Final answer:
Calculating the percentage of homozygous dominant individuals in a population at Hardy-Weinberg equilibrium involves using the Hardy-Weinberg principle equations. After computing the frequency of the recessive allele q, one finds the frequency of the dominant allele p. Finally, by applying p² to ascertain the homozygous dominant genotype frequency and multiplying by the population size, the number of homozygous dominant individuals is determined.
Step-by-step explanation:
The student has asked how to calculate the percentage of homozygous dominant individuals in a population of 14,500 when 38% of the individuals are recessive homozygotes for a certain trait in a population that is in Hardy-Weinberg equilibrium. To solve this, we can use the Hardy-Weinberg principle, which states that the frequencies of alleles and genotypes in a population will remain constant from generation to generation in the absence of other evolutionary influences.
Firstly, we identify that the frequency of homozygous recessive individuals (aa) is given as 38% (0.38). Since this represents q² in the equation p² + 2pq + q² = 1, where p is the frequency of the dominant allele and q is the frequency of the recessive allele, we can calculate q by taking the square root of q², thus q = √0.38.
After finding the value of q, we can calculate the value of p using the equation p + q = 1. Consequently, we also find p², which represents the frequency of the homozygous dominant genotype (AA). Multiplying the frequency of AA by the total population size gives us the number of homozygous dominant individuals.
Step-by-step calculation:
- Calculate q: q = √0.38
- Calculate p: p = 1 - q
- Calculate p²
- Calculate the number of AA individuals: (p²) * (total population size)
To find the percentage of homozygous dominant individuals, we divide the number of AA individuals by the total population size and multiply by 100.