 5

Window=1 Iteration=7
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 4      max edges/level: 10
mean edges/node:  1.084  mean count/edge: 5

Window=1 Iteration=8
Time for building model:         1 second
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 4      max edges/level: 10
mean edges/node:  1.081  mean count/edge: 5

Window=1 Iteration=9
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 5      max edges/level: 10
mean edges/node:  1.075  mean count/edge: 4

Window=1 Iteration=10
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 5      max edges/level: 11
mean edges/node:  1.074  mean count/edge: 4

Starting phasing iterations

Window=1 Iteration=11
Time for building model:         0 seconds
Time for sampling (singles):     1 second
DAG statistics
mean edges/level: 5      max edges/level: 11
mean edges/node:  1.055  mean count/edge: 4

Window=1 Iteration=12
Time for building model:         0 seconds
Time for sampling (singles):     1 second
DAG statistics
mean edges/level: 6      max edges/level: 12
mean edges/node:  1.052  mean count/edge: 3

Window=1 Iteration=13
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 6      max edges/level: 12
mean edges/node:  1.049  mean count/edge: 3

Window=1 Iteration=14
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 6      max edges/level: 13
mean edges/node:  1.048  mean count/edge: 3

Window=1 Iteration=15
Time for building model:         0 seconds
Time for sampling (singles):     0 seconds
DAG statistics
mean edges/level: 6      max edges/level: 11
mean edges/node:  1.047  mean count/edge: 3

Number of markers:               49868
Total time for building model: 7 seconds
Total time for sampling:       5 seconds
Total run time:                15 seconds

End time: 10:52 AM CET on 05 Jan 2023
beagle.08Jun17.d8b.jar (version 4.1) finished

Vcf files can both be compressed (gz) or uncompressed. IGV needs it in an uncompressed format, so decompress using

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gunzip -c Results/Allvariants_africa_phased.vcf.gz > Results/Allvariants_africa_phased_t.vcf
gunzip -c Results/Allvariants_africa_phased.vcf.gz > Results/Allvariants_africa_phased_t.vcf

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gunzip -c Results/Allvariants_westeurasia_phased.vcf.gz > Results/Allvariants_westeurasia_phased_t.vcf
gunzip -c Results/Allvariants_westeurasia_phased.vcf.gz > Results/Allvariants_westeurasia_phased_t.vcf

This command outputs the decompressed to stdout, which then is written into your file name of choice using >.

Browsing the phased results¶

Download the phased VCF files to your computer and open them in IGV (integrative genomics viewer):

Choose Human hg19 as the reference genome.
Click File > Load from File... and select you phased VCF file.

Explore phases of haplotypes at two positions in the alignment:

Select chr2, zoom all the way in and select find the base at position 136608646. First, take a look at the WestEurasian samples. Consider these questions while zooming further out:

What does the haplotypes look like?
Do you see any long streches of homozygosity?
Which haplotypes agree?
How wide is the region where they agree?

To help derive your answers, make use of the metadata file: Data/metadata/Sample_meta_subset.tsv

Now, compare it with the African samples.

Try to search the position chr2:136608646 in the UCSC genome browser. Remember we are using the Hg19 assembly version of the reference human genome. Can you find anything that explains your observations? (HINT: https://omim.org/entry/601806#0004)

Estimating a recombination map¶

We use LDhat, a package for the analysis of recombination rates from population genetic data, to estimate a recombination map from the vcf files. The proportion of crossovers occurring between two genes can be used to indicate the distance between them, and thus enable the construction of a genetic map that illustrates how all genes in the genome are related in space.

Format input data for LDhat¶

LDhat needs its input data in a particular format (LDhat manual). We will use vcftools to produce these input files from the phased VCF file.

For Africa:

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vcftools --gzvcf Results/Allvariants_africa_phased.vcf.gz --chr 2 --ldhat --out Results/recmap_data_africa
vcftools --gzvcf Results/Allvariants_africa_phased.vcf.gz --chr 2 --ldhat --out Results/recmap_data_africa

VCFtools - 0.1.16
(C) Adam Auton and Anthony Marcketta 2009

Parameters as interpreted:
	--gzvcf Results/Allvariants_africa_phased.vcf.gz
	--chr 2
	--out Results/recmap_data_africa
	--phased
	--ldhat

Using zlib version: 1.2.11
After filtering, kept 10 out of 10 Individuals
Outputting in phased LDhat format
After filtering, kept 49868 out of a possible 49868 Sites
Run Time = 0.00 seconds

West Eurasia

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vcftools --gzvcf Results/Allvariants_westeurasia_phased.vcf.gz --chr 2 --ldhat --out Results/recmap_data_westeurasia
vcftools --gzvcf Results/Allvariants_westeurasia_phased.vcf.gz --chr 2 --ldhat --out Results/recmap_data_westeurasia

VCFtools - 0.1.16
(C) Adam Auton and Anthony Marcketta 2009

Parameters as interpreted:
	--gzvcf Results/Allvariants_westeurasia_phased.vcf.gz
	--chr 2
	--out Results/recmap_data_westeurasia
	--phased
	--ldhat

Using zlib version: 1.2.11
After filtering, kept 10 out of 10 Individuals
Outputting in phased LDhat format
After filtering, kept 49868 out of a possible 49868 Sites
Run Time = 0.00 seconds

Have a look at the two files produced

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head Results/recmap_data_westeurasia.ldhat.locs
head Results/recmap_data_westeurasia.ldhat.locs

49868	144999.5650	L
135000.2770
135000.5000
135000.6740
135001.3970
135001.5380
135001.5950
135001.8450
135001.8870
135002.6710

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head Results/recmap_data_westeurasia.ldhat.sites
head Results/recmap_data_westeurasia.ldhat.sites

20	49868	1
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>ERR1025619-0

How do you think the information is encoded in these files?

Running LDhat¶

To speed up computations you can make a lookup table first. That takes a while, so we did if for you. But it is done using the complete program that comes with LDhat as below (command is ineffective because commented with the # symbol). The parameters are

-n 20:the number of haplotypes (2 * 10).
-rhomax 100: maximum rho ($4N_e r$) alowed: 100 (recommended).
-n_pts 101: number of points in grid: 101 (recommended).
-theta 0.0001: human theta ($4N_e \mu$).

In [23]:

            
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#Data/software/builds/LDhat/complete -n 20 -rhomax 100 -n_pts 101 -theta 0.0001
#Data/software/builds/LDhat/complete -n 20 -rhomax 100 -n_pts 101 -theta 0.0001

The output is a file that will serve as a look up table for the algorithm. It includes coalescent likelihoods for each pairs of SNPs using a grid of recombination rates. You can find it in Data/ldhat/new_lk.txt.

The next step is to calculate the recombination map. This command will take some time to run (~ 6 min). The options we are using are

-lk: likelihood lookup table.
-its: number of iterations of the MCMC.
-samp: number of iterations between sampling events, i.e how often to sample from the MCMC.
-burn: how many of the initial iterations to discard. Here we set it to zero to leave keep all samples. Then we look later how much burnin to discard.

Africa:

In [28]:

            
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Data/software/builds/LDhat/rhomap -seq Results/recmap_data_africa.ldhat.sites \
                                        -loc Results/recmap_data_africa.ldhat.locs \
                                        -prefix Results/recmap_data_africa. \
                                        -lk Data/ldhat/new_lk.txt -its 100000 -samp 500 -burn 0
Data/software/builds/LDhat/rhomap -seq Results/recmap_data_africa.ldhat.sites \
                                        -loc Results/recmap_data_africa.ldhat.locs \
                                        -prefix Results/recmap_data_africa. \
                                        -lk Data/ldhat/new_lk.txt -its 100000 -samp 500 -burn 0

Starting rate estimation
Seed = -1672909642
Analysing 20 haploid sequences of length 49868 seg sites
Reading sequences in fasta format
Reading data for pair types

Checking likelihood file is exhaustive:...OK
Calculating distribution of pair types
Completed classification of pair types
Old = 275: New = 0: Missing = 0
Max number of haplotypes for n=20 is 275
Reading likelihoods for pair types

Initial likelihood = -461301.893

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After 100000 runs - likelihood = -45586295.387664

Final block length = 27638.644688


Final Acceptance rates:
Change Block Rate =   	 0.9120	 Move Changepoint =	 0.5978
Split Block =         	 0.6573	 Merge blocks =    	 0.6568
Change Hotspot Heat = 	 0.9134	 Move Hotspot =    	 0.8442
Insert Hotspot =      	 0.8205	 Delete Hotspot =  	 0.1748
Change Hotspot Scale =	 0.5683


Total Program Run Time
199.44 seconds

West Eurasia:

In [30]:

            
                Copied!
                
Data/software/builds/LDhat/rhomap -seq Results/recmap_data_westeurasia.ldhat.sites \
                                        -loc Results/recmap_data_westeurasia.ldhat.locs \
                                        -prefix Results/recmap_data_westeurasia. \
                                        -lk Data/ldhat/new_lk.txt -its 100000 -samp 500 -burn 0
Data/software/builds/LDhat/rhomap -seq Results/recmap_data_westeurasia.ldhat.sites \
                                        -loc Results/recmap_data_westeurasia.ldhat.locs \
                                        -prefix Results/recmap_data_westeurasia. \
                                        -lk Data/ldhat/new_lk.txt -its 100000 -samp 500 -burn 0

Starting rate estimation
Seed = -1672909842
Analysing 20 haploid sequences of length 49868 seg sites
Reading sequences in fasta format
Reading data for pair types

Checking likelihood file is exhaustive:...OK
Calculating distribution of pair types
Completed classification of pair types
Old = 275: New = 0: Missing = 0
Max number of haplotypes for n=20 is 275
Reading likelihoods for pair types

Initial likelihood = -206613.220

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Run    91000: LK -20511352.903: ChangePoints 30008: Hotspots  350: MapLen 9520.433
Run    91500: LK -20513017.522: ChangePoints 29890: Hotspots  346: MapLen 10053.130
Run    92000: LK -20511591.411: ChangePoints 29811: Hotspots  343: MapLen 10451.970
Run    92500: LK -20510671.763: ChangePoints 29744: Hotspots  348: MapLen 10284.319
Run    93000: LK -20511509.324: ChangePoints 29645: Hotspots  353: MapLen 9492.915
Run    93500: LK -20510769.301: ChangePoints 29558: Hotspots  362: MapLen 10268.225
Run    94000: LK -20510985.164: ChangePoints 29474: Hotspots  364: MapLen 10061.878
Run    94500: LK -20510691.643: ChangePoints 29359: Hotspots  358: MapLen 9830.065
Run    95000: LK -20510917.503: ChangePoints 29279: Hotspots  359: MapLen 9747.605
Run    95500: LK -20508652.981: ChangePoints 29171: Hotspots  377: MapLen 9803.780
Run    96000: LK -20508678.613: ChangePoints 29095: Hotspots  375: MapLen 10329.438
Run    96500: LK -20508525.327: ChangePoints 28999: Hotspots  378: MapLen 10070.690
Run    97000: LK -20509679.050: ChangePoints 28918: Hotspots  385: MapLen 9713.606
Run    97500: LK -20509676.955: ChangePoints 28812: Hotspots  363: MapLen 9627.811
Run    98000: LK -20512223.040: ChangePoints 28724: Hotspots  362: MapLen 10514.651
Run    98500: LK -20510824.504: ChangePoints 28618: Hotspots  349: MapLen 9166.607
Run    99000: LK -20510690.015: ChangePoints 28551: Hotspots  365: MapLen 9352.152
Run    99500: LK -20509631.842: ChangePoints 28468: Hotspots  362: MapLen 9484.920
Run   100000: LK -20508912.020: ChangePoints 28386: Hotspots  354: MapLen 8794.590
After 100000 runs - likelihood = -20508912.020311

Final block length = 8794.589999


Final Acceptance rates:
Change Block Rate =   	 0.9136	 Move Changepoint =	 0.5972
Split Block =         	 0.6664	 Merge blocks =    	 0.6553
Change Hotspot Heat = 	 0.9179	 Move Hotspot =    	 0.8482
Insert Hotspot =      	 0.5967	 Delete Hotspot =  	 0.3343
Change Hotspot Scale =	 0.5670


Total Program Run Time
199.892 seconds

When rhomap completes, it writes three files:

acceptance_rates.txt: acceptance rates of the MCMC. If they are lower than 1%. The program should be run with more iterations.
summary.txt: (quoting the manual) for each SNP interval, the estimated genetic map position, the estimated recombination rate, and the hotspot density (the number of hotspots per kb per iteration).
rates.txt: (quoting the manual) is the output from each sample detailing the recombination rate (expressed in $4N_e r$ per kb) between each SNP.

Analyze results in R¶

Shift to the popgen course kernel

We now import the resulting files from LDhat in R using a function create by the author of LDhat. The resulting summary file from this function will be useful to perform some analysis later on. First of all we open a specific port to allow LDhat to pull from the web.

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Sys.setenv(https_proxy = "http://in:3128", http_proxy = "http://in:3128")
Sys.setenv(https_proxy = "http://in:3128", http_proxy = "http://in:3128")

And we load some practical R functions written by the author of LDhat:

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source("Data/software/ldhat.r")
source("Data/software/ldhat.r")

One of the loaded functions is summarise.rhomap, which produces two plots:

A graph of the recombination rate across on each polymorphic loci, along with confidence intervals.
A plot showing how estimation of recombination rate has progressed with each MCMC sample. Notice that the initial run of MCMC samples are atypical. This is the "burn-in" of the MCMC. We want to remove that, so take notice of how many samples it corresponds to. We can produce a new set of estimates that excludes this burn-in using the stat program that comes with LDhat:

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summarise.rhomap(rates.file = "Results/recmap_data_africa.rates.txt", 
                 locs.file="Results/recmap_data_africa.ldhat.locs")
summarise.rhomap(rates.file = "Results/recmap_data_africa.rates.txt", 
                 locs.file="Results/recmap_data_africa.ldhat.locs")


Summarise output from MCMC estimation of recombination rates in INTERVAL (LDhat 2.1)

Number of SNPs = 49868
Number of samples = 200
Burn-in period = 60 samples

Mean posterior total map length (4Ner) = 26130

A matrix: 49868 × 4 of type dbl
	Mean	q2.5	Median	q97.5
V1	2.613138e+04	23785.882864	26069.415174	28385.479705
V2	3.189734e-02	0.025865	0.029567	0.035765
V3	3.992060e-02	0.025865	0.043708	0.043708
V4	9.631160e-02	0.024798	0.028421	1.918469
V5	2.736505e-02	0.017521	0.031514	0.038252
V6	4.063312e-02	0.032641	0.037666	0.051794
V7	4.063312e-02	0.032641	0.037666	0.051794
V8	4.349214e+00	0.044223	0.064577	3.550377
V9	1.664489e+00	0.044223	0.066685	18.440217
V10	4.124480e+00	0.044223	0.063903	5.174799
V11	1.629410e-01	0.044223	0.049674	1.294076
V12	1.805922e-01	0.031657	0.044223	1.599889
V13	5.249856e-01	0.051482	0.077049	5.445120
V14	5.328709e-01	0.068693	0.100676	5.241806
V15	1.303271e-01	0.032116	0.059856	1.245262
V16	5.269492e-02	0.023354	0.047348	0.062195
V17	1.977770e-02	0.013310	0.013310	0.033842
V18	2.588744e-02	0.014321	0.028075	0.046243
V19	4.578547e-02	0.014321	0.057221	0.080184
V20	1.161124e-01	0.044611	0.102761	0.205164
V21	1.427766e-01	0.101665	0.143676	0.164953
V22	1.293949e-01	0.110037	0.124383	0.142881
V23	1.040705e-01	0.091605	0.109707	0.113214
V24	8.734096e-02	0.062407	0.092143	0.110971
V25	3.160621e-02	0.025196	0.032159	0.034215
V26	1.227352e-02	0.008880	0.010745	0.025634
V27	8.402359e-02	0.008273	0.012991	1.244819
V28	1.905990e+00	0.054245	0.055165	27.779378
V29	1.009730e+00	0.054303	0.054404	16.634594
V30	7.561011e-01	0.054007	0.054007	8.262071
⋮	⋮	⋮	⋮	⋮
V49839	0.586216440	0.031562	0.056239	0.0794900
V49840	0.974319851	0.065961	0.075527	0.0980010
V49841	0.007697255	0.004473	0.006455	0.0094510
V49842	0.005525369	0.004473	0.006285	0.0063020
V49843	0.022602567	0.015801	0.023371	0.0252310
V49844	0.022344156	0.015801	0.023371	0.0252310
V49845	0.022344156	0.015801	0.023371	0.0252310
V49846	0.022809418	0.017714	0.023687	0.0248860
V49847	0.042730369	0.038590	0.045245	0.0517460
V49848	0.052503574	0.041647	0.052997	0.0570870
V49849	0.076682972	0.071164	0.076231	0.0866190
V49850	0.066261078	0.065214	0.065214	0.0757580
V49851	0.036610000	0.036610	0.036610	0.0366100
V49852	1.449330099	0.004324	0.004551	0.2046920
V49853	1.241954085	0.148428	0.188482	0.1919550
V49854	0.021525397	0.015358	0.021410	0.0264370
V49855	0.095291624	0.026010	0.037250	0.7975540
V49856	0.308145390	0.002027	0.012100	3.0291185
V49857	0.264792326	0.012100	0.054931	3.3697010
V49858	0.101107525	0.045241	0.060264	0.7046035
V49859	0.050659894	0.016604	0.027333	0.0291340
V49860	0.052553489	0.020644	0.022739	0.0424400
V49861	0.078084936	0.072679	0.072679	0.0809410
V49862	0.037792092	0.006486	0.034480	0.0653140
V49863	0.066067355	0.054728	0.069046	0.0741110
V49864	0.069768418	0.054728	0.072821	0.0914680
V49865	0.459128191	0.038259	0.048496	0.0734020
V49866	0.183878007	0.027343	0.043061	2.5778320
V49867	0.924676695	0.012427	0.012427	16.4605740
V49868	0.716506589	0.012427	0.012427	2.6543440

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summarise.rhomap(rates.file = "Results/recmap_data_westeurasia.rates.txt", 
                 locs.file="Results/recmap_data_westeurasia.ldhat.locs")
summarise.rhomap(rates.file = "Results/recmap_data_westeurasia.rates.txt", 
                 locs.file="Results/recmap_data_westeurasia.ldhat.locs")


Summarise output from MCMC estimation of recombination rates in INTERVAL (LDhat 2.1)

Number of SNPs = 49868
Number of samples = 200
Burn-in period = 60 samples

Mean posterior total map length (4Ner) = 9083

A matrix: 49868 × 4 of type dbl
	Mean	q2.5	Median	q97.5
V1	9.082536e+03	7827.229838	9129.172401	10276.272171
V2	1.170069e-01	0.025280	0.025280	0.051955
V3	2.439478e-01	0.025280	0.025280	0.051955
V4	6.286420e-01	0.034076	0.045759	0.061479
V5	9.706494e-02	0.060174	0.106324	0.106324
V6	2.426546e+00	0.020655	0.020719	0.063227
V7	1.267250e+00	0.015742	0.015809	0.057953
V8	8.257790e-01	0.015742	0.015809	0.026906
V9	8.283066e-01	0.061092	0.061092	0.061092
V10	3.497593e-02	0.025078	0.041306	0.041306
V11	3.497593e-02	0.025078	0.041306	0.041306
V12	3.497593e-02	0.025078	0.041306	0.041306
V13	1.180946e-01	0.011927	0.011927	0.044104
V14	5.538109e-01	0.011927	0.011927	0.054185
V15	1.453568e+00	0.072399	0.096895	0.114998
V16	1.088630e+00	0.116805	0.139150	0.179734
V17	5.203582e-01	0.116805	0.139150	0.179734
V18	7.539596e-02	0.024511	0.033726	0.166236
V19	2.861689e-02	0.020121	0.031811	0.036492
V20	3.703006e-02	0.018987	0.043647	0.047888
V21	5.844671e-02	0.039730	0.061148	0.075459
V22	9.468301e-02	0.055296	0.105718	0.120439
V23	9.715167e-02	0.088925	0.090417	0.120317
V24	9.347979e-02	0.074971	0.095352	0.120317
V25	3.535339e-01	0.061758	0.080481	0.116355
V26	1.945912e+00	0.022691	0.026865	0.042297
V27	5.981196e-01	0.020159	0.035832	0.039467
V28	1.799674e-01	0.014335	0.030014	0.034264
V29	9.353603e-03	0.005234	0.008616	0.014335
V30	1.609916e-02	0.005234	0.015646	0.032405
⋮	⋮	⋮	⋮	⋮
V49839	0.06651661	0.0503210	0.061078	0.1121540
V49840	0.24313234	0.0153550	0.017703	0.0288010
V49841	0.22909041	0.0028390	0.002839	0.0056380
V49842	0.04566733	0.0410680	0.043297	0.0491100
V49843	0.04846508	0.0423940	0.042472	0.0516590
V49844	0.04893842	0.0423940	0.042472	0.0516590
V49845	0.05061794	0.0423940	0.042472	0.0516590
V49846	0.12274001	0.0376180	0.042662	0.0457490
V49847	0.02067860	0.0162540	0.016873	0.0257440
V49848	0.01550357	0.0032940	0.013618	0.0290840
V49849	0.01838629	0.0032940	0.014886	0.0303390
V49850	0.01913597	0.0058480	0.015104	0.0303390
V49851	0.07972413	0.0290840	0.062745	0.1429740
V49852	0.11719965	0.0496675	0.062745	0.0993540
V49853	0.61020563	0.0153580	0.044142	1.1420175
V49854	0.63870461	0.0313220	0.034424	0.0420650
V49855	0.35492528	0.0317810	0.044280	5.1593470
V49856	0.09521762	0.0317810	0.034620	0.6275670
V49857	0.04222535	0.0193270	0.019849	0.0603330
V49858	0.02535775	0.0196190	0.022831	0.0287040
V49859	0.04967957	0.0311970	0.059201	0.0700730
V49860	0.03521587	0.0279130	0.035458	0.0489670
V49861	0.43848079	0.0065310	0.009718	0.0212170
V49862	0.45544142	0.0212900	0.022707	0.0232680
V49863	0.10086994	0.0941530	0.100551	0.1029810
V49864	0.09510103	0.0885890	0.094153	0.1029810
V49865	0.55970066	0.0861250	0.116425	2.0796960
V49866	2.83878516	0.0246590	0.032664	23.7454800
V49867	0.09245043	0.0332600	0.044615	0.7473165
V49868	0.03723034	0.0306600	0.032024	0.0515200

Bash Shift to the Bash kernel

We run LDhat stat. This produces a file called res.txt that describes the confidence in the estimated recombination rate along the sequence.

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Data/software/builds/LDhat/stat -input Results/recmap_data_africa.rates.txt \
                                -loc Results/recmap_data_africa.ldhat.locs \
                                -burn 60
mv res.txt Results/recmap_data_africa.res.txt
Data/software/builds/LDhat/stat -input Results/recmap_data_africa.rates.txt \
                                -loc Results/recmap_data_africa.ldhat.locs \
                                -burn 60
mv res.txt Results/recmap_data_africa.res.txt


Reading data: 200 lines (miss first 60) of 49868 points.........Data read successfully



Mid = 70, L95=4, U95=136

........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................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Average total change in rate = 197978.749
Average total # changes = 38819.829

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Data/software/builds/LDhat/stat -input Results/recmap_data_westeurasia.rates.txt \
                                -loc Results/recmap_data_westeurasia.ldhat.locs \
                                -burn 60
mv res.txt Results/recmap_data_westeurasia.res.txt
Data/software/builds/LDhat/stat -input Results/recmap_data_westeurasia.rates.txt \
                                -loc Results/recmap_data_westeurasia.ldhat.locs \
                                -burn 60
mv res.txt Results/recmap_data_westeurasia.res.txt


Reading data: 200 lines (miss first 60) of 49868 points.........Data read successfully



Mid = 70, L95=4, U95=136

........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................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Average total change in rate = 68903.672
Average total # changes = 38438.436

Shift to the popgen course kernel

Now we to plot the final results. To have the positions of the loci for which we have estimated mean recombination rates, we will merge the new dataset created with the summary files generated by LDhat:

In [1]:

            
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library(ggplot2)
library(dplyr)
library(tidyr)
library(magrittr)
library(ggplot2)
library(dplyr)
library(tidyr)
library(magrittr)

Attaching package: ‘dplyr’


The following objects are masked from ‘package:stats’:

    filter, lag


The following objects are masked from ‘package:base’:

    intersect, setdiff, setequal, union



Attaching package: ‘magrittr’


The following object is masked from ‘package:tidyr’:

    extract

We plot the mean of the recombination rate along genome positions. In blue we visualize the average rec. rate, and in gray the 95% confidence interval

In [5]:

            
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summary <- read.table('Results/recmap_data_africa.summary.txt', header = T)
rates <- read.table("Results/recmap_data_africa.res.txt", header=T)
rates %>%
  filter(Loci > 0) %>%
  mutate(pos=summary$Position.kb.*1000) %>%
  ggplot(aes(x=pos, y=Mean_rho, ymin=L95, ymax=U95)) +  
  geom_line(color='blue') +
  geom_ribbon(alpha=0.1) +
  theme_bw()
summary <- read.table('Results/recmap_data_africa.summary.txt', header = T)
rates <- read.table("Results/recmap_data_africa.res.txt", header=T)
rates %>%
  filter(Loci > 0) %>%
  mutate(pos=summary$Position.kb.*1000) %>%
  ggplot(aes(x=pos, y=Mean_rho, ymin=L95, ymax=U95)) +  
  geom_line(color='blue') +
  geom_ribbon(alpha=0.1) +
  theme_bw()

In [4]:

            
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summary <- read.table('Results/recmap_data_westeurasia.summary.txt', header = T)
rates <- read.table("Results/recmap_data_westeurasia.res.txt", header=T)
rates %>%
  filter(Loci > 0) %>%
  mutate(pos=summary$Position.kb.*1000) %>%
  ggplot(aes(x=pos, y=Mean_rho, ymin=L95, ymax=U95)) +  
  geom_line(color='blue') +
  geom_ribbon(alpha=0.1) +
  theme_bw()
summary <- read.table('Results/recmap_data_westeurasia.summary.txt', header = T)
rates <- read.table("Results/recmap_data_westeurasia.res.txt", header=T)
rates %>%
  filter(Loci > 0) %>%
  mutate(pos=summary$Position.kb.*1000) %>%
  ggplot(aes(x=pos, y=Mean_rho, ymin=L95, ymax=U95)) +  
  geom_line(color='blue') +
  geom_ribbon(alpha=0.1) +
  theme_bw()

Look at the plots and ponder the following questions:

Are there any recombination hotspots?
Are there any regions where the estimated recombination rate is really low?
Can you see any hotspots in Africans that are not found in West Eurasians - other the othe way around?
What does the recombination rate look like around the lactase gene?