Various Types of Corals and algae have different photosynthetic needs as well as metabolism of micro/macro nutrients. But this is the basis of the comparative advantage. I'm not trying to harp on iron (the original discussion is on how algae can grown in one place and not another, which is because of comparative advantages) but I'll continue with the iron example for now
Iron is necessary for both green algaes and zooxanthellae inside of corals. It's also extremely limited in ocean waters, often far scarcer than copper. fun facts: 1) many marine microbes have adapted to not use iron-based biochemistry, such as ammonia oxidizing archaea, which have a copper based biochemistry, 2) microbes that do use iron often have elaborate iron sequestering mechanisms, such as one of my faves, siderophores, which actually leave cells and grab necessary ions, then return them to the cell!! Needless to say, the competition strategies for iron (and other nutrients) can be elaborate and are still being understood. That said, iron is generally accepted to be more vital to green algaes evidenced by their genomes containing more iron-containing proteins and enzymes (
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3296057/). Additionally there have been a number of studies that add iron to the ocean waters to observe the extent of algae blooms, which show that it is a limiting resource (
https://doi.org/10.1126/science.1131669). I'm assuming there wasn't a coral bloom along with it lol. In fact, some zooxanthellae are able to survive in *extremely* low iron environments, like Symbiodinium necroappetens, which are even found in bleached corals!
But to the main point, iron deficiencies can hurt both coral and algae. The idea of comparative advantages is: which gets hurt more?? With sufficient iron, it appears that algae can outcompete corals. This might indicate that lowering iron to just above the threshold of corals dying would give you the best comparative advantage and largest coral/algae growth ratio (for clarification, if possible to even dial this in, I'm NOT suggesting to do this, just giving the extreme scenarios)
Again backing up to the actual discussion, as to why algae can grow in one place over another (it's not iron in this case), it's the advantage of light that is optimized for algae growth. Reiterating, if certain nutrients are scarce (i.e. iron or anything that is important for the organisms growth) the algae with the advantage will grow faster and preferably soak up those scarce nutrients. An important point is that we don't even need to know all the nutrients because the same type of algae is competing with itself in another location, almost guaranteeing that it is using the same necessary resources. This argument isn't even about biology, it's physical and deals with probabilistic landscapes. I'll also reiterate that there are a lot of factors at play in anyone's personal tank, but the above is a nice first order approximation (also just the basic idea of a refugium/ATS as a nutrient export lol).
And since we're throwing around credentials in this thread, I'll say that I have a Masters in biochemical engineering and a PhD in molecular biophysics (though if you ask me, this doesn't actually matter since it's the argument that should hold weight, not the credentials).