A population of fruit flies is in Hardy-Weinberg equilibrium. The recessive allele for cross-veinless wings (v) has a frequency of 0.81, and the dominant V allele for normal wings has an allele frequency of 0.19. What is the percentage of homozygous recessive (cross-veinless-winged) flies in the population? (Nearest %).
Question
A population of fruit flies is in Hardy-Weinberg equilibrium. The recessive allele for cross-veinless wings (v) has a frequency of 0.81, and the dominant V allele for normal wings has an allele frequency of 0.19. What is the percentage of homozygous recessive (cross-veinless-winged) flies in the population? (Nearest %).
Solution
To determine the percentage of homozygous recessive (cross-veinless-winged) flies in the population, we can use the Hardy-Weinberg equilibrium principle. The Hardy-Weinberg equation is given by:
where:
- is the frequency of the dominant allele (V),
- is the frequency of the recessive allele (v),
- represents the frequency of homozygous dominant individuals (VV),
- represents the frequency of heterozygous individuals (Vv),
- represents the frequency of homozygous recessive individuals (vv).
Given:
We need to find , the frequency of homozygous recessive individuals.
Now, calculate :
To express this as a percentage, multiply by 100:
Rounding to the nearest percent:
Therefore, the percentage of homozygous recessive (cross-veinless-winged) flies in the population is approximately 66%.
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