Multilocus models and linkage disequilibrium

Analysis of single locus models, as above, has yielded a great deal of insight into the dynamics of populations. However, genetic mapping methods rely fundamentally on the relationships between linked markers, both for linkage and association mapping. Therefore we must also understand the relationships between loci.

The simplest multi-locus model considers the relationship between two biallelic loci on the same haplotype, or gamete. Consider two loci, 1 and 2, segregating alleles 'A' and 'a', and 'B' and 'b', respectively. Then there are four allele frequencies: PA, Pa, PB and Pb, and four haplotype frequencies: PAB, PAb, PaB and Pab. If an allele at site 1 is drawn at random from the population, it will be an'A' with probability pA and an'a' with probability pa; likewise with locus 2. Then by the rules of probability, if the allele frequencies at each locus are independent of one another, the probability of drawing a certain two-locus haplotype is just the product of the two individual allele frequencies. For example, assuming independence, the predicted frequency of the AB haplotype is simply PAPB. When two alleles are statistically independent of each other, they are said to be in linkage equilibrium. When individuals are sampled from a single population, it is normally the case that pairs of loci located on different chromosomes, or pairs that are far apart on the same chromosome, will be in linkage equilibrium. However, when loci are sufficiently close together, there is often statistical correlation between the alleles at each locus. This correlation is referred to as ''linkage disequilibrium" or ''LD.''

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