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where $P_1$ through $P_4$ are allele frequencies at site i in an outgroup, a candidate-admixed population, a comparison population without the admixture, and the archaic source, respectively. The estimator exploits a simple logic: if population $P_2$ has interbred with the archaic lineage $P_4$ and $P_3$ has not, $P_2$ should share systematically more rare variants with $P_4$ than $P_3$ does, in proportion to the fraction of its genome that traces to that admixture event. This is why admixture claims in the literature are reported as percentages with confidence intervals rather than as a binary yes/no — the estimate is statistical, built from many thousands of sites, not read off a single marker.

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