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For a large population with random mating, the Hardy Weinberg law allows one to calculate the frequency of each of the three genotypes from knowledge of the frequency of the individual alleles, and vice versa. The Hardy Weinberg equation is stated as follows:

p^2+2pq+q^2 = 1

p+q = 1, and p^2+2pq+q^2 = 1

It assumes that p and q stand for the frequencies of two alleles of a gene, with p being the frequency of the normal allele and q being the frequency of the disease causing allele.

p^2 is the frequency of homozygous normal, 2pq is the frequency of heterozygotes (carriers in AR diseases) and q^2 is the frequency of homozygous disease state. q^2 will be equal to incidence in AR diseases.

For example, assume that the frequency of the recessive allele for cystic fibrosis, which is an AR disease is 1/50. That means q=1/50. Applying the Hardy Weinberg Law, incidence of cystic fibrosis will be (1/50)^2 = 1/2500; the frequency of carriers will be 2pq. Since we know the value of q, and p+q=1, p will be 0.98 or 49/50 which is approximately equal to 1. Hence, 2pq = 2x1x1/50 = 1/25.

Another example, if the frequency of Tay Sachs disease (an AR disease), in Ashkenazi Jewish population is 1/400, that is another way of saying that q^2=1/400, hence q=1/20. So, the carrier frequency will be 2pq or 2x19/20x1/20 which is approximately 1/10.

When a couple presents for genetic counselling, calculating the risk of an inherited disease to their offspring will be influenced both by whether the disease is AR,AD,XR,XD or mitochondrial and also by the carrier or diseased state of the parents. If one or both parents do not have a history of inherited disorder in question in their families, then their risk will be similar to that of the general population.

The equation needs to be interpreted differently for X linked disorders. Because males are hemizygous for X-linked genes, the frequency or incidence of an X-linked disorder in males is directly equal to the frequency of the disease allele in the population, which will be q. On the other hand, the frequency of diseased females will be q^2, as females need to inherit two diseased X chromosomes to be affected. For example, if the frequency of the allele for color blindness is 0.08 or 8/100 that means 8/100 males will have color blindness while (8/100)2 or 0.0064 or 64/10,000 females will be color blind. Phenotypically normal females , in X linked recessive disorders, may be either homozygous or heterozygous (carrier state). So, the frequency of phenotypically normal females will be p^2+2pq. In the above example, p will be 1-0.08 = 0.02.

In X linked dominant conditions, the value for q will be equal to disease frequency in males, as males have only one X chromosome.

**LOD or logarithm of the odds score:** It is a statistical estimate of whether two genes, or a gene and a disease, are linked to one another. Genes are said to be linked, when they are located close together on the chromosome, that they are inherited together, as the frequency of recombination between them is quite low. LOD score is used for linkage analysis. Positive LOD scores favour the presence of linkage, whereas negative LOD scores indicate that linkage is less likely.

An LOD score > 3.0 is considered evidence for linkage. LOD score of 3 means the odds are a thousand to one that the two genes are linked, and therefore inherited together. On the other hand, a LOD score < −2.0 is considered evidence to exclude linkage.

**Linkage equilibrium and disequilibrium:** 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. Positive linkage disequilibrium exists when two alleles occur together on the same haplotype more often than expected, and negative linkage disequilibrium exists when alleles occur together on the same haplotype less often than expected.

In other words, if you multiply the frequencies of each allele occurring independently, for example “pxq”, positive linkage disequilibrium is implied when observed frequency > pxq and negative linkage when observed frequency < pxq.

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