Coloration in the peppered moth (Biston betularia) is determined by a single gene with two alleles showing complete dominance. Dark moths are homozygous dominant or heterozygous for the gene, light moths are homozygous recessive. In a sample of 100 moths, you determine that 64 of the moths are dark. According to the Hardy-Weinberg rule, the expected frequency of the dominant allele is ___.

Question

A.  0.4
B.  0.36
C.  0.6
D.  0.64
E.  cannot be determined

Clarify Question
· What is the key concept addressed by the question?
· What type of thinking is required?
· What key words does the question contain and what do they mean?
 
Gather Content
· What do you already know about the Hardy-Weinberg principle? How does it relate to the question?
 
Consider Possibilities
· What other information is related to the question? Which information is most useful?
 
Choose Answer
· Given what you now know, what information and/or problem solving approach is most likely to produce the correct answer?
 
Reflect on Process
· Did your problem-solving process lead you to the correct answer? If not, where did the process break down or lead you astray? How can you revise your approach to produce a more desirable result?

Answer 1

A.  0.4

Clarify Question
· What is the key concept addressed by the question?
        o This question is asking you to calculate various frequencies for a population in Hardy-Weinberg equilibrium. What are the formulas involved in calculating the frequencies for a population in Hardy-Weinberg equilibrium?
· What type of thinking is required?
        o This is an analyze question because you have to calculate various frequencies for a population in Hardy-Weinberg equilibrium.
· What key words does the question contain and what do they mean?
        o Dominant phenotype, which refers to the physical trait of a version of a gene inherited from a single parent.
        o Recessive allele, which refers to the physical trait of a version of a gene inherited from both parents.
        o Hardy-Weinberg equilibrium, which refers to populations whose genotype frequencies do not change from generation to generation.
        o Allele, which refers to a version of a gene.
        o Homozygous, which means that both alleles for a gene are the same.
        o Heterozygous, which means that the alleles for a gene are different.
 
Gather Content
· What do you already know about the Hardy-Weinberg principle? How does it relate to the question?
        o To solve this problem you will need to apply the Hardy-Weinberg equations. Recall that there are two equations involved in the Hardy-Weinberg principle. One equation is p + q = 1; where p is the frequency of the dominant allele, q is the frequency of the recessive allele, and 1 is 100% of the alleles. The other equation is p2 + 2pq + q2 = 1; where p2 is the frequency of the homozygous dominant genotype, 2pq is the frequency of the heterozygous genotype, q2 is the frequency of the homozygous recessive genotype, and 1 is 100% of the individuals. How are these two equations related? How can we go from a phenotype frequency to an allele frequency? Which phenotype frequency is the same as one of the genotype frequencies?
 
Consider Possibilities
· What other information is related to the question? Which information is most useful?
        o The question provides you with the frequency of the dominant phenotype. The recessive phenotype is equivalent to the homozygous recessive genotype. If you can calculate the frequency of the homozygous recessive genotype, then which allele frequency can you determine?
 
Choose Answer
· Given what you now know, what information and/or problem solving approach is most likely to produce the correct answer?
        o To answer this question you must determine which phenotype frequency matches a genotype frequency. Keep in mind that you may have a dominant phenotype with either a homozygous dominant or heterozygous genotype. What genotype do you have if you express the recessive phenotype?
        o How do you get from a value that is squared, like p2, to a value that is not squared but has the same variable, like p? What is the mathematical function involved in this process?
 
Reflect on Process
· Did your problem-solving process lead you to the correct answer? If not, where did the process break down or lead you astray? How can you revise your approach to produce a more desirable result?
        o This question asked you to determine the frequency of the dominant allele in peppered moths.
        o Answering this question correctly depended not only on distinguishing between genotypic and phenotypic frequencies, but on your ability to break down, or analyze, various frequencies.
        o If you got the correct answer, excellent! If you got an incorrect answer, where did the process break down? Did you remember how to calculate the square root of a decimal? Do you understand that the recessive phenotype must have a homozygous recessive genotype? Therefore, the frequency of the recessive phenotype must equal the frequency of which genotype? Did you have trouble breaking down the Hardy-Weinberg equations to determine the correct answer?