Ugo Perego summarizes the genetic studies done on Joseph's alleged paternity of various children.
Ugo A. Perego, “Joseph Smith, the Question of Polygamous Offspring, and DNA Analysis,” in The Persistence of Polygamy: Joseph Smith and the Origins of Mormon Polygamy, ed. Newell G. Bringhurst and Craig L. Foster (Independence, Mo.: John Whitmer Books, 2010), 233–56
[Ugo Perego reviews the genetic evidence for Moroni Pratt, Zebulon Jacobs, Orrison Smith, Oliver Buell, Mosiah Hancock, and Josephine Lyon. He concludes that genetic testing either rules out or fails to confirm that JS is the biological father of these children.]