BSMS205 · Genetics

Allele Frequency

Chapter 20 · Part IV · Population Genetics

Today's central question

Rare
or
common?

One genome tells you almost nothing

A harmless polymorphism in millions of people?
A brand-new disease mutation in this one person?
Somewhere in between?

From a single genome, you cannot tell.

Meaning lives in the population

Individual

A private event
Signal or noise?
Unknown significance

Population

Shaped by mutation
Filtered by selection
Randomised by drift

The modern reference dataset

141,456

people sequenced · gnomAD v2

Hundreds of millions of variants cataloged
Detects alleles present in one copy out of 282,912
Karczewski et al. 2020, Nature

Roadmap for today

Defining allele frequency
How to calculate it · worked example
Minor Allele Frequency (MAF)
Variant categories by frequency
How selection shapes frequency
Summary & what comes next

§ 1

Defining
Allele Frequency

What fraction of copies carry this variant?

Allele frequency = the proportion of a specific allele
among all alleles at that locus in a population.

Operates on a single locus, not the whole genome
Measured within a population — frequencies differ between groups
Ranges from zero (absent) to one (fixed)

Why humans need the factor of two

alleles per person per locus

Humans are diploid
One allele from mother
One allele from father
Each person contributes two to the population count

A concrete example

Position on chromosome twenty-one: chr21:2,232,323
Most people: genotype A / A
One person in gnomAD: genotype A / T (heterozygous)
Everyone else: A / A
Sample size: 141,456 people

Your task

What is the allele frequency of T at this locus?

Step one · count total alleles

141,456 people × 2 alleles = 282,912 total alleles

Every person contributes two copies of chromosome twenty-one
The denominator of our fraction

Step two · count the variant alleles

One heterozygote → 1 T allele
Everyone else → 0 T alleles

Total observed: 1 T allele
The numerator of our fraction

Step three · divide

1 ÷ 282,912 = 0.0000035

0.00035%

≈ three point five per million

Extremely rare — but detectable only at this sample size.

§ 2

The General
Formula

The formula

Allele frequency = variant alleles ÷ (2 × individuals)

Heterozygote contributes 1 variant allele.
Homozygote contributes 2 variant alleles.

Four scenarios in gnomAD

Total alleles in denominator: 282,912

Scenario	Hets (AT)	Homs (TT)	T alleles	Frequency
Very rare	1	0	1	0.00035%
Rare	2	3	8	0.0028%
Low frequency	10	0	10	0.0035%
More common	0	10	20	0.0071%

Look at the rare row: two heterozygotes plus three homozygotes gives two plus six equals eight T alleles.

§ 3

Minor Allele
Frequency (MAF)

Two alleles at one position

Major allele

92%

reference / "normal"

Minor allele

MAF = 0.08

Why we track the minor, not the major

The major allele is usually the reference baseline
Variation, not uniformity, is what we study
MAF is the natural axis for GWAS, population genetics, disease risk
It also gives us a clean common vs rare shortcut

A rough rule of thumb

Label	MAF	Intuition
Common	> 5%	Many people carry it
Low frequency	1 – 5%	Uncommon but not rare
Rare	< 1%	Few people carry it

A starting point only — as we'll see, real cutoffs vary by context.

§ 4

Variant Categories
by Frequency

The cutoffs are not universal

"The threshold of MAF in rare variants
has not yet been clearly defined."

Published cutoffs vary from 0.1% to 5%
Depends on disease, penetrance, sample size, method
Momozawa & Mizukami 2021, J Hum Genet

Different fields, different cutoffs

Study	Common	Low	Rare	Ultra-rare
1000 Genomes 2022	> 1%	0.5 – 5%	≤ 1%	Singletons
Schizophrenia 2022	> 1%	—	< 0.1%	Singletons only
AD / dementia GWAS	> 5%	1 – 5%	< 1%	—
COVID-19 severity	≥ 5%	1 – 5%	0.1 – 1%	< 0.1%

Byrska-Bishop 2022 · Akingbuwa 2022 · Andrews 2023 · Fallerini 2021

Why the variation?

Disease biology — highly penetrant disorders need stricter cutoffs
Sample size — large cohorts can resolve finer frequency tiers
Technology — array GWAS (> 5%), WGS (down to singletons)
Functional biology — 90% of singleton heritability is at MAF < 0.01%

Why does this variation exist? Four reasons. First, disease biology. For highly penetrant disorders like severe neurodevelopmental syndromes, the important variants are extremely rare, so the cutoffs get stricter. Second, sample size. You cannot meaningfully resolve ultra-rare variants in a sample of five hundred people, so those studies lump all rare variants together. Third, technology. Classic array-based GWAS could only reliably work above five percent. Whole-genome sequencing can go all the way down to singletons. Fourth, functional biology. One study found that ninety percent of singleton-driven heritability for gene expression comes from variants below zero point zero one percent. That tells us where the biological action is, and motivates stricter ultra-rare definitions.

A working framework

Category	MAF	Allele age	Selection
Common	> 5%	Many generations	Neutral / weak
Low-frequency	1 – 5%	Intermediate	Mild
Rare	< 1%	Recent — hundreds to thousands of years	Purifying
Ultra-rare	< 0.1%	Very recent	Strong purifying
Private / singleton	≈ 0%	1 – 10 generations · often de novo	Unfiltered

Common variants · old survivors

Persisted through many generations
Mostly non-coding or low functional impact
Selection had time — and did not remove them
Plenty of people carry them → ideal for GWAS

Rare variants · selection's fingerprint

A striking gnomAD result

Most loss-of-function variants
in gnomAD are singletons.

Breaks a gene → reduces fitness → selection removes it
New LoF variants keep arising through mutation
They just can't spread before selection catches them

Karczewski et al. 2020, Nature

Private variants · untested by evolution

Too new for selection to judge
Often arise de novo in this generation
Most will disappear within a few generations
A rare few persist — or, if lucky, spread

§ 5

How Selection
Shapes Frequency

Selection is a filter

Beneficial → passes through, spreads
Neutral → drifts randomly, sometimes survives
Harmful → caught and removed

A variant's frequency is a record of which process dominated.

The more severe, the rarer

Variant type	Protein effect	Typical frequency
Synonymous	No amino acid change	Often common
Missense	One amino acid changed	Intermediate
Nonsense	Protein truncated	Almost always rare

A gradient of selection intensity, visible in the data.

When does selection even work?

s > 1 / N_e

s — selection coefficient (fitness impact)
N_e — effective population size
Below this threshold → variant behaves as neutral → drift wins

Population size sets the floor

Large N_e

1 / N_e is tiny
Even weak selection is felt
Deleterious alleles purged
Few mildly harmful variants persist

Small N_e

1 / N_e is large
Only strong effects overcome drift
Mildly harmful variants behave neutrally
More deleterious alleles persist

Humans: N_e ≈ 10,000 – 50,000 (depends on ancestry).

Why LoF variants persist despite selection

Mutation rate > 0 → new LoF variants constantly arise
Finite population → selection needs time to act
Some linger for a few generations before being removed
A handful drift upward briefly before selection catches up

Frequency vs effect size · the master picture

Alzheimer's disease genetic architecture: allele frequency vs effect size — Alzheimer's disease architecture · Andrews et al. 2023, *EBioMedicine* 90:104511 (CC BY-NC-ND 4.0).
**APP / PSEN1 / PSEN2**: rare + huge effect · **APOE ε4/ε4**: ~2% + OR ~12 · **GWAS hits**: common + small effect.

Finally, let's put everything together in one master picture. This plot is from an Alzheimer's review by Andrews and colleagues in twenty twenty-three. On the x-axis, minor allele frequency, on a log scale. On the y-axis, effect size, measured as odds ratio, also on a log scale. Look at three regions. In the top left, extremely rare variants in A P P, P S E N one, and P S E N two, with very large effects — these cause autosomal dominant Alzheimer's disease. In the middle, the A P O E epsilon four double-allele genotype, at around two percent frequency, with a big odds ratio of roughly twelve. And in the bottom right, hundreds of common GWAS hits, each with a small effect. This inverse relationship — rare goes with large effect, common goes with small effect — is not limited to Alzheimer's. It appears across complex diseases, and it is exactly what selection predicts. Big effects cannot reach high frequency, because selection will not let them.

§ 6

Summary

What to take away

Allele frequency = variant alleles ÷ (2 × N)
Categories reflect allele age and selection intensity
LoF variants are mostly singletons — selection's fingerprint in gnomAD
Large N_e lets selection see even weak effects
Big effect size → cannot reach high frequency

Why this matters in practice

Variant interpretation — pathogenic vs benign hinges on frequency
Study design — GWAS vs rare-variant burden tests
Disease architecture — common + small, or rare + large?
Drug target prioritisation — protective LoFs are gold

Why does this matter in practice? Four places. First, variant interpretation. When you look at a genetic test result, the single most important piece of information is usually the allele frequency. Pathogenic variants are almost always rare. Second, study design. If your variants are common, you run a G W A S. If they are rare, you switch to rare-variant burden tests. The statistical strategy follows the frequency. Third, understanding disease architecture. For any given disorder, you want to know: is the heritability mostly explained by common small-effect variants, or rare big-effect ones? Fourth, and increasingly important, drug target prioritisation. When you find a gene where loss-of-function variants protect people from a disease, that gene is gold for drug development.

Next lecture

Why do the same variants
have different frequencies
in different populations?

Chapter 21 · Population Structure