You can build the necessary libXp libraries from the Ubuntu source distribution.
Download the source package from

[packages.ubuntu.com]

You will need three files.

libxp_1.0.2-2.dsc
libxp_1.0.2.orig.tar.gz
libxp_1.0.2-2.diff.gz

a. Copy these 3 files to a new directory. In this directory type the command:

dpkg-source -x libxp_1.0.2-2.dsc

b. This will build a new sub-directory called "libxp-1.0.2".

cd libxp-1.0.2

and type the command

dpkg-buildpackage -uc -us -rfakeroot -b

Note: for this build to complete, I needed first to install these packages

dh-autoreconf quilt x11proto-print-dev libpng16

apt-get install dh-autoreconf quilt x11proto-print-dev libpng16*

c. When the build completes, you will have the following two packages in the parent directory:

cd ..

libxp6_1.0.2-2_amd64.deb
libxp-dev_1.0.2-2_amd64.deb

d. Now install these two packages on your Ubuntu 16.04 LTS system

dpkg -i libxp-dev_1.0.2-2_amd64.deb libxp6_1.0.2-2_amd64.deb

and afni will run properly under Ubuntu 16.04 LTS.

Brad