Question

With regards to population genetics, how does linkage disequilibrium work? If different loci are very close together, alleles might be inherited together more often than expected. What does that mean with regards to frequency of those alleles within a population of perhaps 100 individuals (animals)?

Answer 1

In population genetics, linkage disequilibrium is the non-random association of alleles at different loci in a given population. Loci are said to be in linkage disequilibrium when the frequency of association of their different alleles is higher or lower than what would be expected if the loci were independent and associated randomly. Two or more alleles are said to be in linkage equilibrium when they occur randomly in a population. Conversely, alleles are in linkage disequilibrium when they do not occur randomly with respect to each other.

It works as:

Suppose that among the gametes that are formed in a sexually reproducing population, allele A occurs with frequency Pa at one locus Pa is the proportion of gametes with A at that locus), while at a different locus allele B occurs with frequency Pb. Similarly, let Pab be the frequency with which both A and B occur together in the same gamete Pab is the frequency of the AB haplotype.

The association between the alleles A and B can be regarded as completely random—which is known in statistics as independence—when the occurrence of one does not affect the occurrence of the other, in which case the probability that both A and B occur together is given by the product Pa Pb of the probabilities. There is said to be a linkage disequilibrium between the two alleles whenever Pab differs from PaPb for any reason.

Partb)

Consider a population of 100 at Hardy-Weinberg equilibrium for a gene with two alleles, A and a. Let p = the relative frequency of the A allele, let q = the relative frequency of the a allele, and let p = q = 0.5. For no drift to occur, the frequencies of the alleles in successive generations must remain at 0.5. If N is the population size of diploid organisms, then the number of A alleles (denoted k) is equal to 2pN.

Pr(k | p, n) = [n! / k! (n - k)!]pk(1-p)n-k

Putting values in this bionomial exapansion we get the probability as 0.056