Algae start growing when they receive certain chemical signals telling them it is a good time to start a growth cycle. A tank full of healthy, growing plants will prevent the small ammonia surges that are one of the signals algae look for. Consistent CO2 concentration in the water during all lights-on periods will eliminate the fluctuating CO2 level that is another signal to the algae. As far as nutrients go, algae always have plenty to eat, but can't always be assured of access to light for long enough to go through a growth cycle. That is the major problem algae faces.