2. Genotypes of leopard frogs from a population in central Kansas were determined for a locus (M) that encodes the enzyme malate dehydrogenase. The following numbers of genotypes were observed: Total sample studied = 107.
Genotype Number
M1M1 20
M1M2 45
M2M2 42
a.) Calculate the allelic frequencies for this population. (2 pts)
b.) What are the actual genotypic frequencies in the above populations? (1.5 pts)
c.) What would the expected numbers for each genotype if the population were in Hardy-Weinberg equilibrium? (1.5 pts)
To calculate the allelic frequencies for this population, we need to know the total number of alleles. Since each individual has 2 alleles, we can multiply the number of individuals by 2 to get the total number of alleles.
a) Calculation for allelic frequencies:
Total number of alleles = Total sample studied x 2
= 107 x 2
= 214
Now, let's calculate the frequency for each allele.
Frequency of M1 allele = Number of M1M1 genotypes x 2 + Number of M1M2 genotypes
= 20 x 2 + 45
= 40 + 45
= 85
Allelic frequency for M1 allele = Frequency of M1 allele / Total number of alleles
= 85 / 214
≈ 0.3972 (rounded to four decimal places)
Frequency of M2 allele = Number of M2M2 genotypes x 2 + Number of M1M2 genotypes
= 42 x 2 + 45
= 84 + 45
= 129
Allelic frequency for M2 allele = Frequency of M2 allele / Total number of alleles
= 129 / 214
≈ 0.6028 (rounded to four decimal places)
Therefore, the allelic frequencies for this population are approximately:
M1 allele frequency ≈ 0.3972
M2 allele frequency ≈ 0.6028
b) To calculate the genotypic frequencies, we can divide the number of each genotype by the total number of individuals in the population.
Genotypic frequency for M1M1 genotype = Number of M1M1 genotypes / Total sample studied
= 20 / 107
≈ 0.1869 (rounded to four decimal places)
Genotypic frequency for M1M2 genotype = Number of M1M2 genotypes / Total sample studied
= 45 / 107
≈ 0.4206 (rounded to four decimal places)
Genotypic frequency for M2M2 genotype = Number of M2M2 genotypes / Total sample studied
= 42 / 107
≈ 0.3925 (rounded to four decimal places)
Therefore, the genotypic frequencies in the population are approximately:
M1M1 genotype frequency ≈ 0.1869
M1M2 genotype frequency ≈ 0.4206
M2M2 genotype frequency ≈ 0.3925
c) In Hardy-Weinberg equilibrium, the expected frequencies for each genotype can be calculated using the allelic frequencies.
Expected frequency for M1M1 genotype = (M1 allele frequency)^2
≈ (0.3972)^2
≈ 0.1578 (rounded to four decimal places)
Expected frequency for M1M2 genotype = 2 x (M1 allele frequency) x (M2 allele frequency)
≈ 2 x 0.3972 x 0.6028
≈ 0.4788 (rounded to four decimal places)
Expected frequency for M2M2 genotype = (M2 allele frequency)^2
≈ (0.6028)^2
≈ 0.3634 (rounded to four decimal places)
Therefore, the expected numbers for each genotype if the population were in Hardy-Weinberg equilibrium are approximately:
Expected number for M1M1 genotype ≈ 0.1578
Expected number for M1M2 genotype ≈ 0.4788
Expected number for M2M2 genotype ≈ 0.3634