Polygamy and Fertility?

In the recently published statement of the LDS church on polygamy, it is suggested that Joseph Smith Jr's thinking on polygamy began concurrently with his Bible revision project, specifically the Old Testament, after the arrival in Kirtland, Ohio, in 1831.

It is noteworthy that up to that point in their marriage, and especially in Kirtland, all of the children that Emma Smith bore died at birth.

• Alvin Smith (b. and d. June 15, 1828)
• twins Thaddeus and Louisa (b. and d. April 30, 1831)

The first child to be born of Emma Smith and live to full age was not born until 1832. The remaining children of Emma and Joseph are:

• Joseph Smith III (November 6, 1832-December 10, 1914)
• Frederick Granger Williams Smith (June 29, 1836–April 13, 1862)
• Alexander Hale Smith (June 2, 1838-August 12, 1909)
• Don Carlos Smith (b. 1840, died at fourteen months) 

and 

• David Hyrum Smith (November 17, 1844–August 29, 1904). 

Now, when people (such as Daniel Bachman) speak of the spring of 1831, they are talking about the revelations in Doctrines and Covenants and not about living celestial marriage. 

Joseph Smith Jr did not try anything in the direction of polygamy until 1835, with Fanny Alger. By then, Joseph Smith III had been born and was almost three years old.