Author Brian Hales examines mainstream Mormon (The Church of Jesus Christ of Latter-day Saints) polygamy or plural marriage extensively in several volumes: Joseph Smith's Polygamy: Toward a Better Understanding, Joseph Smith's Polygamy, Volume 1 History (and volumes 2 and 3). Also Richard Bushman's Joseph Smith: Rough Stone Rolling examines polygamy in the early Mormon church. For polygamy in the Utah territory, Brigham Young: Pioneer Prophet, by John Turner and Brigham Young: American Moses by Leonard J. Arrington.
In Utah in the late 1840's until 1890 when polygamy was banned so that Utah could be eligible for statehood (and reaffirmed in 1904 for Mormons in other countries such as Canada and Mexico), there were no noticeable or documented migrations of men leaving the church or Utah because of a lack of women. Certainly, Utah, like many frontier territories, had a ratio of more men than women, but it also experienced great influxes of convert immigrants from Europe. As well, many men from Utah left for other places on church missions, military duty (ie the Mexican War and the Mormon contingent in California), or work elsewhere in mines and on ranches. Brigham Young also organized colonization efforts into new territories in Canada, Mexico, and surrounding territories such as Nevada and Arizona. All these efforts meant a number of men were mobile and able to find wives outside of Utah.
Only 15-20% of marriages were polygamous during this time, and most involved 2 wives.
It also depended on the level of faith or activity in the church, as less active men pursued women of a similar standing.