Interestingly, while these days most societies are monogamous, polygyny(1) has not completely disappeared. Looking around the world, a few societies and cultures still allow and/or practice polygyny. There are some societies, such as some African indigenous tribes, where men have multiple wives. However the most well known cases that still practice polygyny are parts of the Muslim world and parts of the Church of Jesus Christ of Latter-Day Saints (Mormons) – more specifically the so called Mormon Fundamentalists.Of course, you're asking the obvious question: "But correlation isn't causation, so is there any evidence one begets the other?" Right you are. And actually, no, the Belgians concede, it doesn't really appear that there's any connection at all. ("We conclude that there is no direct causality in either way, but that other factors cause specific changes in both alcohol use and marriage arrangements.") Although this is only implied and not literally written in the paper, the authors add, "However, writing about booze and sex is a sure-fire way to get a lot of attention, and so we felt the paper was nevertheless a good use of our time."
What is intriguing is that these two groups are characterized by another distinguishing characteristic: they do not consume alcohol. While these groups are not the only social groups in the 21st centuries which do not consume alcohol, alcohol is widely consumed around the world these days – and in virtually all monogamous societies. Hence, it is intriguing that the two main social/religious groups which still practice polygyny also do not consume alcohol.
(1) 1 Since the term “polygamy” is often use instead of “polygyny”, an important distinction should be pointed out: polygamy (from Greek : πολύ - many, and γάμος – marriage) refers to the case of an individual (male or female) having several partners at the same time; polygyny (from Greek : πολύ - many, and γυνή – woman) occurs when a man has multiple women at the same time; polyandry (from Greek : πολύ - many, and άνδρας – man) when a woman has multiple men at the same time. However, since polyandry is very rare, many authors often use polygamy when referring to polygyny.
Mostly I pass it along for the footnote, which was news to me.