Final answer:
Two loci are in linkage equilibrium when their alleles assort independently and meet the conditions of the Hardy-Weinberg equilibrium, which includes no mutation, large population size, random mating, no migration, and no natural selection. In contrast, linkage disequilibrium occurs when alleles at different loci are combined in a population more often than expected by chance, often due to being closely located on the same chromosome.
Step-by-step explanation:
Two loci are said to be in linkage equilibrium when the alleles at these loci are associated at frequencies that would be expected if they assort independently. Usually, this term is used in the context of population genetics to describe non-random associations between alleles at different loci.
Linkage Equilibrium and the Hardy-Weinberg Principle
In population genetics, the Hardy-Weinberg theorem describes a model where allele and genotype frequencies remain constant - that is, in equilibrium - across generations in an ideal and infinite population that is not affected by evolutionary forces such as natural selection, mutation, migration, non-random mating, or genetic drift. For two loci to be in linkage equilibrium, they would not only have to meet the five conditions specified by the Hardy-Weinberg equilibrium (no mutation, no migration, large population size, random mating, and no natural selection), but they would also not be physically linked on the same chromosome or, if they are, recombination between them must occur frequently enough to produce genetic combinations in proportions similar to those from independent assortment.
Linkage Disequilibrium
Conversely, linkage disequilibrium is where the combination of alleles at different loci occurs together in a population more often (or less) than would be expected from a random formation of haplotypes from alleles based on their frequencies. If the recombination frequency between two genes is less than 50 percent, indicating that these genes are relatively close on the same chromosome, they are said to be linked, which could lead to linkage disequilibrium.
Linkage maps, created using recombination frequencies, showcase the locations of genes on chromosomes and can reveal the relative positions of loci and whether they may exhibit linkage disequilibrium or equilibrium.