In many species, either the male or the female spends more on their mutual offspring. Among polygynous lions, a single male donates sperm and little else to the pride of related females, who hunt and care for the cubs communally; the males are big and have lots of decorative hair. Among polyandrous cuttlefish, the females leaves as many eggs in a male's nest as the male is willing to take care of, and then races off to find another male to take care of more eggs; the females are big and have lots of useless decorations. In most cases of polygamy, the "harem gender" devotes more to the offspring than the "promiscuous gender." In some species (humans for example) the two genders have disparate biological investments in the offspring but you find monogamy.

Why?

One of the reasons is that the potentially promiscuous gender isn't sure when the potential harem gender is actually fertile... the only way a male can be sure that a female's child is theirs is to guard her from other males during her fertile periods until pregnancy is ensured. Sexual crypsis is the biological term for "hiding fertility status" (think encrypted fertility). It has two effects big enough for my to put them in this node:

1. With humans, mate guarding usually involves attention and resources devoted to the female and it is in her interests to prolong and promote the guarding. (Did you think you were hanging out together because you loved each other?!? What made you think that?) If the female might be fertile at any point in the month, the male would tend to spend all his time guarding her and have little time to guard other females. Thus sexual crypsis (in the olden days before genetic testing) encourages monogamy. Storks and some varieties of ferret are sexually cryptic and appear monogamous.

2. While it might be easy for a guy to beat up anyone who looks at her on one specific day out of the month, its hard to keep watch around the clock all year. This affords women the opportunity to "sneak off" and fool around... and sexual crypsis doesn't just make spread the guys attention thin, it also allows the "partner in adultery" to imagine that they snuck in at just the right time and the child is actually theirs. If "all the men of the villages" think that they might be the father, and the husband is sure he's the father, the woman's child will have many more resources devoted to it than otherwise. So sexual crypsis (absent genetic testing) also encourages adultery. When biologists started testing those storks and ferrets they got a bit of a surprise. Storks and ferrets cheat too.

See late entries in Why do men like women's breasts?