Applying Emil Je?ábek's results on the dual structure to closed classes of reversible mappings, we define a most general conservation monoid mapping for each conservation arity. We use these to investigate and explore when these collapse or become trivial, guided by Aaronson et al's work on the case for ancilla closed classes of reversible binary mappings. We will also present work in progress towards ideas of dual structures for ancilla and borrowed bit closure.