1. All of the various possible descendants have not been tested for paternity yet.

    Ugo Perego stated:

    Perego said that brings to five the number of people that some believed were Smith descendants whose paternal DNA does not match up with his. To date, at least seven other early Latter-day Saints have been identified in various historical documents or in later writings as potential Smith offspring, he said.

    Hales assembled a list of potential progeny and those who have been tested for paternity: Allegations of Joseph’s Paternity. Although Hales discounts the possibility that Joseph was father in most of these, they have not yet been eliminated with genetic testing.

    In fact, Don Bradley recently (December 24, 2018) claimed that he had identified a child of Joseph Smith by polygamy and is currently doing Y-chromosomal testing to confirm or falsify his hypothesis.

  2. Smith may have used John C. Bennett’s services or he or someone in Nauvoo perhaps learned to perform abortions from him.

    See Hale’s LDS apologetic/scholarly perspective here.

    So, good evidence supports the fact that Bennett was practicing abortion and that he could cover up a trail of philandery using it. Sarah Pratt claimed Bennett practiced abortion on some of Joseph Smith’s plural wives, but most LDS scholars discount her testimony due to possible exaggeration and inconsistencies in it.

    LDS scholars also discount the abortion hypothesis because, they say, it would make Joseph look hypocritical since he taught that celestial marriage was for the purpose of raising up seed. However, the fact that he was sealed to a 7 month pregnant woman strongly suggests that raising up seed was not a huge practical concern for Joseph.

    Finally, it is important to note that Bennett was only around Joseph Smith for some of the time he was engaged in plural marriage.

  3. Various birth control methods, including withdrawal, may have been used.

  4. Joseph was likely not having much sex with his plural wives in comparison to Emma.

    • Some of his wives were kicked out of his home by Emma (Fanny Alger, Eliza Partridge, Emily Partridge) thus likely terminating any potential sexual relationships with these women.
    • Emma was a limiting factor in access to Joseph (Emily Partridge stated: “Emma knew that we were married to him, but she never allowed us to live with him” and the letter to Sarah Ann Whitney: “the only thing to be careful of; is to find out when Emma [Smith] comes then you cannot be safe, but when she is not here, there is the most perfect safty”)
    • Since polygamy was not widely acknowledged, Joseph had to keep liasons secretive in general, and this was described as difficult (e.g., Sarah Ann Whitney letter: “only be careful to escape observation, as much as possible”)
    • Emily Partridge testified that she slept in the same bed with Joseph “Only one night” although her testimony seems to indicate sexual intercourse on some other occasions.
    • An examination of his marriage timeline suggests that, at times, he was marrying one or more new plural wives every few weeks. It is difficult to imagine anyone having sustained sexual relationships with any given wife under such circumstances.

      Brian Hales wrote:

      An important consideration is the phenomenon of diminishing returns. After a certain point, the addition of new plural wives did not necessarily increase Joseph’s opportunity for additional sexual encounters with each plural wife. Such a dynamic would, inevitably, have curtailed chances for conception on the part of his plural wives.

  5. For the polyandrous unions, Joseph may have been competing for fertilization with an existing married partner

    For some of Smith’s polyandrous marriages, the paternity of his children was unclear to the mother. For instance, Sylvia Sessions told her daughter Josephine that she was sired by Joseph Smith, but it turns out she was not fathered by Smith. This strongly indicates that Sessions was sleeping with Smith and her legal husband in close temporal proximity.

  6. For the polyandrous unions, if a woman is already pregnant, then she cannot cannot become pregnant again.

    For instance, Zina Huntington Jacobs was 7 months pregnant when she was sealed to Joseph Smith. If they consummated their sealing at that time, then she could not have become pregnant.

Discussion

Until/unless progeny via a polygamous reliationship is discovered, it is difficult to know with absolute certainty that Joseph Smith was having sex with anyone except Emma. Still, as discussed above, a variety of possibilities exist to help potentially account for Joseph Smith not impregnating his plural wives. Regardless of direct DNA evidence from progeny, significant first-hand testimony exists that Joseph did have sex with many of his wives. In addition, other early practioners of polygamy—who were introduced to the practice by Joseph Smith—were impregnating their wives (e.g., Brigham Young), so we have good reason to believe that Joseph’s polygamy was not practiced in radically different terms (i.e., completely asexual).