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Scaffold S3 — HWE genotype counting

Five rounds. Rounds 1–4: given the allele frequency p and the number of individuals N, predict the heterozygote count Aa under Hardy–Weinberg equilibrium. The reveal also shows the observed counts, which sometimes deviate from HWE — and the F-statistic that measures that deviation. Round 5 reverses direction: given observed counts, compute p and predict the expected Aa.

Locked — answer the pretest above first.

Running tally — Aa count

What you just did has a name

HWE gives three expected counts as functions of p and N: AA = p²·N, Aa = 2pq·N, aa = q²·N. You predicted the middle one five times. In round 1 (panmictic simulation) the observed count sat exactly on HWE. In round 2 (a pedigreed wild population) it sat slightly below — a small positive F — because some parents are related. In round 3 (a sibling mating colony) the heterozygote count was far below HWE — a large positive F. Round 4 (two populations fixed for opposite alleles, pooled) had zero heterozygotes despite p = 0.5 — F = 1. Round 5 reversed direction: you recovered p from counts and computed a partial inbreeding value.

F = 1 − Hobs / Hexp is the detection tool. It tells you a population is not in HWE. It does not tell you which cause produced the deviation: inbreeding, assortative mating, or pooled subpopulations (Wahlund effect). Round 3 was the first. Round 4 was the third. Same F, different biology. You distinguish them with other evidence — pedigree, mating data, substructure.

This is null-model reasoning in miniature: HWE holds when five assumptions hold; every violation shows up as a deviation from Hexp. Rejecting HWE tells you something is happening. The scaffold's job is to make that reflex automatic.