Final answer:
To find the expected numbers of AA, Aa, and aa genotypes, assuming random mating, the Hardy-Weinberg principle and given allele frequencies are used to calculate expected genotype frequencies: p² for AA, 2pq for Aa, and q² for aa. Then, multiply these frequencies by the total population number.
Step-by-step explanation:
The question asks us to calculate the expected numbers of genotypes AA, Aa, and aa, assuming random mating in the given populations, with the population being polymorphic for alleles A and a. To achieve this, we use the Hardy-Weinberg principle, which states that the genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences, provided that the conditions of random mating, large population size, no mutations, no migration, and no natural selection are met.
Using the provided allele frequencies (p for A and q for a where p + q = 1), we can calculate the expected genotype frequencies with the formulas p² for AA, 2pq for Aa, and q² for aa. Given p = 0.7 and q = 0.3 (notice that p + q = 1), the expected genotype frequencies would be:
- AA: p² = (0.7)² = 0.49
- Aa: 2pq = 2(0.7)(0.3) = 0.42
- aa: q² = (0.3)² = 0.09
To determine the actual expected numbers, we multiply these frequencies by the total number of individuals in the population, which is 140:
- AA: 0.49 × 140 = 68.6, which we round to 69
- Aa: 0.42 × 140 = 58.8, which we round to 59
- aa: 0.09 × 140 = 12.6, which we round to 13