Generally, both a decaying mulch and a living mulch are going to positively benefit a productive tree.
The living mulch (plants) can serve many functions: shade the soil to reduce water evaporation, build soil with roots, fix nitrogen (legumes), produce biomass to later be used as dry mulch, bring up nutrients from subsoil (dynamic accumulators), fill up niche space (depending on the type of tree the rhizosphere will have open zones that can be tapped into), attract beneficial insects and pollinators, fumigate the soil of nematodes, provide habitat/shelter for invertebrate species, block out unwanted species, and more...
The decaying mulch (
wood chips, leaves, etc.) will also serve many functions, especially in the short term: conserve moisture in soil, keep soil warm in winter, block out unwanted species, add organic matter to soil and build soil life, and more...
In the early stages of setting up a
polyculture dominated by a productive tree it is worthwhile to bring in available dry mulch to get the system started. Ideally, once the polyculture is established you can just chop and drop mulch, always maintaining both living and decaying mulch.
Elan