topic 3 - population genetic expectations and natural selection

Hardy-Weinberg Equillibrium

Expectation when there is no evolution - theorem provides the expected relationship between alleles, genotypes and phenotypes in diploid populations

1. No gene flow from other populations

2. No mutation

3. No drift

4. Non non-random mating

5. No selection

6. Recombination not relevant

Allele

Alternate forms of DNA sequence (or gene)

Genotype

Allelic composition of an individual or cell (single gene) (BB Bb bb)

Phenotype

Form or character of an individual (BB, Bb: brown; bb: white)

Diploid

Mendelian ratio

3:1 ratio

p + q = 1

Frequency of alleles added together equals 1

p² + 2pq + q² = 1

p² = BB

2pq = 2Bb

q² = bb

Practice question: Allele frequencies for a locus are p=0.5 and q=0.5. What is the expected frequencies of the three genotypes?

f(AA) = p² = (0.5)² = 0.25

f(Aa) = 2pq = 2×0.5×0.5 = 0.5

f(aa) = q² = (0.5)² = 0.25

Practice question: Use the following three genotype frequencies (BB, Bb, bb) to calculate the allele frequencies (B and b). fBB = 0.64 fBb = 0.32 fbb = 0.04

f(B) = f(BB) + ½f(Bb) = 0.64 + ½ *0.32 = 0.80

f(b) = f(bb) + ½f(Bb) = 0.04 + ½ *0.32 = 0.20

Step-by-step procedure for testing Hardy-Weinberg Equillibrium (HWE)

1. Count the total number of alleles

2. Calculate allele frequencies from observed data

3. Calculate expected genotype frequencies using the Hardy-Weinberg formula (p², 2pq, q²)

4. Work out how many individuals you would expected in each genotype

5. Perform a statistical test called a chi-squared test

Chi square test

(O-E)²/E

Tasters (p² + 2pq) = 0.53

Non-tasters (q²) = 0.47

a) Calculate q (frequency of the t allele)

b) Calculate p (frequency of the T allele)

a) q = f(t) + square root of q² = square root 0.47 = 0.686 = 0.69

b) p = q-1 = 0.31

f(TT) = p² = 0.31 × 0.31 = 0.0961 = 0.1

f(Tt) = 2pq = 2 × 0.31 × 0.69 = 0.4278 = 0.4

f(t) = q² = 0.69 × 0.69 = 0.4761 = 0.5