IBS vs. IBD

Regarding the question what's IBD and IBS, here is my understanding:

A SNP (or a segment of DNA) is identical by state (IBS) if they have the same alleles in two of more individuals. For example, if person A has genotype A/C at a SNP position while person B has A/T at the position, then that SNP position has a IBS=1 status. IBD is a IBS that their shared alleles are from a common ancestor. That is, in my above example, if A and B’s parents have genotype A/C(mom) and A/T (dad), then we don’t know if the shared “A” allele in A and B came from mom or dad. In that case, it’s just an IBS, not an IBD. But if their parents’ genotypes are A/G (mom) and C/T (dad), then we know for largely sure the “A” is from mom, not from dad. So, it’s both an IBD and IBS. In practice, for a pair of individuals, without knowing their parents, we could estimate their IBD likelihood for each SNP using their IBS information. I think the math behind is Bayesian theorem. 

PLINK use IBS-based clustering to remove sample outliers (which have too-far IBS distance from the rest), see here: http://pngu.mgh.harvard.edu/~purcell/plink/strat.shtml

PLINK use IBD to detect samples too-close to each other (e.g. relatives, contamination). See here: http://pngu.mgh.harvard.edu/~purcell/plink/ibdibs.shtml

Below is a nice piece for how to use IBD to detect relative. From Anderson, C. et al. Data quality control in genetic case-control association studies. Nat Protoc. 5, 1564–1573 (2010).

The expectation is that IBD = 1 for duplicates or monozygotic twins, IBD = 0.5 for first-degree relatives, IBD = 0.25 for second-degree relatives and IBD = 0.125 for third- degree relatives. Owing to genotyping error, LD and population structure, there is often some variation around these theoretical values and it is typical to remove one individual from each pair with an IBD value of > 0.1875, which is halfway between the expected IBD for third- and second-degree relatives. For these reasons an IBD value of > 0.98 identifies duplicates.

Another review on this is also worthy reading: Joseph E. Powell, Peter M. Visscher & Michael E. Goddard. Reconciling the analysis of IBD and IBS in complex trait studies. Nature Reviews Genetics 11, 800-805 (2010)

The following slide (from http://ibgwww.colorado.edu/workshop2005/cdrom/ScriptsA/evans/IBDestimation/IBD--2005.pdf) could be easier to understand IBD vs. IBS:

SNP allele coding schema

There are three types of different SNP allele coding schemes (so far). No idea why the scientists have to make things so confusing sometimes...

Here you go:

• TOP/BOT from Illumina: Simply saying, for unambiguous cases (incl. A/G, A/C, T/G, T/C), A is always allele A (or allele 1) and on TOP strand, and T is also allele A (or allele 1) but on BOT strand. The other variation is allele B (or allele 2). For ambiguous cases (e.g. A/T and G/C), strand is easy to assign, but allele A and B is ambiguous. So, Illumina use a 'sequence walking' to assign allele A/B by the first unambiguous pair of the flanking sequence. Detail explanation in their tech doc. 
• Forward/Reverse for dbSNP: dbSNP use the orientation determined by mapping SNP flanking sequence (of the longest submission) to a contig sequence using BLAST. A refSNP can have multiple submissions, each of which might have their own orientation depending on whether the flanking sequence is from plus strand or minus strand. The submission with the longest flanking will be taken as instantiate sequence for the refSNP during BLAST analysis for the current build. So, the strand of a dbSNP refSNP is determined by (1) the sequence of the longest submission (or the exemplar), and (2) the strand of contig it maps to. A good example can be found here. See more details here:  http://www.ncbi.nlm.nih.gov/books/NBK44455/#Build.define_the_term__orientation_as_us
• Plus/Minus strand for Genome Annotation, HapMap, 1000 Genome Project: The plus (+) strand is defined as the strand with its 5′ end at the tip of the short arm (see Ref #3 below). SNP alleles reported on the same strand as the (+) strand are called ‘plus’ alleles and those on the (−) strand are called ‘minus’ alleles. This also applies to the imputed results from 1000 Genome, e.g. a0 is for REF (reference) allele and a1 for ALT (alternate) allele. 

Several notes:

1. dbSNP does not use TOP/BOT schema: http://www.ncbi.nlm.nih.gov/books/NBK44393/#Submit.does_dbsnp_use_topbot_nomenclatur_1
2. Minor/Major alleles are just a relative term. They can change between different populations/dataset. So, it really makes no sense to use/think that allele2 is minor allele, G in A>G is minor allele, or so. Minor allele can be reference allele. 
3. In the Illumina genotyping final report (e.g. "FinalReport.txt"), use "Allele1 - Forward" and "Allele2 - Forward" to construct .lgen file for plink. See post: https://www.biostars.org/p/16982/  -- Forward is from dbSNP, Plus is from 1000 Genome. See #6 below. 
4. SNPs from dbSNP reverse strand need to flip before merging with imputed SNPs, using flip_strand option in plink.
5. Allele 1 (in allele 1/2 setting) need to be forced to reference allele before merging with imputed SNPs, using --reference-allele option in plink.
6. Important note: The FinalReport.txt from Illumina genotype tool GenomeStudio can also export other columns like "Allele1 - Forward", "Allele2 - Forward", "Allele1 - Plus", "Allele2 - Plus". I called Illumina tech that the Forward is for dbSNP, and Plus is for 1000 Genome. Be cautious that dbSNP and +/- can also be change between different version of dbSNP or genome building. (Full description is here, login required). To get to know which version your allele is referred to, you have to get the manifest file from your base caller. 

References:

1. https://triticeaetoolbox.org/wheat/snps.php
2. http://gengen.openbioinformatics.org/en/latest/tutorial/coding/
3. http://www.sciencedirect.com/science/article/pii/S0168952512000704
4. https://mathgen.stats.ox.ac.uk/impute/1000GP%20Phase%203%20haplotypes%206%20October%202014.html
5. http://genome.sph.umich.edu/wiki/IMPUTE2:_1000_Genomes_Imputation_Cookbook

PLINK2 vs. SNAP for linkage disequilibrium (LD) calculation

Among other ways to calculate SNPs in linkage disequilibrium (LD), two methods have been used in many literatures: PLINK2 and SNAP

With PLINK2, SNPs in LD can be calculated using parameters like:
PLINK2 -r2 dprime --ld-window-kb 1000 --ld-window 10 --ld-window-r2 0.8
SNAP is a web-based service with pre-calculated data: https://www.broadinstitute.org/mpg/snap. You can set the population, distance limit, r2 threshold.

Note that PLINK2 has one more control: --ld-window

In its manual (https://www.cog-genomics.org/plink2/ld), it says "By default, when a limited window report is requested, every pair of variants with at least (10-1) variants between them, or more than 1000 kilobases apart".

That means PLINK2 limits SNPs with two kinds of radius: both the genomic distance (--ld-window-kb) and the number of SNPs apart (--ld-window), while SNAP only has the distance limit. Both of them have the r2 threshold.