Recently (a few months ago) the Jomon have been shown to have carried not only Neanderthal DNA, but also Denisovan DNA. This evidences their ties with Melanesians/Papuans.
The study shows that Ainu are related to Sahulians (Papuans/Australian Aborigines). The level of Ainu admixture in ethnic Japanese highlighted by this study is consistent with higher Papuan+Melanesian admixture detected by others among Japanese than among other East Asians (http://oi57.tinypic.com/34ga841.jpg)