Strip ancestry estimation to its minimum viable instrument and you get the f4-ratio: two f4-statistics, 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 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 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, no covariance matrix to invert. For a damaged archaic genome or a target with too few SNPs for a stable model, 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 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, and below rank, one honest division.
Where it loses#
Everywhere else, frankly. The ratio hard-codes exactly two sources — three-way mixtures must go to qpAdm's least-squares machinery. 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, 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. 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, 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. 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.
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.)
