Duplicity as a snap package will run just fine on Ubuntu Xenial (16.04). You do not have to do anything other than install it, like so:
$ sudo snap install duplicity --classic
This will replace the old 0.7 series duplicity, which is EOL, with the newer 0.8 series duplicity which is backwards compatible, as always.
Note: there are no PPAs supporting Xenial at this time. Xenial is locked to version 3.5 of Python and that is too old for the 0.8 series. The snap system is self-contained, so I could use a newer version that works with duplicity.