Moroni Pratt not son of Joseph Smith says DNA researcher

Sarah Pratt, mother of Moroni Pratt

"Following another mission, this time to England, Pratt arrived in Nauvoo, Illinois, in July 1841. During Pratt's absence, Joseph Smith had begun practicing plural marriage. One of the women he approached was [Pratt's wife] Sarah, who rejected his advances. The next spring Sarah told Orson of Smith's proposals. Pratt became depressed and on 14 July disappeared; however, he was found near the Mississippi River and was persuaded to return home."  [Utah History Encyclopedia: Orson Pratt]   

Rumors have since circulated that Joseph Smith fathered Moroni Pratt, son of Sarah Pratt.  New DNA evidence sheds light on this proposed child of Joseph Smith. 
 
Excerpts of DNA solves a Joseph Smith mystery, by Michael De Groote, Deseret News
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Historians and critics have struggled for more than a century to identify children Joseph Smith may have had through polygamous marriages in the 1840s. If definitive answers could be found, it would shed light on how plural marriage was introduced to Mormons by Joseph Smith in Illinois. Brigham Young succeeded Joseph Smith as leader of the LDS Church and announced the practice publicly in Utah. The church ended polygamy in 1890.

Oliver Buell was not Joseph Smith's son.

Orson Pratt, actual Father
of Moroni Pratt

But questions remain today — particularly whether Joseph Smith, ... had any children through a polygamous wife.
[A] descendant had read that Moroni Pratt wasn't the son of early LDS apostle Parley P. Pratt, but that he was really the son of Joseph Smith. He wanted to know if Perego could use DNA to tell if Moroni Pratt was really Joseph Smith's son.
He took other DNA samples from Pratt's descendants and made the comparison. Moroni Pratt was not Joseph Smith's son, he was Parley P. Pratt's son.
The Joseph Smith family association referred others to Perego. These were people who wanted to join the association because they had read references in books like Brodie's that listed their ancestor as a possible child of Joseph Smith. DNA gave the conclusive answers that rumor and speculation couldn't give:

Joseph Smith, proposed
father of Moroni Pratt

Zebulon Jacobs was not Joseph Smith's son.
Orrison Smith was not Joseph Smith's son.
Mosiah Hancock was not Joseph Smith's son..
"I am a scientist. I look at the data objectively. I don't care if the results are positive or negative. It doesn't affect my trust in religion or in science," Perego said. "If I were to find a child from Joseph Smith from a plural marriage, I would think that was cool because we would learn something more about what was going on."
But not every case can be solved. A few alleged children of Joseph Smith died as infants and their burial places are not known. Descendants of daughters are particularly difficult to test conclusively because the easy-to-identify Y chromosome signature only works to identify male descendants.
[Images of Sarah Pratt, Orson Pratt and Joseph Smith]