“…Eight years later we find qpAdm -based protocols routinely employed in large-scale screens of ancient human or animal populations for admixture (often between closely related sources) and used as formal tests for admixture (see Lazaridis et al 2016, Skoglund et al 2017, Harney et al 2018, Mathieson et al 2018, Antonio et al 2019, Narasimhan et al 2019, Fernandes et al 2020, Marcus et al 2020, Ning et al 2020, Wang et al 2020, Yang et al 2020, Calhoff et al 2021, Papac et al 2021, Librado et al 2021, Sirak et al 2021, Wang et al 2021, Yaka et al 2021, Zhang et al 2021, Allentoft et al 2022, Bergström et al 2022, Changmai et al 2022a, Changmai et al 2022b, Gnecchi-Ruscone et al 2022, Lazaridis et al 2022, Maróti et al 2022, Oliveira et al 2022, Patterson et al 2022, Brielle et al 2023, Lee et al 2023, Taylor et al 2023 for examples). qpAdm fits admixture models to a matrix of f 4 -statistics of the form f 4 (“left” group i , “left” group j ; “right” group i , “right” group j ), which in the absence of missing data at the group level can be reduced to a smaller matrix f 4 (target group, “left” group j ; “right” group 1 , “right” group j ), considering algebraic relationships between different f 4 -statistics (Peter 2016).…”