Final answer:
Using the Hardy-Weinberg principle, we calculated that in a population of 1,000 Drosophila, with 160 showing the recessive phenotype for vestigial wings, the frequency of the recessive allele 'a' (q) is 0.4, and the dominant allele 'A' (p) is 0.6. The corresponding genotype frequencies are: AA (36%), Aa (48%), and aa (16%).
Step-by-step explanation:
When dealing with a population that is in Hardy-Weinberg equilibrium, it is essential to remember that allele and genotype frequencies are stable and can be predictable. In the case of Drosophila, given that 160 out of 1000 individuals show the recessive phenotype for vestigial wings, we can presume that these are homozygous recessive individuals (aa). Therefore, the frequency of the recessive allele 'a', represented as q, can be found by taking the square root of the recessive phenotype frequency, which is 160/1000 or 0.16. Taking the square root gives us q = 0.4. Following the Hardy-Weinberg equation, p + q = 1, we can then determine the frequency of the dominant allele 'A', represented as p, which would be 1 - q, thus p = 0.6.
With these frequencies, it is then possible to calculate the genotype frequencies for the population. The frequency of homozygous dominant genotype (AA) is p², the frequency of heterozygous genotype (Aa) is 2pq, and the frequency of homozygous recessive genotype (aa) is q². With p = 0.6 and q = 0.4, we have the following frequencies: AA = (0.6)², Aa = 2(0.6)(0.4), and aa = (0.4)².
The Hardy-Weinberg principle is a fundamental concept in biology that provides a mathematical baseline to compare actual populations to an ideal non-evolving population. This allows scientists to understand and predict how evolutionary forces could be acting upon different alleles and genotypes within a population.