There's not actually an easy answer so I don't know if I can make it simple. Let's see if I can explain the initial cycle a little bit and then people can ask questions. Hopefully, by the end it will make sense.
What is the cause of the initial algae cycle Typically, people put live rock in that is not fully cured. There are algaes/sponges/worms etc. that die and rot during this process producing Ammonia. The Ammonia Oxidizing bacteria will go through a population explosion. They need a few things including Ammonia, Carbon, phosphates, and living space. Now they have them all. Even if you filled the tank with RO/DI water that is 100% phosphate free, there's still plenty of phosphates as phosphates naturally adsorb to CaCO3 which is what your LR is made of. A bacterium doesn't have a mouth so it utilizes enzymes to literally make a soup and they are able to liberate the adsorbed phosphates right off of the LR or LS.
The end product of this population explosion is Nitrites and a lot of phosphates as the Ammonia Oxidizing bacteria start starving to death. The phosphates were originally chemically bound to the CaCO3 and not bio-available but now they are.....but not for long. Now Nitrite Oxidizing bacteria are going through a population explosion and are grabbing the phosphates like white on rice. Some of the phosphates might have been nabbed by algaes but not too much because bacteria are more efficient. The Nitrites will slowly go down and the end result will be Nitrates and a lot of bio-available phosphates as the Nitrite Oxidizing bacteria die off.
So what are you left with after the initial cycle? Quick answer is Nitrates and phosphates....BOTH OF WHICH ARE ALGAE FOOD. If you have algae spores in your tank, you're going to get algae.
Brown diatom algae occurs when there are silicates present in the water or in the pore space of the LR. Diatoms grow, utilize all of the silicates and disappear if your top-off water or water change water is free of silicates. Additionally, many people will grow Scypha sponges
that will also aborb Silica in your overflows, sumps, etc. Diatoms don't turn to green algae, it is usually just starved out by more efficient critters like sponges or starved out due to lack of Silica added to the tank.
There are MANY forms of green algae....I don't know how many in total.
Red algae (I'll assume you are talking about cyanobacteria vs Rhodophyta) can grow anytime there's phosphates, nitrates, and light.
Not all tanks go through a diatom stage. I just set up a new mantis tank about 3 weeks ago with 100% pure RO/DI water, rock that didn't have Silica in it, etc.
Algae For dummies 
