Ugo Perego et al. discuss the reconstruction of Joseph's Y chromosome and determine genetically that he is not the biological father of various children (Moroni Pratt, Zebulon Jacobs, Orrison Smith).
Ugo A. Perego, Natalie M. Myres, and Scott R. Woodward, "Reconstructing the Y-Chromosome of Joseph Smith: Genealogical Applications," Journal of Mormon History 31, no. 2 (Fall 2005): 42–60
[Perego et al. conclude based on the reconstruction of Joseph Smith's Y chromosome that he cannot be the father of Moroni Pratt, Zebulon Jacobs, and Orrison Smith.]