Hardy–Weinberg & Population Genetics – Comprehensive Study Notes
Population Dynamics & Gene Pools
Goal of this section:
Quantitatively track how genetic makeup (dominant/recessive alleles, homozygous/heterozygous states) changes within populations over time.
Use calculated values to infer why a recessive or dominant allele may be trending upward or downward (environmental pressure, mating success, etc.).
Gene pool concept:
Imagine collecting every allele carried by individuals in a defined population (e.g., the classroom).
Greater allelic variation → higher probability that at least some individuals possess genotypes conferring survival & reproductive success under environmental change (biodiversity advantage).
Natural sources of variation reviewed in earlier units: meiosis (independent assortment, crossing-over) & random fertilization.
Three Frequencies We Can Measure
Genotype frequency – proportion of individuals with each genotype (e.g., BB, Bb, bb).
Phenotype frequency – proportion showing each physical trait (e.g., black vs white coat).
Allele frequency – proportion of each allele in the gene pool (e.g., B vs b).
Snapshot nature: Each set of frequencies represents a single moment; comparing successive snapshots lets us infer evolutionary trends.
Hardy–Weinberg Principle (H–W)
Co-formulated (1908) by Godfrey Hardy (mathematician) & Wilhelm Weinberg (physician).
Provides two algebraic relationships that connect allele & genotype frequencies if five idealized conditions are met for the instant of sampling.
5 equilibrium conditions (rarely all true in nature, but assumed for calculations):
Large population size – random events don’t swamp the whole population.
Random mating – no sexual selection or mating preferences.
No mutation – alleles themselves are stable in that moment.
No migration – closed population (no gene flow in/out).
No natural selection – every phenotype equal for survival & reproduction.
Even though these assumptions are unrealistic in the long term, H–W still works as a null model. Deviations between successive snapshots highlight evolutionary forces.
Symbol & Formula Summary
Symbols (must be memorised):
p = frequency of the dominant allele.
q = frequency of the recessive allele.
By definition p + q = 1(100 %).
Genotype-frequency expansion (squaring the binomial):
(p + q)^2 = p^2 + 2pq + q^2 = 1
where
p^2 → homozygous dominant frequency.
2pq → heterozygous frequency.
q^2 → homozygous recessive frequency.
Complete dominance & one trait at a time only – the scheme fails for incomplete dominance, codominance, multiple alleles, or linked loci.
Step-by-Step Calculation Workflow (Recommended)
Identify data type in the prompt: Are given numbers genotype counts, phenotype counts, or direct allele frequencies?
Start with the recessive phenotype whenever only phenotype data are supplied, because only one genotype ( q^2 ) produces it.
Convert counts → frequencies (divide by total population size; express as decimals).
Solve sequentially:
If recessive phenotype available → q^2. Take square root to get q.
Compute p = 1 – q.
Plug p & q into p^2 or 2pq as needed.
(Optional) Convert frequency to expected number of individuals: multiply by population size.
Keep answers to 3 decimal places (course convention).
Common mistake flagged by instructor: Starting with 34/50 would incorrectly assume all blue are one genotype; always start from recessive phenotype.
Worked Example 4 – Cystic Fibrosis among Caucasian Newborns
Incidence given: 1 in 1 700 newborns affected (recessive disease).
q^2 = 1 / 1700 = 0.000588.
q = \sqrt{0.000588} = 0.0243.
p = 1 – 0.0243 = 0.9757.
Carrier (heterozygote) frequency: 2pq = 2(0.9757)(0.0243) = 0.0474 ≈ 4.7 % of Caucasian newborns are carriers.
Genetic Equilibrium vs Micro-Evolution
If successive snapshots show no significant change in p or q → population is in genetic equilibrium (no evolution detectable during period).
Detectable change (even small) over time → micro-evolution is occurring.
Researchers plot allele-frequency trajectories + environmental data (climate, predators, human activity) to hypothesize selective forces.
Real-World Illustrations Mentioned
Alberta has Canada’s highest proportion of blood-type O donors – hypothesis: migration & subsequent reproductive patterns created “stocking of the pond”.
Shifts between dominance of deer antler size, peacock trains, etc. result from changing sexual-selection pressures.
Practical & Exam Tips
A calculator is essential; provided formula sheet lists only:
p + q = 1 and (p + q)^2 = p^2 + 2pq + q^2 = 1 plus amino-acid table for later genetics.
Most exam items ask for carrier (heterozygous) frequency because it requires full use of both equations.
Always label what each calculated number represents ( p,q,p^2,2pq,q^2 ) to avoid mixing them up.
Maintain three decimal places unless question specifies otherwise.
Intellectual caution: H–W is a null expectation; real populations almost always break ≥1 assumption, so significant deviations must be interpreted, not ignored.