QpAdm - what it means in practice

As we saw in my previous posts the correlation between fit and standard error is very meaningful.  We saw that the Basques are a loose mixture of East European Steppe  and ancient Iberian people, but they are only far descendants of those two groups and we can't prove that these two are their only ancestor, although they definitely forwarded genes to Basques.  I made similar test showing that the Greeks are distant descendants of Iron Age Anatolians and Bronze Age Balkanians, but again we can't be prove that those two were their only ancestors.  Probably not.

                                Balkans_BronzeAge Anatolia_IA
best coefficients:     0.470                        0.530
Jackknife mean:      0.475197121             0.524802879
std. errors:              0.077                         0.077 

fixed pat  wt  dof     chisq       tail prob
00  0     8    15.062       0.0579554     0.470     0.530

On the other hand,  qpAdm showed that the Finns are very strictly descendants of Iron Age Scanian, Iron Age Baltic and Iron Age Saami people, but we can't prove exact proportions of those thee admixtures, which we saw in high standard errors.  It is easy to understand that admixtures of close populations are not as easy determinable as admixtures of distant populations, because close relatives share much common ancestry.   

But how accurate are results showing very distant ancestry and moderately low standard errors, if the fit is poor?  I tested it.  Following tests show admixtures of Iron Age Saami people in Ostrobothnia Levaluhta.
  

We see that there is only a small difference in admixtures of Iron Age Saamis generated by present-day Finns and Iron Age Scandinavians in conjunction of Bolshoy outlier.  Chisq is high, tail prob. below 0.4, but std. err. only 6% max.  Nothing obliges such a high admixture similarity, because the genetic distance between Finns and Scandinavians is rather high.  Such a similarity is achieved only by a big genetic distant of Bolshoy outlier. 

Another example, although not equally striking.

Chisq is between 10 and 21, tail prob. between 0.006 and 0.24.  FI21 shows best fit.  Std.error is 5% in FI4 and FI12, highest (9%) in case of FI21.