Bushman writes on Joseph's relationship with Fanny Alger and plural marriage generally; believes it was probably Joseph's first plural marriage in mid-1830s which he resumed in 1841.
Richard Lyman Bushman, Joseph Smith: Rough Stone Rolling (New York, NY: Alfred A. Knopf, 2005), 323–327, 437–446
[Richard Bushman writes on Joseph Smith's relationship with Fanny Alger; highlights the ambiguity in the historical record but seems to side on the idea that it was JS's first plural marriage, which he then resumed in 1841 by subsequently marrying Louisa Beaman.]