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Concept explainers
(a)
To determine:
The frequency of the gray allele f.
Introduction:
Evolution occurs due to change in allele frequencies. The frequency of an allele is calculated as: the number of copies of an alleletotal number of alleles in the population
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Explanation of Solution
It has been mentioned that there are 100 Fraggles in the population out of which 84 have green fur and 16 have gray fur. A dominant allele F confers green fur, and a recessive allele f confers gray fur. The allelic frequency of the gray allele f can be calculated as:
Allele frequencies:p+q=1,
where, p=frequency of dominant allele, q=frequency of recessive allele
Genotype frequency=p2+2pq+q2=1,
where, p2=frequency of dominant genotype (FF)
2pq=frequency of heterozygous genotype (Ff)
q2=frequency of recessive genotype (ff)
Genotype frequency=the number of individuals with the dominant/recessive genotypetotal size of the populationGreen fur=84100=0.84Gray fur=16100=0.16As Genotype frequency=2p+2pq+q2=1p2+2pq=0.84, q2=0.16therefore, q=0.4Grey allele (f)=0.4
Thus, frequency of the gray allele f is 0.4.
(b)
To determine:
The frequency of the green allele F.
Introduction:
According to Hardy-Weinberg equilibrium, the allele frequencies and genotype frequencies do not change from one generation to the next.
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Explanation of Solution
Genotype frequency=the number of individuals with the dominant/recessive genotypetotal size of the population
Fraggles with Green fur=84100=0.84Fraggles with Gray fur=16100=0.16As Genotype frequency=2p+2pq+q2=1p2=frequency of dominant genotype (FF)2pq=frequency of heterozygous genotype (Ff)q2=frequency of recessive genotype (ff)p2+2pq=0.84, q2=0.16therefore, q=0.4Grey allele (f)=0.4Allele frequencies:p+q=1p=frequency of dominant alleleq=frequency of recessive allelep+q=1p=1-0.4=0.6Thus, frequency of the green allele (F)=0.6
(c)
To determine:
The number of Fraggles that are heterozygotes (Ff).
Introduction:
Individuals that contain different alleles of a gene are called heterozygous. Individuals that carry two identical alleles of a gene are called homozygous. In case of homozygous individual, the identical alleles may be either dominant or recessive.
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Explanation of Solution
There are 100 Fraggles in a population out of which 84 have green fur and 16 have gray fur.
Fraggles with Green fur=84100=0.84Fraggles with Gray fur=16100=0.16
Genotype frequency=2p+2pq+q2=1p2=frequency of dominant genotype (FF)2pq=frequency of heterozygous genotype (Ff)q2=frequency of recessive genotype (ff)p2+2pq=0.84, q2=0.16
therefore, q=0.4Grey allele (f)=0.4
Allele frequencies:p+q=1p=frequency of dominant alleleq=frequency of recessive allelep+q=1p=1-0.4=0.6Thus, frequency of the green allele (F)=0.6As, p2+2pq+q2=1p2=0.36q2=0.162pq=2(0.6)(0.4)=0.48Thus, the number of heterozygotes (Ff)=0.48
(d)
To determine:
The number of Fraggles that are homozygous recessive (ff).
Introduction:
The study of population genetics is based on the relationship between allele frequencies and genotype frequencies. Some or all the assumptions of Hardy-Weinberg equilibrium are violated in a real population.
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Explanation of Solution
Genotype frequency=2p+2pq+q2=1p2=frequency of dominant genotype (FF)2pq=frequency of heterozygous genotype (Ff)q2=frequency of recessive genotype (ff)
As it was calculated that p=0.6, q=0.4, 2pq=0.48p2+2pq+q2=1q2=0.16Thus, the number of homozygous recessive fraggles (ff)=0.16
(e)
To determine:
The number of Fraggles that are homozygous dominant (FF).
Introduction:
Hardy-Weinberg equilibrium allows inferring characteristics of a population based on limited information. The genotype frequencies in a population can be estimated using allele frequencies.
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Explanation of Solution
Genotype frequency=2p+2pq+q2=1p2=frequency of dominant genotype (FF)2pq=frequency of heterozygous genotype (Ff)q2=frequency of recessive genotype (ff)
As it was calculated that p=0.6, q=0.4, 2pq=0.48p2+2pq+q2=1p2=0.36Thus, the number of homozygous dominant fraggles (FF)=0.36
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Chapter 12 Solutions
BIOLOGY:THE ESSENTIALS (LL) W/CONNECT
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