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Population Genetics- Hardy Weinberg Law - Hardy- Weinberg Equation - Hardy- Weinberg Problems

Application of ' Hardy - Weinberg Law' in Calculating Gene frequencies in a population

Hardy Weinberg law
Hardy-Weinberg Equilibrium
Hardy and Weinberg developed this calculation to show that equilibrium in genotype frequencies will occur after one generation of random mating, and those genotype frequencies can be calculated from allele frequencies. The equilibrium frequencies will be maintained from generation to generation unless some force changes the allele frequencies. The introduction of simple algebra started the science of population genetics, and allows us to quantify the evolutionary effects of different levels of selection on homozygotes and heterozygotes, or on dominant or recessive alleles.

The Hardy-Weinberg formula shows that, in the absence of selection, the proportion of two alleles (p and q) of a gene will remain constant in a population, regardless of whether they are dominant or recessive.
Hardy- Weinberg Equation : (p+q)2=  p2+2pq+ q2=1 ; p+q=1
 Where ‘p’ and ‘q’ represents allele frequency; p2, 2pq, and q2 are genotype frequency
 A number of factors can "break" the equilibrium and cause one allele to become more plentiful than the other. These things include :

(1) Selective advantage or disadvantage
(2) Genetic drift
(3) Non-random mating 
(4) Influx of new alleles

Problem:  1
A population of 208 people of MN blood group was sampled and it was found that 119 were MM group, 76 of MN group and 13 of NN group. Determine the gene frequencies of M and N in the population. 
a) Check whether the above population agrees the Hardy- Weinberg law of equilibrium?
Frequency of M = (119 X 2) + 76
Frequency of M =238 +76
Frequency of M = 314
Frequency of N = (13 X 2) + 76
Frequency of N = 26+76
Frequency of N = 102
Gene frequency of M allele = M / (M+N)
M = 314 / (314 +102)
M = 314 / 416
Gene frequency of M allele = 0.75
Gene frequency of N allele = N / (M+N)
N= 102 / (314 + 102)
N= 102 / 416
N = 0.245
Gene frequency of N allele =0.25
(b) Check whether the above population agrees the Hardy- Weinberg law of equilibrium?
M= 0.75, N = 0.25
M+N =1 or (p +q =1) 
here 0.75 +0.25 = 1.
so it agrees with the Hardy- Weinberg law of equilibrium.
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