Investigation 2: Mathematical Modeling of Hardy-Weinberg
Investigation 2 uses a spreadsheet model to track an allele frequency, q, generation after generation, so you can isolate how drift or selection alone reshape a population's gene pool without waiting for real organisms to reproduce.
A real population takes years and resources to track, and you can never turn off selection or chance in the wild to see what's left. A spreadsheet model fixes that. You set starting allele frequencies, population size, and whether selection acts, then let a formula recalculate q generation after generation. Because you built it, you know exactly which force is running: pure drift, pure selection, or both.
To isolate drift, you remove selection entirely and let allele frequencies change only through random sampling of which individuals happen to reproduce. In a population of 10, q bounces wildly, sometimes hitting 0 or 1 (fixation) within a few dozen generations, just from chance. In a population of 1000, q wanders only slightly from its starting value even after 100 generations, because random sampling error shrinks as population size grows. Same starting conditions, wildly different outcomes, and the only variable is size.
Selection works differently and more predictably. When aa is lethal, every aa individual is removed each generation, so q falls according to qn = q0 / (1 + n times q0). Plug in q0 = 0.5 and n = 5: q5 = 0.5 / (1 + 5 times 0.5) = 0.5/3.5, about 0.143. Notice the rate of decline slows sharply as q gets small, which sets up the key misconception question: why doesn't the allele just disappear. This investigation sits alongside the real Hardy-Weinberg equation, giving you the dynamic, generation-by-generation version of the static equilibrium formula.
Key terms
- Allele frequency (q)
- The proportion of one allele's copies among all copies of that gene in the population.
- Genetic drift
- Random change in allele frequency caused by chance variation in which individuals reproduce, strongest in small populations.
- Fixation
- The state where an allele's frequency reaches 1, meaning every individual in the population carries it.
- Lethal recessive
- An allele that causes death only when present in two copies (homozygous recessive), leaving heterozygous carriers unaffected.
- Selection coefficient
- A measure of how strongly a genotype is disfavored by selection, ranging from 0 (no disadvantage) to 1 (lethal).
Watch it explained
- How it worksHow does a model let you switch off selection and watch what drift alone does?
- How it worksWalk me through allele frequency over 100 generations in populations of 10 and 1000.
- Worked exampleFind what happens to q over five generations when the recessive homozygote is lethal.
- Common mistakeWhy doesn't a harmful recessive allele get eliminated from a population entirely?
Check yourself
End of topic.