Hardy-Weinberg Equilibrium: The Null Hypothesis of Evolution
If 500 people left Earth tomorrow and settled on Mars, never to return, what would their descendants look like in 10,000 years? Would they still be human? Could they still have children with someone from Earth?
To answer those questions properly, you have to start somewhere counterintuitive: a mathematical theorem that describes what a population looks like when nothing is happening. No evolution. No selection. No drift. Just... stasis.
That theorem is Hardy-Weinberg equilibrium, and it's the most important null hypothesis in all of biology.
The question behind the equation
Evolution is change in allele frequencies over time. But before you can measure change, you need to know what no change looks like. You need a baseline: a mathematical description of a population that is not evolving.
In 1908, mathematician G.H. Hardy and physician Wilhelm Weinberg independently derived that baseline. Their insight was surprisingly simple: if you have a population where mating is random, no one is migrating in or out, no mutations are occurring, the population is infinitely large, and no allele confers a survival advantage, then allele frequencies don't change. Ever.
That's the equilibrium. Not a balance of forces, but the absence of forces.
The math: simpler than it looks
Consider a single gene with two alleles: A and a. Let p be the frequency of A and q be the frequency of a. Since these are the only two options:
p + q = 1
If mating is random, the probability of any genotype in the next generation is just the product of allele frequencies:
| Genotype | Frequency |
|---|---|
| AA | p² |
| Aa | 2pq |
| aa | q² |
And that's the Hardy-Weinberg equation:
p² + 2pq + q² = 1
The crucial property: these frequencies are self-sustaining. Once a population reaches HWE, it stays there forever, as long as the five assumptions hold.
Why the assumptions matter more than the math
The equation itself is trivial algebra. What makes Hardy-Weinberg powerful is the list of things that must be true for it to hold:
- No mutation: alleles don't change into other alleles
- No migration: no one enters or leaves the population
- Random mating: mate choice isn't influenced by genotype
- Infinite population size: no sampling error (genetic drift)
- No natural selection: all genotypes survive and reproduce equally
These assumptions are never all true simultaneously in nature. That's the point. Hardy-Weinberg doesn't describe reality. It describes the null hypothesis against which reality is tested. Every violation of these assumptions is a mechanism of evolution.
When you observe a population whose genotype frequencies don't match HWE predictions, you've detected evolution happening. The pattern of the deviation tells you which force is acting.
A worked example: sickle cell trait
Sickle cell disease is caused by a single nucleotide change in the beta-globin gene. The allele (HbS) is recessive for disease but provides heterozygote advantage against malaria. In regions where malaria is endemic, HbS frequency is maintained at roughly q = 0.1.
Under HWE, you'd expect:
- HbA/HbA (normal): (0.9)² = 0.81
- HbA/HbS (carrier, malaria-resistant): 2(0.9)(0.1) = 0.18
- HbS/HbS (sickle cell disease): (0.1)² = 0.01
In non-malarial populations, HbS frequency is much lower because the heterozygote advantage disappears and homozygotes are selected against. The departure from what you'd expect in a neutral population is the signature of balancing selection, one of the four forces we'll cover in Part 2.
Hardy-Weinberg Equilibrium
Adjust allele frequency p to see how genotype frequencies change under equilibrium assumptions.
Genotype frequencies
p²
2pq
q²
Population (N=100)
At p ≈ 0.5, heterozygotes (Aa) are the most common genotype. Maximum genetic diversity occurs at equal allele frequencies.
p²+2pq+q²=1
What the interactive shows you
Play with the allele frequency slider above. Notice that the heterozygote frequency (the green curve) is always maximized at p = q = 0.5. This is when genetic diversity is highest. At the extremes, one allele dominates and the population is nearly monomorphic.
In a real population, if you measured genotype frequencies and they matched these curves exactly, you'd conclude: no detectable evolutionary forces are acting on this gene. The moment they diverge (more homozygotes than expected, fewer heterozygotes, a skewed distribution), something is pushing.
Back to Mars
Here's why this matters for the question we opened with. The Mars colony of 500 people violates at least three HWE assumptions from day one:
- Finite population: 500 is not infinity. Genetic drift will be enormous. Rare alleles will be lost; others will fix by chance alone.
- No migration: once the colony is established, gene flow with Earth stops (or becomes negligible). The two populations evolve independently.
- Non-random mating: in a small, closed community, mate choice is constrained by who's available. Assortative mating becomes unavoidable.
And that's before considering that Mars imposes novel selection pressures (different gravity, different radiation environment, different atmospheric composition) that Earth doesn't.
Hardy-Weinberg tells us what equilibrium looks like. The Mars colony is a list of reasons why equilibrium is impossible. Everything that happens next (the divergence, the drift, the adaptation) is the story of how those violations compound over generations.
That's what Part 2 is about: the four forces that break the equilibrium, and how they interact to drive populations apart.
Next in this series: The Four Forces: Mutation, Drift, Migration, and Selection. Why Hardy-Weinberg never actually holds, and what happens when it breaks.
Series: Understanding Speciation