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Question
In a non-evolving population, there are two alleles for a particular gene, R and r. The frequency of R allele is 30 percent. What are the frequencies of all the possible genotypes?
In a non-evolving population, there are two alleles for a particular gene, R and r. The frequency of R allele is 30 percent. What are the frequencies of all the possible genotypes?
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Solution
The correct option is D 9% RR, 42% Rr, 49% rr
A population that exists in Hardy-Weinberg equilibrium is said to be a non- evolving population.
Hardy-Weinberg principle given by Hardy and Weinberg states that the frequencies of alleles tend to remain constant from one generation to the next in sexually reproducing populations under certain conditions.
The Hardy-Weinberg equation is an algebraic equation which is an expression of the Hardy-Weinberg principle. The frequencies of alleles and the genotypic ratios can be calculated with the help of this equation.
According to the Hardy-Weinberg equation, if there are two alleles for a particular gene where A represents the dominant allele and a represents the recessive allele, then the frequency of A is p and a is q.
Combined frequencies of all alleles for a gene in a population is equal 1.
Therefore, p+q=1.
The frequency of homozygous dominant individuals (AA) in the population would be equal to pxp or p2
The frequency of homozygous recessive individuals (aa) in the population would be equal to qxq or q2
Since there are two ways of forming the heterozygote Aa, (allele A from the father and a from mother and vice versa) the frequency of heterozygous dominant individuals (Aa) in the population would be 2pq.
The sum of all three genotypic frequencies is p2+2pq+q2=1 which is a binomial expansion of (p+q)2
Therefore, p = frequency of the dominant allele (A)
q = frequency of the recessive allele (a)
p2 = frequency of the homozygous dominant individuals (AA)
q2 = frequency of the homozygous recessive individuals (aa)
2pq = frequency of the heterozygous dominant individuals (Aa)
Considering the question given, three genotypes are possible for a gene with two alleles. Hence, the possible genotypes for a gene with two alleles, R and r is RR, Rr and rr.
Given that the dominant allele (R) has frequency of 30%, and hence p = 0.3, since this is a Hardy-Weinberg population, we can assume that p + q = 1
Therefore, the frequency of the recessive allele, q = 1-p = 1-0.3 = 0.7
If p and q are known, then the frequencies of the three genotypes may be calculated using the Hardy-Weinberg equation,
p2+2pq+q2=1
p2=(0.3)2=0.09=9%RR
2pq=2(0.3)(0.7)=0.42=42%Rr
q2=(0.7)2=0.49=49%rr
A population that exists in Hardy-Weinberg equilibrium is said to be a non- evolving population.
Hardy-Weinberg principle given by Hardy and Weinberg states that the frequencies of alleles tend to remain constant from one generation to the next in sexually reproducing populations under certain conditions.
The Hardy-Weinberg equation is an algebraic equation which is an expression of the Hardy-Weinberg principle. The frequencies of alleles and the genotypic ratios can be calculated with the help of this equation.
According to the Hardy-Weinberg equation, if there are two alleles for a particular gene where A represents the dominant allele and a represents the recessive allele, then the frequency of A is p and a is q.
Combined frequencies of all alleles for a gene in a population is equal 1.
Therefore, p+q=1.
The frequency of homozygous dominant individuals (AA) in the population would be equal to pxp or p2
The frequency of homozygous recessive individuals (aa) in the population would be equal to qxq or q2
Since there are two ways of forming the heterozygote Aa, (allele A from the father and a from mother and vice versa) the frequency of heterozygous dominant individuals (Aa) in the population would be 2pq.
The sum of all three genotypic frequencies is p2+2pq+q2=1 which is a binomial expansion of (p+q)2
Therefore, p = frequency of the dominant allele (A)
q = frequency of the recessive allele (a)
p2 = frequency of the homozygous dominant individuals (AA)
q2 = frequency of the homozygous recessive individuals (aa)
2pq = frequency of the heterozygous dominant individuals (Aa)
Considering the question given, three genotypes are possible for a gene with two alleles. Hence, the possible genotypes for a gene with two alleles, R and r is RR, Rr and rr.
Given that the dominant allele (R) has frequency of 30%, and hence p = 0.3, since this is a Hardy-Weinberg population, we can assume that p + q = 1
Therefore, the frequency of the recessive allele, q = 1-p = 1-0.3 = 0.7
If p and q are known, then the frequencies of the three genotypes may be calculated using the Hardy-Weinberg equation,
p2+2pq+q2=1
p2=(0.3)2=0.09=9%RR
2pq=2(0.3)(0.7)=0.42=42%Rr
q2=(0.7)2=0.49=49%rr
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