I read an article last night claiming that a set of ancient Finnish remains from the Iron Age is related to the Sami people. I don’t disagree, but they’re much closer to the Russians than the Sami, and in general, these are plainly Roma people, that are in turn related to Heidelbergensis (just like the Russians). I’m not going to completely dismiss the results of a peer-reviewed article in Nature, though at the same time, my work is incomparably more precise than typical genetic analysis. See Section 7.1 of A New Model of Computational Genomics [1]. As such, I’m going to assume that they are related to the Sami (which is consistent with my work), and that the modern day Sami are a mix between these ancient people, and others that do not descend from Heidelbergensis, which would produce the match distribution on the left below, for the modern Sami, that shows a mix of Roma and non-Roma populations. So on net, I would say that this ancient Finnish population eventually mixed with people that are more closely related to modern day Sami, specifically the Saqaaq, over time, eventually producing the modern genetic distribution of the Sami people.

Below is the updated dataset that now includes 10 of these ancient Finnish genomes. All of the code you need to run these examples is in [1].

https://www.dropbox.com/s/zwt1bcqqmqkleca/mtDNA.zip?dl=0