The Matsumae clan rule over the Ainu must be understood in the context of the expansion of the Japanese feudal state. Medieval military leaders in northern Honshu (ex. Northern Fujiwara, Akita clan) maintained only tenuous political and cultural ties to the imperial court and its proxies, the Kamakura shogunate and Ashikaga shogunate. Feudal strongmen sometimes located themselves within medieval institutional order, taking shogunate titles, while in other times they assumed titles that seemed to give them a non-Japanese identity. In fact, many of the feudal strongmen were descended from Emishi military leaders who had been assimilated into Japanese society. The Matsumae clan were of Yamato descent like other ethnic Japanese people, whereas the Emishi of northern Honshu were a distinctive group related to the Ainu. The Emishi were conquered and integrated into the Japanese state dating back as far as the 8th century and as result began to lose their distinctive culture and ethnicity as they became minorities. By the time the Matsumae clan ruled over the Ainu, most of the Emishi were ethnically mixed and physically closer to Japanese than they were to Ainu. From this, the "transformation" theory postulates that native Jōmon peoples changed gradually with the infusion of Yayoi immigrants into the Tōhoku, in contrast to the "replacement" theory that posits the Jōmon was "replaced" by the Yayoi.