The chlorine/CYA relationship has been known definitively since at least 1974 as described in this scientific peer-reviewed paper. For more info, I suggest you take a look at the "Chlorine/CYA Relationship" section of this post, look at this thread in The China Shop, and this post on why the FC/CYA ratio is a decent proxy proportional to the hypochlorous acid concentration.
In simplest terms, there is a race between algae growth that is accelerated by nutrient levels (phosphates and nitrates being most limiting), sunlight and temperature and is decelerated by hypochlorous acid and any algaecides that may be present. Regardless of algae nutrient levels, the growth is ultimately limited by sunlight and temperature so there is a hypochlorous acid level that will kill algae faster than it can reproduce without the need for any algaecide. The problem is that the hypochlorous acid level is not just dependent on the Free Chlorine (FC) level and pH, but also on the Cyanuric Acid (CYA) level since most of the chlorine is bound to CYA in a series of compounds called chlorinated isocyanurates that are not strong oxidizers nor disinfectants (i.e. they don't kill algae). So it is critically important to maintain a high enough FC/CYA ratio to be able to kill algae faster than it can reproduce. If you maintain that ratio, then you won't get algae and won't need any supplemental algaecides or phosphate removers to prevent such growth. Ben Powell was first to create the Best Guess Chlorine Chart based on scientific principles and his own experience.
In my own pool through most of my pool ownership I have prevented algae growth using only 12.5% chlorinating liquid with no algaecide, phosphate removers, clarifiers, flocculants or weekly shocking. It costs me around $15 per month for my 16,000 gallon pool, but I have a mostly opaque pool cover that keeps my chlorine usage to around 1 ppm FC per day even though the pool is used every day for 1-2 hours. A similar story (with somewhat higher chlorine demand) is true for literally tens of thousands of pool owners on this and other related websites.

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