Is there a high probability that nitrate levels will increase in a fish
tank in direct proportion to increased fish food input after the plants
(if any are present) have consumed the maximum amount of ammonia they
are capable of processing?

Yes. Almost certainly.

What conditions must be present where adding any amount of fish food to
a fish tank would not cause an increase in nitrates? Are these
conditions probable in a common home aquarium?

Lack of available oxygen will prevent the nitrification cycle
from converting ammonia to nitrate. It happens.


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