RYE

In Kartvelian 'rye' is დიკა [dika]. In Ukrainian/Russian 'dik-' means 'wild'.

Does rye have any relevance to wilderness?

Yes. In fact, it used to be considered a weed (or a wild cereal):
http://lingvoforum.net/index.php?topic=26176.0

Hence, the Ukrainian/Russian word dikiy must be regarded now as possibly derived from the Kartvelian root dik.