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Phenotype frequencies in a specific generation can be calculated using the Hardy-Weinberg Equilibriums. Using known allele frequencies, genotype frequencies can be approximated with the equation p² for homozygous dominant, 2pq for heterozygous, and q² for homozygous recessive. These genotype frequencies can then be used to calculate phenotype frequencies.
To calculate phenotype frequencies in the 5th generation we must refer back to Mendelian genetics and specially Hardy-Weinberg Equilibrium. Using known allele frequencies (p and q), we can estimate genotype frequencies using the following formula: p² for homozygous dominant (YY), 2pq for heterozygous (Yy), and q² for homozygous recessive (yy), this is for sexual reproduction and assumes certain conditions such as random mating, large population size, no mutation, no migration etc.
For phenotype, we must know which alleles are dominant, in this case let's say "Y" is dominant. Therefore, both individuals with genotype YY (p²) and Yy (2pq) will exhibit the same phenotypic characteristic in this case as both will have yellow peas. Thus, the frequency of yellow pea phenotype is (p² + 2pq) and the frequency of the green pea phenotype characteristics (qq) is q². These, by rule, must sum up to 1 (p² + 2pq + q² = 1).
You also have to consider that each generation is a repeat of these ratios. So the 5th generation will have the same genotype and phenotype frequencies as the 1st, 2nd, 3rd, and 4th generations provided the Hardy-Weinberg conditions are met.
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Answer:
The number of moths in 5th generation (G5) with:
Typica phenotype (white) = 878
Carbonaria phenotype (black) = 54
total moths observed = 932
5th generation Phenotype frequency:
f (Typica) = Number of Typica phenotype in G5/ total moths in 5th gen
f (Typica) = 878/ 932
= 0.94
f (Carbonaria) = Number Carbonaria phenotype in G5/ total moths in 5th gen
f (black) = 54/ 932
= 0.057
