---
title: "The f4-ratio: ancestry estimation with one statistic, and when it beats qpAdm"
description: "Before qpAdm there was the f4-ratio — one number, two f4-statistics, an ancestry proportion. How the classic estimator works, the famous results built on it, and the precise trade against qpAdm."
canonical: https://www.ancestrify.io/blog/f4-ratio-ancestry-estimation
date: 2026-09-01T09:20:00+00:00
updated: 2026-09-24
author: "Andi Thomaj"
---

# The f4-ratio: ancestry estimation with one statistic, and when it beats qpAdm

Strip ancestry estimation to its minimum viable instrument and you get the **f4-ratio**: two
[f4-statistics](/blog/f4-statistics-explained), one divided by the other, out comes an admixture
proportion with a standard error. It predates qpAdm, produced some of the field's most famous
numbers — your Neanderthal percentage descends from it — and it still beats the bigger machine in
one specific situation. Knowing which situation is the point of this post.

## The estimator

Suppose population **X** is a mix of two sources, with α the fraction from the lineage related to
**A** and 1−α from the lineage related to **B**. Take an outgroup **O**, and a reference
population **C** that is *more closely related to A than to B* but received none of X's mixture.
Then two f4-statistics do the work:

- **f4(A, O; X, C)** — how much of the drift shared between A and C runs through X. Only the
  α-fraction of X's ancestry descends from the A-side lineage, so this statistic carries α copies
  of that shared drift.
- **f4(A, O; B, C)** — the same shared drift measured through B, a population that is *entirely*
  B-lineage: the full, undiluted measuring stick.

Their ratio is α. No optimisation, no model search — one division, jackknifed
[the standard way](/blog/how-to-read-qpadm-p-value-z-score-standard-error) for its error bar. The
canonical deployments: archaic ancestry (X = a modern human, the ratio metering Neanderthal
admixture against a full Neanderthal genome) and the ANI/ASI cline of India — Reich and
colleagues' 2009 estimate that Ancestral North Indian ancestry runs 39–71% across groups was an
f4-ratio result years before qpAdm existed, and
[the South Asian recipes](/blog/qpadm-models-south-asian-ancestry) still reconcile against it.

## Where it beats qpAdm

**Extreme data poverty.** A ratio needs its five populations and nothing else — no
[right set to construct](/blog/how-to-choose-qpadm-sources-and-outgroups#the-standard-right-sets), no covariance matrix to
invert. For a damaged archaic genome or a target with
[too few SNPs for a stable model](/blog/how-many-snps-does-qpadm-need), the ratio often still
returns a usable number where qpAdm's machinery starves.

**Transparency under dispute.** Every assumption sits in plain sight: five named populations, one
topology claim. When two analysts disagree, arguing about one f4-ratio's premises is tractable in
a way [a rejected twelve-population model](/blog/why-qpadm-models-get-rejected) is not — which is
why methods sections still quote ratios as sanity anchors beside fancier machinery, and why a
ratio is the right *first* number before a modelling session:
[lowest rank first](/blog/qpadm-best-practices), and below rank, one honest division. Testing the
lowest rank first is statistical parsimony: the simplest model that fits, relative to the right set
used, not a head count of the migrations in anyone's history.

## Where it loses

Everywhere else, frankly. The ratio hard-codes **exactly two sources** — three-way mixtures must
go to [qpAdm's least-squares machinery](/blog/understanding-qpadm). It never tests its own
premise: feed it an X that is *not* an A/B-lineage mixture, or a C that secretly received X-side
gene flow, and it returns a confident, wrong α — there is no p-value, no
[rank test](/blog/qpwave-explained), no rejection. qpAdm's entire advantage is that it is a
*test* first and an estimator second: the model can fail, and
[failure is information](/blog/why-qpadm-models-get-rejected). And the ratio's topology
requirements (a C cleanly closer to A than B, an O clean of everything) get unbuildable exactly
where modern questions live — closely related sources,
[below-the-FST-floor distinctions](/blog/is-qpadm-still-reliable), overlapping histories.

The division of labour, then: **f4-ratio** for two-source questions with clean topology and
scarce data, or as the fast anchor a bigger model must not contradict; **qpAdm** whenever sources
might number more than two, premises need testing, or
[the proportions will carry real weight](/qpadm). Same currency,
different denominations — and the analyst who can spend both is the one whose numbers survive
review.

Terms used here are defined in the [glossary](/glossary).

## References

- Reich, D., Thangaraj, K., Patterson, N., Price, A. L. & Singh, L. (2009). Reconstructing Indian
  population history. *Nature*, 461, 489–494. (The ANI/ASI f4-ratio.)
- Green, R. E. et al. (2010). A draft sequence of the Neandertal genome. *Science*, 328, 710–722.
  (Archaic ancestry ratio estimation.)
- Patterson, N. et al. (2012). Ancient admixture in human history. *Genetics*, 192(3),
  1065–1093. (The f4-ratio formalism, qpF4ratio.)
- Peter, B. M. (2016). Admixture, population structure, and F-statistics. *Genetics*, 202(4),
  1485–1501. (The estimator's assumptions, precisely.)