Thank you Javad Ahmadpanah for the suggestion.

Dear Arpan,

There are also online tools like PICcalc, but for biallelic markers you won't need a software. You can just do it with R (or any other statistical software) using a simple algorithm based on minor allele frequency (maf).

When calculating the PIC, you first calculate heterozygosity, i.e. one minus the squared allele frequencies. For an SNP this is simply 1-(maf^2+(1-maf)^2). Then you substract a term for identically heterozygous trios, which for an SNPs is just 2*maf^2*(1-maf)^2.

So, PIC = 1- (maf^2+(1-maf)^2))-(2maf^2(1-maf)^2) ... This could be simplified by some algebra - I hope there are no mistakes.

If you use this formula on a vector of mafs, you can rapidly calculate the PIC for many markers in one step.

Best regards,

Jens

Thank you Dr. Tetens for your valuable suggestion. It really helped me. 

Sir kindly tell me how this term for identically heterozygous trios has come?

Best regards,

Arpan Upadhyay

Dear Arpan,

I will try to explain it. Assume a biallelic marker with allele frequencies p and q. The probability of being heterozygous for an individual randomly chosen from the population is then 2pq. Under the assumption of random mating, the probability for a dam and a sire to be both heterozygous is 2pq*2pq, which gives 4*p^2*q^2. 50% of the offspring will also be heterozygous, so the conditinal probability for an identically heterozygous trio to occur is 0.5*4*p^2*q^2 = 2*p^2*q^2. In case of a biallelic marker such as an SNP, one of the frequencies, say p, would be the MAF and the other simply 1-MAF. For multiallelic markers, the probabilities have to be summed up over every possible heterozygous constellation (see attached file). Hope that helps?

Best regards,

Jens

Thanks a lot sir. Got your point.

with best regards,

Arpan Upadhyay

Prof. Tetens' explanation is almost perfect. :) One point should be added is that,  PIC  is an index for evaluating the informative extent of a SNP marker, therefore n is the number of  alleles at a locus in the formula. Botstein et al.(1980) proposed this algorithm to answer the question " how does the degree of polymorphism at a marker locus influence the probability of detection of linkage to the index locus" . More details please reference the following link. I hope it will help and make it more clear. 

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1686077/?page=7

https://www.ncbi.nlm.nih.gov/pubmed/6247908

Best regards,

Yingying

Yingying's addition is of course perfectly right ;-)

I just think of the relationship and difference between these two concepts (heterozygosity and PIC). Heterozygosity or gene diveristy (in nonrandom mating system) was proposed by Nei (1975 or earlier), who wanted to quantify genetic variation  by examing the marker loci. Before "Heterozygosity", the measurement " the proportion of polymorphic loci " was popular, and 1% rule was used to defined "what kind of locus is polymorphic", He thought this definition was arbitrary, and questioned "why not 5%" . But the drawback of "1% rule " he argued in genetic diversity study can be overcome nowaday by examing large number of samples and markers in a population.

Botstein' s PIC is more specific in linkage study. Assumptions are a parent carrying a rare dominat allele / disease allele (that is essential for the deduction of a parent genotype in index locus by a offspring, I think), pedigree is known, HWE. Given the marker genotypes in parents and a offspring. In this concept, frequecies of all possible mating types of the parents and the probability (p) of a offspring is informative should be calculated. And  then multiplying the mating frequeny by p, and finally summing up  the values for all mating types. That result is PIC.

This paper might explain Botstein' s original proposal. https://fas.org/sgp/othergov/doe/lanl/pubs/00326695.pdf

And others might  develope PIC concept.https://www.karger.com/Article/Abstract/22855

An online tool for calculating heterozygosity and polymorphism information content for variants / markers with up to 20 alleles is available here: https://www.genecalculators.net/pq-chwe-polypicker.html.

1+sum(the probabilities of alleles on the power 4) - sum(the square of the probabilities of alleles) - the square of [sum(the square of the probabilities of alleles)]

Hello, you can try GDI call Online Calculator http://www.msrcall.com/Gdicall.aspx