Keep in mind that mortality prior to reaching one's first birthday was upwards of 50% in most premodern societies, so the key factor here seems to me to be not only fertility, but the ability to wield social capital over multiple generations (employing court physicians, wetnurses, etc) to ensure that all those kids actually live to adulthood. Hence why I find this study so interesting - it's using genetic evidence to map the flows of social power across generations (like with the dynasties of Genghis and the Qing).