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Population genetics - Essay Example

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If the frequency of an allele A is pin both sperm ad eggs and the frequency of allele a is q =1-p, then the consequences of random unions. The probability that both sperm and egg will carry A is p2, and this will be be the number of AA homozygotes in the next generation…
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Population genetics
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The Hardy-Weinberg Equilibrium If the frequency of an allele A is pin both sperm ad eggs and the frequency of allele a is q p, then the consequences of random unions. The probability that both sperm and egg will carry A is p2, and this will be be the number of AA homozygotes in the next generation. Heterozygotes will be (pxq) + (qxp) = 2pq and the chance of homozygotes aa will be q2. The three genotypes will be in the frequencies p2:2pq:q2. The allelic frequency of p will not change and is still p and this equilibrium will go on forever.
The equilibrium distribution

AA Aa aa
P2 2pq q2
is called the Hardy-Weinberg equilibrium after those who independently discovered it.
The Hardy-Weinberg equilibrium means that sexual reproduction does not cause a constant reduction in genetic variation in each generation; on the contrary, the amount of variation remains constant: generation after generation in the absence of a disturbing factor. The equilibrium is the direct consequence of the segregation of alleles at meiosis in heterozygotes.
Numerically, the equilibrium shows that irrespective of the particular mixture of genotypes in the parental generation, the genotypic distribution after one round of mating is completely specified by the allelic frequency p.
Consider the following example of three populations with a p=0.3
aa AA Aa
I 0.3 0.0 0.7
II 0.2 0.2 0.6
III 0.1 0.4 0.5
After one generation of random mating, each of the three populations will have the same the same genotypic frequencies:
AA Aa aa
(0.3)2=0.09 2(.03)(0.7)=0.42 (0.7)2=0.49
and they will remain so indefinitely.
One consequence of the Hardy-Weinberg proportions is that rare alleles are virtually never in homozygous condition. An allele with a frequency of 0.001 occurs in homomygotes at a frequency of only one in a million; most copies of rare alleles are found in heterozygotes. In general, since two copies of an allele are in homozygotes but only one copy of that allele is in each heterozygote, the relative frequency of the allele in the heterozygotes(as opposed to homozygotes) is:
2pq = p
2q2 q
Which for q=0.001 is a ratio 999:1. Thus, the frequency of heterozygote carriers of rare genes that are deleterious in a homozygous condition is much greater than the frequency of the affected homomygotes.
In our derivation of the equilibrium, we assumed the allelic frequency p is the same in sperm and eggs. If p for males is not equal to the p for females in the initial generation, then it takes one generation to equalize the frequencies between the sexes and a second-generation to reach Hardy-Weinberg equilibrium. As an extension of this effect, the Hardy-Weinberg equilibrium theorem does not apply to sex-linked genes even after two generations if male and females start with unequal gene frequencies.
Random matings with respect to particular genes is quite common as an example the MN blood groups in various population have observed values nearly equivalent to Hardy-Weinberg predicted results:
Observed Expected
Population MM Mn NN MM Mn NN
Eskimo 0.835 0.156 0.009 0.834 0.159 0.008
Egyptian 0.278 0.489 0.233 0.274 0.499 0.228
Chinese 0.331 0.486 0.182 0.331 0.488 0.181
Aborigine 0.024 0.304 0.672 0.031 0.290 0.679
In conclusion the Hardy-Weinberg equilibrium theorem is a useful genetic tool in predicting allele frequencies and the above example shows its function when predicting blood groups in populations worldwide.
SOURCE-An Intrductoin to Genetic Analysis David T Suzuki W.H Freeman Co Read More
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