The reverse, actually. The male plants have flowers with stamens but a rudimentary pistil, while the females have the reverse (here). As in animals, only females make babies (berries). The flowers are pollinated by bees, mainly honeybees.
It’s the other way around - the ones with berries are female plants, and the ones without berries are male plants. If you grow asparagus to eat, you generally want to cultivate only the males, as they don’t waste energy producing seeds (berries). This lets the male plants grow larger and tastier.
Both male and female asparagus plants produce flowers. The plants rely on insects to carry pollen from the male flowers to the female flowers. If successfully pollinated, the female flowers will develop into berries, which eventually ripen, fall to the ground, and sprout.
I have never seen flowers, only berries, and they don’t fall. So at the end of the season I guess I should shake them off. And the plants growing in the driveway probably began with berries blown there by the wind.
This year there aren’t many stalks coming up. I think rather than picking them, I’ll just let them all mature.
In nature, the berries are eaten by birds. The seeds pass through the bird’s digestive tract intact and are dispersed that way. Berries usually don’t blow very far.