lol the live rock dose biological filtration NOT chemical!!!!! yes live rock will removes nitrate from the water!!! how ever you need high turn over(20x turn over an hour or more is normal now) and unless you have very low stock levels nitrate will billed up over time so water changes are needed!!! there is controversy over what a skimmer is class as but id say its chemical!!! a skimmer(or protein skimmer) its self dose not remove nitrate but removes proteins which should stop the proteins being turned into ammonia then nitrite and finely nitrate!!! so in this way it help stop nitrates!!! denitrifying bacteria are the ones which brake down nitrate however they are anaerobic meaning they dont like oxygen and so live deep in the live rock and in the deep parts of a dsb(deep sand bed)!!! live rock, dsb's, large refugiums and water changes are the only ways of removing nitrate!!! a refugium removes it by the growth of marine plants!!!!