“How is this child spacing achieved? Mothers breastfeed their babies for at least the first two years of life, and unrestricted breastfeeding suppresses ovulation, preventing further pregnancies. How exactly this mechanism works is still under debate — and do not try this at home: it has been shown that in well-fed, western civilisations with a limited nursing culture breastfeeding alone is not a reliable method of birth control. The continuous, around-the-clock suckling of infants produces hormones in the mother that suppress ovulation, but the energy balance of a lactating woman may also have something to do with it (Thompson 2013).”
It’s also been hypothesized that due to the very low levels of body fat, Paleolithic women only menstruated about 4 times per year. Plus, having more partners doesn’t lead to any more pregnancies than having just one because once pregnant, you’ve got 9 months (at least, probably more) before it’s possible to get pregnant again. Three partners in one year can still only lead to one pregnancy. As I said in the OP, modern hunter-gatherers (even those with just one husband) still have an average of 39 months between babies. It’s not the number of partners that determines the spacing between children, it’s these other factors that have to do with a physically demanding lifestyle, and with babies who suckle at will. Still, it was a very good question.