Hens (of any species) will lay one egg a day until they have a full clutch (for chickens that is usually between 5 and 20, give or take), then either take a break for a day or two (which is usually the case) or go broody (attempt to set on and hatch eggs). Broody hens will also set on eggs of other hens and even duck, guinea, or quail eggs. Roosters have nothing to do with it except for that, obviously, the eggs will not hatch without one. Hens without a rooster are just as likely to go broody and lay just as well as hens in flock with a rooster. However, hens that are setting on eggs and raising chicks will not lay until they are finished.
