Allele Frequencies

The allele frequency is the relative frequency of an allele for a site. This can be polarized according to the major/minor, reference/non-refernce or ancestral/derived. .Therefore the choice of allele frequency estimator is closely related to choosing which alleles are segregating (see Inferring_Major_and_Minor_alleles).

We allow for frequency estimation from different input data:

1. Genotype Likelihoods
2. Genotype posterior probabilities
3. Counts of bases

The allele frequency estimator from genotype likelihoods are from this publication, and the base counts method is from this publication.

For the case of the genotype likelihood based methods we allow for deviations from Hardy-Weinberg, namely we allow for users to supply a file containing inbreeding coefficients for each individual.

Brief Overview

Command:
./angsd -doMaf 
	-> angsd version: 0.576	 build(Jan 16 2014 01:49:06)
	-> Analysis helpbox/synopsis information:
------------------------
analysisMaf.cpp:
-doMaf	0 (Calculate persite frequencies '.mafs.gz')
	1: Frequency (fixed major and minor)
	2: Frequency (fixed major unknown minor)
	4: Frequency from genotype probabilities
	8: AlleleCounts based method (known major minor)
	NB. Filedumping is supressed if value is negative
-doPost	0	(Calculate posterior prob 3xgprob)
	1: Using frequency as prior
	2: Using uniform prior
Filters:
	-minMaf  	0.000000	(Remove sites with MAF below)
	-SNP_pval	1.000000	(Remove sites with a pvalue larger)
Extras:
	-ref	(null)	(Filename for fasta reference)
	-anc	(null)	(Filename for fasta ancestral)
	-eps	0.001000 [Only used for -doMaf &8]
	-beagleProb	0 (Dump beagle style postprobs)
	-indFname	(null) (file containing individual inbreedcoeficients)
NB These frequency estimators requires major/minor -doMajorMinor

Allele Frequency estimation

The major and minor allele is first inferred from the data or given by the user (see Inferring_Major_and_Minor_alleles). This includes information from both major and minor allele, a reference genome (for major) or an ancestral genome.

-doMaf [int]

1: Known major, and Known minor. Here both the major and minor allele is assumed to be known (inferred or given by user). The allele frequency is the obtained using based on the genotype likelihoods.

2: Known major, Unknown minor. Here the major allele is assumed to be known (inferred or given by user) however the minor allele is not determined. Instead we sum over the 3 possible minor alleles weighted by their probabilities.

4: frequency based on genotype posterior probabilities. If genotype probabilities are used as input to ANGSD the allele frequency is estimated directly on these.

8: frequency based on base counts. This method does not rely on genotype likelihood or probabilities but instead infers the allele frequency directly on the base counts.

Multiple estimators can be used simultaniusly be summing up the above numbers. Thus -doMaf 7 (1+2+4) will use the first three estimators. If the allele frequencies are estimated from the genotype likelihoods then you need to infer the major and minor allele (-doMajorMinor)

Allele frequencies from genotype likelihoods

The allele frequency estimators are described in citation. For testing reasons two optimazations are availeble. The BFGS and the EM algorithm. The EM algorithm is much faster then the BFGS. The allele frequencies are estimated by assuming that the site is diallelic and the major or minor alleles can be infered prior to the estimation or the uncertaincy of the minor allele can be incorborated into the model.

Example

Example for estimating the allele frequencies both while assuming known major and minor allele but also while taking the uncertaincy of the minor allele inference into account. The inference of the major and minor allele is done directly from the genotype likelihood

./angsd -out out -doMajorMinor 1 -doMaf 3 -bam bam.filelist -GL 1

Estimator from genotype probabilities

If the genotype probabilities are known the frequencies can be estimated by summing up the posterior probabilities $p(G=g|D)$ where $D$ is the sequencing data and $g\in \{0,1,2\}$ the allele count of the minor allele. The frequency estimate

${\hat {f}}={\frac {1}{2N}}\sum _{i}^{N}\left(2p(G=2|D)+p(G=1|D)\right)$

example

Example of the use of a genotype probability file for example from the output from beagle.

./angsd -out out -doMaf 16 -beagle beagle.file.gz

Estimator from sequencing data

The allele frequencies can be infered directy from the sequencing data citation. This works by using "counts" of alleles, and should be invoked like

-doCounts 1 -doPhat 1

Output data

.mafs

chromo	position	major	minor	ref	knownEM	unknownEM	nInd
21      9719788 T       A       0.000001        -0.000012       3
21      9719789 G       A       0.000000        -0.000001       3
21      9719790 A       C       0.000000        -0.000004       3
21      9719791 G       A       0.000000        -0.000001       3
21      9719792 G       A       0.000000        -0.000002       3
21      9719793 G       T       0.498277        41.932766       3
21      9719794 T       A       0.000000        -0.000001       3
21      9719795 T       A       0.000000        -0.000001       3

The first 4 columns are always defined to be:

1. chromosome name

2. position

3. major allele

4. minor allele

Depending on whether or not a reference and/or ancestral fasta files has been supplied these can occur as column 5 and 6. There are 4 different MAF estimators the estimate for these are given by the names knownEM,unknownEM,knownBFGS,unknownBFGS.

Futhermore if -SNP_pval is supplied it will output the associated p-value of the site being variable.

The nInd column is the effective sample size, as detmined by the genotype likelihoods.

Anders check below:

This pretty explanatory, nInd is the number of individuals where we have "reliable" reads (see bugs section) Depending on -doMaf INT, and -ref FILENAME and -anc FILENAME, extra column will be input.

Theory

ML estimator with known minor

First infer the Major and Minor allele and then use BFGS (-doMaf 1) optimazation or the EM algorithm (-doMaf 2) to estimate the allele frequencies.

$L(D|f)\propto \prod _{i}^{N}p(D_{i}|f)=\prod _{i}^{N}\sum _{g\in \{0,1,2\}}p(D_{i}|G=g)p(G=g|f)$

${\hat {f}}=argmax_{f}L(D|f)$

ML estimator with unknown minor

First infer the Major allele and then use BFGS (-doMaf 4) optimazation or the EM algorithm (-doMaf 8) to estimate the allele frequencies. Here only the Major allele needs to be known and the uncertaincy of infering the minor allele is modelled.

Let $\{M,m\}$ denote the major an minor allele assuming adiallelic site, then the maximum likelihood estimate of this pair is found using the likelihood function

$P(D|M,f)=\prod _{i}P(D_{i}|M,f)=\sum _{m}\sum _{A_{1},A_{2}}P(D_{i}|G=A_{1}A_{2})p(G=A_{1}A_{2}|m,M)p(m),$