For the most part, algae comes and goes at random. The type of algae bloom you get is mostly random.
That said, we know of at least four factors that control algae:
1. Healthy plants produce allelopathic chemicals that are harmful to algae (and sometimes other plants).
It has never been demonstrated that aquatic plants produce allelopathic chemicals, nor has it been demonstrated that if they do, the chemicals are effective against any form of algae, let alone all of the species that annoy us.
2. Water high in humic acid (tannins) content creates conditions inhospitable to most algae (and most bacteria and many plants).
I have never heard of this before. What is the source of this information?
3. We also know that periods of low CO2 availability and high light are more beneficial to algae than plants.
I think it is more accurate to say that fluctuations in the CO2 concentration in the water from day to day can lead to BBA, one form of algae. High light encourages growth of both plants and algae.
4. We know that we can limit the position of some essential nutrients to the soil where plants (being complex organisms) have the ability to extract them and algae does not. Ferrous iron (Fe2+) is commonly cited as an example.
Nutrients in the substrate can leach out into the water. Diana Walstad has said, as I recall, that nutrients are prevented from crossing the substrate/water boundary, but I have read that other experts disagree with this.
All common "systems" of keeping planted tanks use one or more of these methods directly or indirectly.
Algae is rarely a serious problem with low light tanks. When you have medium and higher light, algae become a potential serious problem. Using adequate fertilizing and consistent CO2 concentration from day to day, along with very good regular maintenance will go a long way towards avoiding those problems.