Linkage Disequilibrium

Also known as LD

Consider 2 loci A and B - are the allele frequencies at the two loci independent?
This means there are four possible haplotypes (combinations of the four alleles)
If loci A and B are independent, we expect to observe all four haplotypes in the gene pool to be equal to the product of allele frequencies:

f r e q (A_{i} B_{j}) = p_{A_{i} B_{j}} = p_{A i} p_{B_{j}}

This is the expected frequency if they are independent.

$D$ is what we call linkage disequilibrium, when haplotype frequencies depart from their expectations. $D = p_{observed} - p_{expected}$ , or $D = p_{A_{i} B_{j}} - p_{A_{i}} p_{B_{j}}$

Evolutionary processes can cause linkage disequilibrium by making certain allele combinations more common than others

Effects on LD

Mutation creates LD
Selection can create LD if it favours some haplotypes over others because specific allele combinations have higher fitness
Gene flow creates LD if allele frequencies differ between populations
Recombination decreases LD by re-arranging haplotypes
- During meiosis
- This happens at recombination rate $r$

Decay of LD (Linkage Decay)

Decays at rate $(1 - r)$ each generation: $D^{'} = (1 - r) D$
After $t$ generations: $D_{t} \approx D_{0} e^{- r t}$ (when $r ≪ 1$ )
- Usually $r$ is in the order of $10^{- 7}$ or $10^{- 9}$ between adjacent nucleotides
  !EEB-020-PopulationGenetics-2025, p.91

Using LD to find selection

When a new beneficial mutation arises, it will:
- Be in LD with nearby alleles
- Quickly rise in frequency because of selection
- Reduce genetic diversity at nearby loci because of genetic hitchhiking
  We call this Selective Sweep

When a beneficial mutation arises in a population, the nearby genes that are associated with it will also increase in frequency with it and become less diverse in the population. The mutation has "swept" through the population, taking with it the nearby genetic variation

This can happen even in synonymous (neutral) alleles, if they are associated with a beneficial mutation.