"Are there any statistics on the benefits/detriments of polygamy?"

There are a number of organizations that can provide you with general stats. One organization is at http://www.polygamy.org.  The founder is a former FLDS wife and can provide certain statistic.

There is a research resource located here:  http://www.apologeticsindex.org/122-polygamy-research-resources .  The site contains numerous links to resources.  Keep in mind that most information and research-based organizations consider polygamist communities cults, because they practice severe "isolation" techniques consistent with cult behavior, generally.  If that colors your perspective on the information these organizations are providing, then perhaps you want to go to the source.

You can also read Jon Krakauer’s excellent book, "Under the Banner of Heaven," which profiles the history of the LDS movement (and later the FLDS movement, which still practices polygamy).  There are few stats in the book (some, but not a lot), but there is significant factual data about the polygamist movement and what positive and negative aspects to it are present.  I found it to be a fascinating read.  Indeed, years before this current debacle in Texas, he chronicles the lives of the followers of Warren Jeffs (whose father Roland Jeffs was the former leader until his death).

Good luck.  I hope you figure out what many people who’ve studied the groups have learned.

By the way, I do know there are quite alarming statistics about the birth defects among the kids. 

Since it is illegal & if practiced it is kept quite secret, I doubt that a polygamous group would want anything made public. 

 

Unless there is signigicant in-breeding, there should be no detrimental effects.  I don't recall any specific problems from multiple spouses in my readings of history.  There were problems when siblings married or aunt's & nephews or neices & uncles married in Ancient Egypt or successive marriages of 1st cousins in Medieval to Modern Europe.

 

You posed a fine question.