1. 525 jackrabbits in the desert. Big ears (B) are dominant among jackrabbits, while stubby ears (b) are recessive. Of the study of this population, 189 rabbits have stubby ears.
Calculate:
1.The frequency of the "bb" genotype
2.The frequency of the "b" allele
3.The frequency of the "B" allele
4.The frequencies of the genotypes "BB" and "Bb"
5.The frequencies of the two possible phenotypes in your study population.
B+b=1,
(B+b)^2=BB+2Bb+bb=1
genotype BB=Big ears
genotype Bb=Big ears
genotype bb=Stubby ears
Since each rabbit has two alleles for ear type, 525*2=1,050 total alleles
Since 189 rabbits have the genotype bb, 189/525= 0.36, the phenotype frequency for stubby ears. This means that 1-0.36=0.64, the phenotype frequency for big ears.
plugging in the value for bb that we obtained into BB+2Bb+bb=1, we get
BB+2Bb+0.36=1 rearrangement gives,
BB+2Bb=0.64
Since the genotype frequency is 2;1 for Bb:BB, I will let BB=x, and Bb=2x, and solve for x.
x+2x=0.64
3x=0.64
x=0.64/3
x=0.213, meaning 21.3% of the remaining population of jackrabbits have the genotype BB (112 jackrabbits), and the other 42.6% have the genotype Bb (224 jackrabbits). Converting to decimals gives you the genotype frequencies:
Genotype BB frequencies= 0.213
Genotype Bb frequencies= 0.426
To determine the frequency of B alleles, multiply [(112*2)+(224*(1/2))]/total number of alleles(1,050)=0.32
Since B+b=1, solving for b
b=1-0.32=0.68
Remember, the 0.36 that wal calculated for the phenotype frequency of bb is the same as the genotype frequency.
To calculate the frequencies of genotypes and alleles, we need to use the Hardy-Weinberg equation. The equation states that in a population, the frequencies of alleles and genotypes will remain constant from generation to generation if certain assumptions are met. These assumptions include random mating, no mutation, no migration, no selection, and a large population size.
Let's break down the calculations step by step:
1. The frequency of the "bb" genotype can be calculated by dividing the number of individuals with the "bb" genotype by the total population size.
Frequency of "bb" genotype = Number of individuals with "bb" genotype / Total population size
In this case, the number of rabbits with the "bb" genotype is 189.
Frequency of "bb" genotype = 189 / 525 = 0.36 or 36%
2. The frequency of the "b" allele can be calculated by considering that in a population, the frequency of alleles adds up to 1 (100%).
Frequency of "b" allele = 1 - Frequency of "B" allele
Since the "bb" genotype represents the "b" allele, we can use the frequency of the "bb" genotype to calculate the frequency of the "b" allele.
Frequency of "b" allele = Frequency of "bb" genotype = 0.36 or 36%
3. The frequency of the "B" allele can be calculated by subtracting the frequency of the "b" allele from 1.
Frequency of "B" allele = 1 - Frequency of "b" allele
Frequency of "B" allele = 1 - 0.36 = 0.64 or 64%
4. The frequencies of the genotypes "BB" and "Bb" can be calculated using the frequencies of the "B" and "b" alleles.
Frequency of "BB" genotype = (Frequency of "B" allele)^2
Frequency of "Bb" genotype = 2 * (Frequency of "B" allele) * (Frequency of "b" allele)
Frequency of "BB" genotype = (0.64)^2 = 0.4096 or 40.96%
Frequency of "Bb" genotype = 2 * 0.64 * 0.36 = 0.4608 or 46.08%
5. The frequencies of the two possible phenotypes can be calculated by considering the genotypes and their corresponding phenotypes.
The "BB" genotype represents the dominant phenotype (big ears), and the "Bb" and "bb" genotypes represent the recessive phenotype (stubby ears).
Frequency of individuals with the dominant phenotype = Frequency of "BB" genotype
Frequency of individuals with the recessive phenotype = Frequency of "Bb" genotype + Frequency of "bb" genotype
Frequency of individuals with the dominant phenotype = 40.96%
Frequency of individuals with the recessive phenotype = 46.08% + 36% = 82.08%
Therefore, the frequencies of the two possible phenotypes in this study population are approximately 40.96% for the dominant phenotype (big ears) and 82.08% for the recessive phenotype (stubby ears).