  We consider M SNP data from N individuals who are an admixture of K unknown
ancient populations. Let $\Pi_{si}$ be the frequency of the reference allele of
individual i at SNP s. So the number of reference alleles at SNP s for a
diploid individual is binomially distributed with parameters 2 and $\Pi_{si}$.
We suppose $\Pi_{si}=\sum_{k=1}^KF_{sk}Q_{ki}$, where $F_{sk}$ is the allele
frequency of SNP s in population k and $Q_{ki}$ is the proportion of population
k in the ancestry of individual i.
  I am interested in the identifiability of F and Q, up to a relabelling of the
ancient populations. Under what conditions, when $\Pi =F^1Q^1=F^2Q^2$ are $F^1$
and $F^2$ and $Q^1$ and $Q^2$ equal? I show that the anchor condition (Cabreros
and Storey, 2019) on one matrix together with an independence condition on the
other matrix is sufficient for identifiability.
  I will argue that the proof of the necessary condition in Cabreros and
Storey, 2019 is incorrect, and I will provide a correct proof, which in
addition does not require knowledge of the number of ancestral populations.
  I will also provide abstract necessary and sufficient conditions for
identifiability. I will show that one cannot deviate substantially from the
anchor condition without losing identifiability. Finally, I show necessary and
sufficient conditions for identifiability for the non-admixed case.
