As you may know, Ubuntu Mate is the newest official *Buntu flavor and has released Ubuntu Mate 14.10, Ubuntu Mate 14.04 and Ubuntu Mate 15.04 (in this order) since it had been adopted in the Ubuntu family.
The Mate Desktop started as GNOME 2 fork back in 2011, when the Linux systems adopted GNOME 3. Today, MATE is available by default on Fedora, Arch Linux, Linux Mint and BSD (and forks of this systems).
Mate Desktop 1.12.1 has been recently released, bringing mostly bug-fixes.
Installation instructions:
The latest versions of Mate desktop are available via the Ubuntu MATE PPAs, so installing it on Ubuntu 15.10 Wily Werewolf and Ubuntu 16.04 Xenial Xerus should not be too difficult.
Just add the PPA to your system, update the local repository index and upgrade all the packages and install the mate-dock-applet package. Follow the instructions for your system exactly.
How to install MATE Desktop on Ubuntu 16.04 Xenial Xerus:
$ sudo add-apt-repository ppa:ubuntu-mate-dev/xenial-mate
$ sudo apt-get update
$ sudo apt-get upgrade
$ sudo apt-get install mate-dock-applet
Optional, to remove Mate and reverse the system to its previous state, do:
$ sudo apt-get install ppa-purge
$ sudo ppa-purge ppa:ubuntu-mate-dev/xenial-mate
How to install MATE Desktop on Ubuntu 15.10 Wily Werewolf:
$ sudo add-apt-repository ppa:ubuntu-mate-dev/wily-mate
$ sudo apt-get update
$ sudo apt-get upgrade
$ sudo apt-get install mate-dock-applet
Optional, to remove Mate and reverse the system to its previous state, do:
$ sudo apt-get install ppa-purge
$ sudo ppa-purge ppa:ubuntu-mate-dev/wily-mate