Without selection, mutation, migration, drift or non-random mating, allele frequencies do not change — and genotype frequencies settle in one generation to p² + 2pq + q² = 1. It is evolution’s null hypothesis: the state a population sits in when nothing is acting on it, so any deviation is a fingerprint of a force. The mathematician G. H. Hardy jotted it in a 1908 letter, apologizing for intruding on biology.
THE TECHNIQUE p² + 2pq + q² = 1 ; p stays p
The demo checks that the genotype frequencies sum to 1 and the allele frequency is unchanged next generation: live demo
HISTORY & CREDIT Hardy & Weinberg · 1908
“Populations evolve toward Hardy-Weinberg.” — it is the non-evolving baseline; reaching it means no force is acting, and deviation is the signal of one. cited
the baseline · no selection/drift/migration/mutation → frequencies frozen. one generation · genotypes settle to p² : 2pq : q², and p stays p forever after. 1908 · G. H. Hardy (in a letter) & Wilhelm Weinberg, independently.
The stillness against which change is measured. theorem
RECOMMEND FOR I-13 the equilibrium, on the compiler
On i-13, with p=0.6, q=0.4 the genotypes sum to 1 and the allele frequency is unchanged:
$ i13 run lf_hardy-weinberg.i13
RUN OK · 48 step(s)
pp=36 two_pq=48 qq=16 total=100 (=1.00)
p_unchanged = 1 equilibrium = 1
Recommend as a NULL — an identity (B39). p²+2pq+q²=(p+q)²=1 is algebra; the frequency stability is a fixed point of the mating map. NULL — evolution’s null hypothesis.