Allele

Allele Frequencies in a Population of Children

  • Population Size: 500 children

    • Total alleles = 500 children * 2 alleles/child = 1000 alleles

  • Genotype Counts:

    • Homozygous AA (a): 39

      • Calculation of a alleles: 39 homozygous children * 2 = 78 a alleles

    • Heterozygotes (Aa): 279

      • Calculation of a alleles in heterozygotes: 279 heterozygotes * 1 (a allele from each)= 279 a alleles

    • Combination of alleles:

      • Total a alleles = 78 (homozygous) + 279 (heterozygotes) = 357 a alleles

  • Frequency of a allele:

    • Frequency of a in the population = Total a alleles / Total alleles

[ \text{Frequency of } a = \frac{357}{1000} = 0.357 \text{ or 35.7%} ]

  • Frequency of S allele:

    • Given that total frequencies must equal 1:

    • Frequency of S allele = 1 - Frequency of a

    • [ \text{Frequency of } s = 1 - 0.357 = 0.643 \text{ or 64.3%} ]

  • Verifying Frequencies:

    • Total of alleles should add to 1:

    • [ 0.357 + 0.643 = 1 ]

Calculating Expected Genotype Frequencies

  • Assuming a non-evolving population: Expected genotype frequencies can be calculated based on allele frequencies.

    • Homozygous AA (a) frequency = p²

    • Expected AA genotype frequency: [ p^2 = (0.357)^2 ]

    • Expected number of AA = Expected frequency * Total individuals = p² * 500

  • Heterozygotes (Aa) Frequency:

    • Expected Aa frequency = 2pq

      • Where:

        • p = frequency of a (0.357)

        • q = frequency of s (0.643)

    • [ E(Aa) = 2 * 0.357 * 0.643] = Expected number of heterozygotes * Total individuals

  • Homozygous SS (s) Frequency:

    • Expected SS phenotype = q²

    • [ q^2 = (0.643)^2 ]

    • Expected number of SS = q² * Total individuals

Chi-Square Test for Goodness of Fit

  • Purpose: To compare observed genotypes with expected genotypes.

  • Formula:[ \chi^2 = \sum \frac{(O - E)^2}{E} ]Where:

    • O = observed value

    • E = expected value

  • Calculated Observed Values from Population:

    • Observed AA = 39

    • Observed Aa = 279

    • Observed SS = 82

  • Calculate Expected Values:

    • Expected AA, Aa, SS calculated above need to be used in chi-square formula.

  • Expected Counts Examples:

    • Expected AA count = p²*500

    • Expected Aa count = 2pq*500

    • Expected SS count = q²*500

  • After computing all expected counts and observed counts, compute chi-square to validate genetic model applicability to real populations.