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I know I will be contradicted on this, but NO. A skimmer is not absolutely necessary for a FOWLR. 1-1.5 lbs of live rock per gallon, 20% water changes every two weeks and a tank that is not overstocked and you will be fine without a skimmer. I know this to be true because although I have had SW tanks for twelve years I once went a period of five years with no skimmer and never lost a fish.