Linkage Disequilibrium: D, D prime, and r squared

Two loci

Frequency of A

Frequency of B

D' is D as a fraction of the most it could be at these frequencies.

Chromosomes sampled

Haplotypes, not people. 100 people phased give 200.

Decay tab

Recombination fraction c

The slider is logarithmic, from 0.0001 to 0.5.

Generations

Effective size Ne

Sets where LD stops decaying, at about 1/(1 + 4Nec).

Block tab

Markers

Structure

Seed

Same seed, same haplotypes.

How the haplotypes are made: eight ancestral haplotypes related by a coalescent tree. Each marker is one mutation on one branch, so its minor allele is carried by whichever ancestors sit below that branch. Two mutations on the same branch are perfectly correlated; two on nested branches have D' of 1 and whatever r squared their frequencies allow.

Each sampled chromosome then copies one ancestor and occasionally switches to another, the Li and Stephens mosaic model that genotype imputation uses. Under Hotspot blocks the switch probability is near zero inside a block and near one at a hotspot. Under Uniform it is the same everywhere, so LD fades with distance instead of stopping at an edge.

Two loci

D-

D'-

r squared-

chi squared-

Two loci

The same thing in R