Dstatistics

D-statistics, commonly referred to as the ABBA-BABA test, is a population-genetics statistic used to detect admixture or gene flow among populations or lineages. It analyzes genome-wide single nucleotide polymorphism data in a four-taxon framework consisting of an outgroup and three ingroup populations, testing whether the history deviates from a simple tree due to introgression.

In practice, the statistic compares two discordant allele-sharing patterns across many loci: ABBA and BABA. ABBA occurs when the first population carries the ancestral allele and the second and third share a derived allele, while BABA occurs when the second population carries the ancestral allele and the first and third share a derived allele. Under a strictly bifurcating history with no gene flow, ABBA and BABA patterns should be equally frequent.

Quantitatively, D is defined as D = (N_ABBA − N_BABA) / (N_ABBA + N_BABA), where N_ABBA and N_BABA are the counts of the respective patterns across loci. The statistic typically ranges between -1 and 1. Significance is assessed with standard error estimates such as block jackknife or bootstrap over loci. A significantly positive D suggests excess allele sharing between the third population and the second, while a significantly negative D suggests excess sharing between the third population and the first.

D-statistics do not specify the direction, timing, or proportion of admixture on their own. They are often followed by extensions such as the f4-statistic and f4-ratio to estimate admixture proportions, and are implemented in tools like ADMIXTOOLS, Dsuite, and ANGSD. Limitations include sensitivity to ancestral structure, selection, data quality, and outgroup choice.