I think that question has a simple answer, so simple that it is hard to find.
There is no direct relationship between MAF and LD. MAF can be any number below 0.5 at any polymorphic position in the genome. Even though two SNP A/a & B/b may be close together and in linkage disequilibrium they do not have to have the same MAF. This is because , if you think of the origin of the polymorphisms, one of the mutations say A > a events which originated the first SNP will usually have occurred before the other B > b. The first SNP "a" will have spread through the population and on one of these "a" chromosomes containing the first SNP, the second mutation event occurs. So although the "b" SNP occurs on only some chromosomes "a" chromosomes it doesn't occur on any "A" chromosomes and so "b" is in complete linkage disequilibrium with "a", but at a much lower frequency. On the other and, if the second mutation occurs on a different chromosome to the first, it will clearly not be in linkage disequilibrium, even though it could still have much lower MAF.
MAF is important in GWAS (for example) because markers with very low MAF have low heterozygosity and are therefore less informative. In GWAS using smaller numbers of individuals, markers with MAF less than 0.05 are often excluded.
Dear Yuri,
just to add a practical aspect on the relationship between linkage disequilibrium (LD) and minor allele frequency (MAF).
It has been shown (see here: http://www.biomedcentral.com/content/pdf/1471-2164-9-187.pdf; and here: http://www.plosone.org/article/fetchObject.action?uri=info%3Adoi%2F10.1371%2Fjournal.pone.0008451&representation=PDF) that among SNPs with higher MAF the estimated LD tends to be stronger. Atteched you can find an example with cattle data. Of course one must be careful that with higher MAF fewer SNPs are left for the estimation of LD, and this may introduce a bias.
Hope this stimulates some thoughts!
Just to add a bit more. The two main measures of LD are r^2 and D'. They differ primarily in how they treat loci with unqual MAFs. Essentially, r^2 takes MAF into account while D' does not, so you can get a very different r^2 and D' value for the same two loci.
A really good explanation of it can be found at the attached link
https://www.researchgate.net/post/I_have_Linkage_Disequilibrium_LD_data_for_two_SNPs-r2_is_about_014_D_is_around_08_Could_these_SNPs_be_said_to_be_in_strong_LD
Filippo Biscarini It is logical (the mathematical result) if greater MAFs lead to a higher likelihood of LD.
please look at this paper
https://www.frontiersin.org/articles/10.3389/fgene.2015.00337/full
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