Really interesting to see this discussion. Please bare with me while I try and get my head around the maths.. Can you totally overcome depletion of a given element within the water mixture by changing only a percentage of the total water mix?. Unless you change 100% of the total mix?. The diagram posted by
@Randy Holmes-Farley demonstrates this perfectly with regards Alkalinity, but could be applied to any substance that undergoes continual depletion.
You can only slow down the drop in overall percentage of a given substance that is being depleted, compared to not doing any changes at all. If you keep changing only 10% then eventually you will be left with practically 10% of what was in the original mix. Obviously this could be over a very long time, and depends on the amount you change.
This works both ways , you can not remove 100% of a given substance by changing only a percentage of the whole water mix. You would have to find a way to remove only that substance.
Have you all fallen a sleep by now, ha ha. Sorry .
IME, the use of water changes is used to slow down this depletion and to dilute any unwanted elements that were not in the original mix. Either caused by contamination, interaction or waste.
Maybe this is one of the factors behind what is sometimes referred to as old tank syndrome. A depletion of positive elements and a buildup of negative elements over an extended period. That's a whole other discussion, don`t` worry I won`t` go there.
In conclusion.
you may want to just skip to this bit.
IMO. using an accurate measurement to define which elements are in fact out of proportion and adding only those elements within that proportion is the only way I can see how a relative equilibrium can be achieved. Or complete a 100% water change. which does not seem practical in a standard reef tank, but is one regularly used by pico reef enthusiasts like myself.