Many new people who are cycling their tank for the first time are told that various algae blooms are normal during the initial cycle. What they should ask is; why does this happen? And, why does it happen specifically during the initial cycle?
One of the more common ways of cycling a tank is to introduce live rock. However, even cured live rock and sand will experience a small amount of die-off (of algae, worms, sponges, etc.). Heterotrophic (organic material consuming) bacteria will attack whatever is dying off. This produces ammonia and begins the nitrogen cycle.
Reaching a Balance
To understand the cycle, we must first understand the basic needs of the bacteria that run the cycle. Bacterial populations are highly dynamic. They will regulate their populations based on what nutrients are available to them. If there is an excess of a nutrient they use, their populations can explode. Once that nutrient (or nutrients) is gone, their populations will drop. In our tanks, we have many different kinds of bacteria which will all (eventually) reach an equilibrium with each other and with what nutrients are available. The process of getting to this "equilibrium" is what we call "cycling" in a tank.
Needs of Bacteria
There are a few things every bacterium needs to live and reproduce. Some bacteria need Ammonia, some need Nitrites, some need Nitrates, some need Sulphates, etc. However, there are two things all bacteria need; Carbon and Phosphorus. The alkalinity of your saltwater (or CARBONate Hardness) provides all of the Carbon that bacteria will ever need. Now, what about Phosphorus? Let’s say that your rock was almost completely cured, your sand is brand new, and you used RO/DI water that was 100% phosphate free. You might wonder where all the Phosphorus could come from. Phosphates naturally adsorb (chemically bond) with CaCO3 (aka aragonite). Aragonite is present in a lot of sands sold for reef aquariums and is also the principle component of live rock. Thus, sand and live rock can become a source of Phosphorous. Bacteria have the ability to produce enzymes that can "melt" the Phosphorus out of the aragonite. Before the bacteria populate, the Phosphorus is "locked up" chemically and can’t be used by algae. Unfortunately, they can release more phosphate than they use themselves. That extra phosphate helps algae grow. But before you start resenting these bacteria, remember that we NEED these bacteria if anything in our tanks is to survive.
Busy, Busy Bacteria
Now we have the heterotrophic bacteria producing Ammonia and the Ammonia Oxidizing bacteria releasing Phosphorus. The later will convert as much Ammonia to Nitrites as possible. Eventually, the Ammonia source will diminish substantially (almost to nothing). Some of the Ammonia-needing bacteria will go into a "dormant" state, but even more will die. This die-off of bacteria produces small amounts of Ammonia and releases a lot of Phosphorus. This phosphorus is now available for use by algae.
Fortunately, the Nitrite Oxidizing Bacteria are taking up as much Nitrite and Phosphorus as possible (competing with algae). Eventually, the Nitrite Oxidizing Bacteria will face a drop in Nitrites and their populations will drop in response. The process of Nitrification (conversion to nitrate) is quick and easy. Unfortunately, the process of de-Nitrification (conversion of nitrates to something else) is much slower and requires specific conditions. Long-story-short, you are left with a bunch of Nitrates and bio-available phosphorus.
An Algae Finale
Most aquarists know that algae love Nitrates and Phosphates. The Nitrogen Cycle produces both of these. And this is why we do water changes and use protein skimmers. Some aquarists grow macro-algae as a way to control nitrates and phosphates. Others use any variety of mechanical and/or biological filters. In the end, we're all trying to accomplish the same thing, one way or another; to control these products of the nitrogen cycle.
DISCLAIMER: Please understand that all the activities of algae and bacteria in aquariums have yet to be thoroughly studied (or studied much at all). Written here are intelligent speculations based on information known about wild ecosystems applied to what we know (or at least think we know) about aquariums.