4. The beak color of finches has a complete dominance relationship where black b

Question

4. The beak color of finches has a complete dominance relationship where black beaks are dominant over yellow beaks. There are 210 individuals with the genotype DD, 245 individuals with the genotype Dd and a. Find: the frequency of the dominant and recessive alleles and the frequency of individuals with b. The next generation of finches has a population of 400. There are 336 with black beaks and 64 45 individuals with the genotype dd. dominant, heterozygous, and recessive traits. with yellow beaks. Is this population in Hardy-Weinberg equilibrium?

Explanation / Answer

let's consider p is the frequency of dominant allele "D" which gives a phenotype of Black beak and q is the frequency of the recessive allele "d" which gives a phenotype of the yellow beak.

a) Here total number of finches = 210+245+45 = 500

now for allelic frequency, we should always utilize the number of homozygous recessive individual, As its phenotype always occur when both the allele of that particular trait is recessive.

So in case of recessive homozygous (dd), we can write q2 = 45/500 = 0.09 , Therefore q= sqrt(0.09) = 0.3

now for Hardy-Weinberg law, we know that p+q=1

so p=1-q = 1-0.3 = 0.7

Hence, frequency of Dominant allele "D" = p = 0.7

and      frequency of recessive allele "d" = q = 0.3

now genotypic frequency can be calculated by dividing number of individual genotype with total population

in this problem, the frequency of DD genotype = 210/500 = 0.42

                       the frequency of Dd genotype = 245/500 = 0.49

and                   frequency of dd genotype = 45/500 = 0.09

B) Here, in next generation, the total number of finches is 400

now, they have not said the genotype of the finches but the phenotype is given. Black beak phenotype will appear when the dominant allele is expressing only and it is possible in either of two cases of "DD" or "Dd"

now, the genotypic frequency of DD is given by =p2 and frequency of Dd is given by =2pq

therefore, the overall dominant phenotype is given by = p2 +2pq

and here total number of black beak finches is =336

so their phenotypic frequency = p2 +2pq = 336/400 = 0.84

whereas, yellow beak finches are the result of the presence of recessive allele only

So, their phenotypic frequency = q2 = 64/400 = 0.16

now if the population is in Hardy-Weinberg equilibrium then

p2 +2pq+q2 =1

In this population, the sum of p2 +2pq and q2 is equal to 1. So, we can say that this population is in Hardy-Weinberg equilibrium.

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