Anyone else find this an incredibly difficult article to make any sense of? I've read a lot of epidemiological research and I haven't really come across "primiparas" before, why not just call it "first births"? That's what the population genetics papers do. The only technical term in here that I am familiar with is "menarche" (first period/menstrual cycle). The rest just feels like obfuscation to make the authors seem smarter.
The massive Odds Ratios presented further down are suspicious as well - if I saw those kind of effect sizes based on observational data I would be running a lot of sanity checks and models designed to test the stability of my model outputs etc.
I don't think this will be the study to convince me that Evolutionary Psychology is anything more than snake oil.