Cohanim and Yugosleviim

According to the Forward, a new genetic study shows that up to half of Ashkenazi Leviim are almost certainly descended from a joint male ancestor -- who was Slavic. Ie., non-Jewish or a convert, meaning that they could not have been descended directly through the male line from the tribe of Levi.
The authors of the study conclude that most probably,

"some ancestors who contributed genes in the formative years of the Ashkenazi community either were faking their status as Levites or simply mistakenly believed they were Levites when they were not.
"This misidentified Levite would have had to either have been a convert himself, or to have inherited his genes from a convert or even from a non-Jewish father...
"It is... possible that a woman who was married to a Levite but had a son out wedlock, either because of a rape or an affair, still might have raised her son as if he were a Levite."

According to the study, Sephardi Leviim, by contrast, have the same genetic lineage as Cohanim.