For a large population with random mating, the Hardy-Weinberg law lets you calculate the frequency of each of the three genotypes from the frequency of the individual alleles (and vice versa).
The Hardy-Weinberg equation is:
p^2+2pq+q^2 = 1
p+q = 1, and p^2+2pq+q^2 = 1
Here, p and q are the frequencies of two alleles of a gene:
The genotype frequencies are:
In autosomal recessive (AR) diseases, q^2 equals the incidence of the disease.
For example, assume the frequency of the recessive allele for cystic fibrosis (an AR disease) is 1/50. That means q = 1/50. Applying the Hardy-Weinberg law:
Since you know q and p+q = 1:
So:
Another example: if the frequency of Tay-Sachs disease (an AR disease) in the Ashkenazi Jewish population is 1/400, that is another way of saying q^2 = 1/400. Therefore:
So the carrier frequency is:
When a couple presents for genetic counselling, the risk of an inherited disease in their offspring depends on:
If one or both parents have no family history of the inherited disorder in question, their risk is 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 (incidence) of an X-linked disorder in males is directly equal to the frequency of the disease allele in the population, which is q. In contrast, the frequency of affected females is q^2, because females must inherit two disease alleles (two affected X chromosomes) to be affected.
For example, if the frequency of the allele for color blindness is 0.08 (8/100):
In X-linked recessive disorders, phenotypically normal females may be either homozygous normal or heterozygous (carriers). So, the frequency of phenotypically normal females is:
In the above example:
In X-linked dominant conditions, q equals the disease frequency in males, because 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 a chromosome, so they tend to be inherited together because 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. A 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, “p×q”), then:
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