In Utah, women used to marry young. In particular they married Brigham Young, leader of the Mormon Church. The religious leader had 55 wives by whom he had 56 children before he died, aged 76, in 1877. His followers had similar polygamous marriages.

But scientists have now uncovered an odd fact about 19th-century Mormons: the more women in a household, the lower the average birthrate. In other words, the more sister-wives a Mormon woman had, the fewer children she was likely to produce.

"Although it is great in terms of numbers of children for successful males to have harems, the data show that, for every new woman added to a male's household, the number of children that each wife produced goes down by one," said biologist Dr Michael Wade, of Indiana University.

The result is intriguing, because this is the first time scientists have observed humans being affected by what is known as the Bateman gradient, a phenomenon that gets its name from the geneticist who first observed it in fruit flies. The more sexual partners the male fruit fly had, the lower was the fecundity of each of those partners, the 20th-century geneticist Angus Bateman noted.

In fact, examples of the Bateman effect were generally rare, said geneticist Professor Steve Jones of University College London. "The decrease in fecundity of females in these circumstances is not well established. The only other example that I can think of is the Soay sheep. Males fight furiously for females, but after a few weeks the most sexually active males are firing blanks – they have zero sperm left – which means their mates are not being fertilised."

In the study of Mormon families, published in the US journal Evolution and Human Behaviour, the researchers surveyed birth, marriage and death records from the Utah population database, which covers nearly 186,000 adults and 630,000 children who lived or died between 1830 and 1894.

It was during this period that polygamy was slowly being phased out under pressure from state legislators. The results were clear: the more women partnered with a man, the fewer children each of those women had. Exactly why is not clear. Like the Soay rams, men may simply not have had the stamina. Wade says: "It could be owing to competition between women within a plural marriage for shared resources, or it could be owing to other unknown factors."

Neither was polygamy a great deal for males. For every man who had multiple wives, there were many who had none. "For every male that has three mates, there must be two who have none," said Wade. "If a male has even more mates, then the disparity among male reproductive haves and have-nots can become quite high."

The failure of the Utah polygamy experiment should therefore not be seen as that surprising.