Linkage equilibrium means alleles at two different loci are inherited independently, so their combined frequencies match what you'd expect based on individual allele frequencies.

Linkage disequilibrium (LD) occurs when alleles at different loci are inherited together more (or less) often than expected. This usually happens when the loci are physically close on the chromosome, making recombination between them less likely.

LD is important in genetics, especially in Genome-Wide Association Studies (GWAS), to identify gene variants linked to diseases or traits by observing non-random allele combinations.

Linkage Equilibrium:

• Definition: In linkage equilibrium, alleles at two different loci are inherited independently of each other. The combination of alleles at these loci occurs at frequencies that are simply the product of their individual allele frequencies.

• Example: If you have two loci, A and B, with alleles A1, A2 and B1, B2, respectively, the frequency of the combination A1B1 should equal the product of the frequencies of A1 and B1 if the loci are in linkage equilibrium.

  P(A1B1)=P(A1)×P(B1)P(A1B1)

  This means the alleles are not associated with each other and are passed on independently in a population.

Linkage Disequilibrium (LD):

• Definition: In linkage disequilibrium, alleles at different loci are not independently inherited, meaning certain combinations of alleles occur more or less frequently than expected by chance. This often happens when loci are physically close to each other on the same chromosome (they are "linked").

• Reasons for LD:

  1. Physical linkage: The loci are close together on the same chromosome, reducing the likelihood of recombination between them.
  2. Population history: Population bottlenecks, founder effects, or selective sweeps can create LD, even for loci on different chromosomes.
  3. Mutation and selection: A new mutation in a gene can create an association with nearby alleles, which can persist over generations.

• Example: In LD, the frequency of the allele combination A1B1 might be higher (or lower) than the product of the individual allele frequencies:

  P(A1B1)≠P(A1)×P(B1)

  For instance, if loci A and B are close together, recombination between them is rare, so certain allele combinations (like A1B1) might be passed down together more frequently than expected.

Clinical and Genetic Applications:

• Genome-Wide Association Studies (GWAS): LD is important in GWAS, where researchers look for genetic variants associated with traits or diseases. Variants in LD with a causal variant can serve as markers for the disease, even if they are not directly involved.
• Haplotype mapping: LD can be used to map disease-causing genes by identifying regions of the genome where certain alleles are inherited together in affected individuals.
• Recombination: High LD implies that recombination between loci is rare, while low or absent LD indicates more frequent recombination.

Key Difference:

• Linkage equilibrium: Alleles at different loci are inherited independently, and their frequencies conform to statistical expectations.
• Linkage disequilibrium: Alleles at different loci are inherited together more often (or less often) than expected by chance, indicating a non-random association between them.

In summary, linkage equilibrium represents a lack of association between loci, while linkage disequilibrium indicates a correlation or association between genetic loci, often due to physical proximity or population history.