Harris 1966 Measured The Number Of Genotypes At The Alkaline
Harris 1966 Measured The Number Of Genotypes At The Alkaline Phospha
Harris (1966) measured the number of genotypes at the alkaline phosphatase locus in the English population. These are three alleles, designated F, I, and S (for fast, intermediate, and slow mobility in an electrophoretic apparatus). The genotypes observed are SS, SF, FF, SI, FI, II.
The assignment involves calculating observed genotype frequencies, allele frequencies, Hardy-Weinberg equilibrium (HWE) genotype and allele frequencies, observed and equilibrium heterozygosity, and analyzing deviations from HWE conditions.
Paper For Above instruction
The study conducted by Harris (1966) provides critical insights into the genetic structure of the English population concerning the alkaline phosphatase locus. This locus involves three alleles—F, I, and S—that influence enzyme mobility. Understanding the distribution of genotypes and allele frequencies, as well as the assessment of Hardy-Weinberg equilibrium (HWE), offers vital information about the population's genetic dynamics.
Observed Genotype Frequencies
The first step involves calculating the observed frequencies of the six genotypes: SS, SF, FF, SI, FI, and II. Harris's data reports the number of individuals exhibiting each genotype, which we denote as:
- \( n_{SS} \)
- \( n_{SF} \)
- \( n_{FF} \)
- \( n_{SI} \)
- \( n_{FI} \)
- \( n_{II} \)
Suppose Harris's study reports the following counts:
| Genotype | Count |
|------------|--------|
| SS | 30 |
| SF | 50 |
| FF | 20 |
| SI | 40 |
| FI | 55 |
| II | 25 |
Total number of individuals (\( N \)):
\[ N = 30 + 50 + 20 + 40 + 55 + 25 = 220 \]
The observed frequency (\( f_{genotype} \)) of each genotype is:
\[ f_{genotype} = \frac{\text{number of individuals with that genotype}}{N} \]
Thus:
- \( f_{SS} = \frac{30}{220} \approx 0.136 \)
- \( f_{SF} = \frac{50}{220} \approx 0.227 \)
- \( f_{FF} = \frac{20}{220} \approx 0.091 \)
- \( f_{SI} = \frac{40}{220} \approx 0.182 \)
- \( f_{FI} = \frac{55}{220} \approx 0.250 \)
- \( f_{II} = \frac{25}{220} \approx 0.114 \)
Observed Allele Frequencies
Allele frequencies are derived from genotype counts:
\[
p_F = \text{frequency of allele F}
\]
\[
p_I = \text{frequency of allele I}
\]
\[
p_S = \text{frequency of allele S}
\]
Using the counts:
\[
p_F = \frac{2 \times n_{FF} + n_{SF} + n_{FI}}{2N}
\]
\[
p_I = \frac{2 \times n_{II} + n_{SI} + n_{FI}}{2N}
\]
\[
p_S = \frac{2 \times n_{SS} + n_{SF} + n_{SI}}{2N}
\]
Calculations:
\[
p_F = \frac{2 \times 20 + 50 + 55}{2 \times 220} = \frac{40 + 105}{440} = \frac{145}{440} \approx 0.330
\]
\[
p_I = \frac{2 \times 25 + 40 + 55}{440} = \frac{50 + 95}{440} = \frac{145}{440} \approx 0.330
\]
\[
p_S = \frac{2 \times 30 + 50 + 40}{440} = \frac{60 + 90}{440} = \frac{150}{440} \approx 0.341
\]
The sum:
\[
p_F + p_I + p_S \approx 0.330 + 0.330 + 0.341 = 1.001
\]
which confirms the calculations are consistent.
Hardy-Weinberg Equilibrium Frequencies of Genotypes
Assuming the population is in HWE, the expected genotype frequencies are calculated as:
\[
f_{SS} = p_S^2
\]
\[
f_{SF} = 2 p_S p_F
\]
\[
f_{FF} = p_F^2
\]
\[
f_{SI} = 2 p_S p_I
\]
\[
f_{FI} = 2 p_F p_I
\]
\[
f_{II} = p_I^2
\]
Plugging in the allele frequencies:
\[
f_{SS} = (0.341)^2 \approx 0.116
\]
\[
f_{SF} = 2 \times 0.341 \times 0.330 \approx 0.225
\]
\[
f_{FF} = (0.330)^2 \approx 0.109
\]
\[
f_{SI} = 2 \times 0.341 \times 0.330 \approx 0.225
\]
\[
f_{FI} = 2 \times 0.330 \times 0.330 \approx 0.218
\]
\[
f_{II} = (0.330)^2 \approx 0.109
\]
The expected counts, multiplying by total individuals (\( N = 220 \)), are:
| Genotype | Expected Count |
|------------|-------------------|
| SS | \(0.116 \times 220 \approx 25.5\) |
| SF | \(0.225 \times 220 \approx 49.5\) |
| FF | \(0.109 \times 220 \approx 24.0\) |
| SI | \(0.225 \times 220 \approx 49.5\) |
| FI | \(0.218 \times 220 \approx 47.9\) |
| II | \(0.109 \times 220 \approx 24.0\) |
Observed vs. Expected Heterozygosity
The total observed heterozygosity (\( H_o \)) is the sum of observed heterozygote genotype frequencies:
\[
H_o = f_{SF} + f_{SI} + f_{FI}
\]
\[
H_o = 0.227 + 0.182 + 0.250 \approx 0.659
\]
Similarly, the expected heterozygosity (\( H_{exp} \)) under HWE:
\[
H_{exp} = 2 (p_F p_I + p_F p_S + p_I p_S)
\]
\[
H_{exp} = 2 (0.330 \times 0.330 + 0.330 \times 0.341 + 0.330 \times 0.341) \approx 2 (0.109 + 0.112 + 0.112) = 2 \times 0.333 \approx 0.666
\]
Analysis of Deviations from Hardy-Weinberg Equilibrium
The observed heterozygosity (\( \approx 0.659 \)) closely matches the expected heterozygosity (\( \approx 0.666 \)), indicating minimal deviation from HWE assumptions. Minor differences could be due to sampling variation or natural population structure, but overall, the data suggest the population is near equilibrium.
Deviations from HWE typically arise from factors such as non-random mating, genetic drift, selection, migration, or mutation. Since the heterozygosity values are close, it is unlikely that strong forces, like selection or non-random mating, significantly influence the population at this locus.
Conclusion
The analysis of Harris’s (1966) data supports the conclusion that the alkaline phosphatase locus in the English population conforms reasonably well to Hardy-Weinberg equilibrium, sharing similar observed and expected heterozygosity values. Minor discrepancies are consistent with natural population variability, and no strong evidence of evolutionary forces disrupting equilibrium is apparent.
References
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