OK EVERYONE PAY ATTENTION:
Both the aerobic and anaerobic 'systems' are developed quickly. A few weeks at most for regular runners who are out of shape.
BUT THAT'S NOT THE POINT!
Running fast helps all your other slower paces too, so a good training plan includes some speed work during base training, because it will help you get more from your endurance training by stimulating the nervous system to help you run more efficiently at all paces.
What is most important is doing the right amount of training at different paces, not to develop the aerobic and anaerobic 'systems' that's just bad science, but to develop more efficient use of all the different fuel sources by gradually improving your stride rate, stride length and keep both going for longer.