Are mulberry trees self fertile?

And by that I do not mean will they produce fruit by themselves (I know the answer to that one is yes, the one I planted several years ago makes plenty of berries and its the only one around that I know of). What I mean is, are the berries from a single isolated tree fertile, in that they will grow new trees?

Mainly wondering if the birds that beat me to the majority of the berries are out there planting new trees through the woods.