Among a particular population of 100 plants, red flowers are dominant and yellow flowers are recessive. F is the dominant allele and f is the recessive allele. 40 plants are homozygous dominant 44 plants are heterozygous 16 plants are homozygous recessive Use the Hardy-Weinberg equation to calculate the equilibrium frequencies of each genotype.
First, calculate the total number of alleles in the population (200 alleles total for 100 plants):
- Homozygous dominant individuals: 40 plants x 2 alleles each = 80 F alleles
- Heterozygous individuals: 44 plants x 2 alleles each = 88 F alleles
- Homozygous recessive individuals: 16 plants x 2 alleles each = 32 f alleles
Total alleles: 80 + 88 + 32 = 200 alleles
Next, calculate the frequency of each allele:
- Frequency of F allele (p): (80 + 0.5(88))/200 = 0.66
- Frequency of f allele (q): (32 + 0.5(88))/200 = 0.34
Now, calculate the equilibrium frequencies of each genotype using the Hardy-Weinberg equation:
- Frequency of FF genotype: p^2 = (0.66)^2 = 0.4356
- Frequency of Ff genotype: 2pq = 2(0.66)(0.34) = 0.4488
- Frequency of ff genotype: q^2 = (0.34)^2 = 0.1156
Therefore, the equilibrium frequencies of each genotype in the population are:
- FF genotype: 43.56%
- Ff genotype: 44.88%
- ff genotype: 11.56%