Not intended to be racial in nature. I was wondering that given the scale of the empire back then, it seems impossible for the Romans to have completely emigrated from that region when the Ottomans took over.
They are related; DNA studies have shown a substantial but minority infusion of genes from Central Asia; but by and large the Turks of today are descendants of the area's previous inhabitants.
The region of Asia Minor and Thrace, in other words, can be seen as multi-ethnic as relating to biology but containing a mono-linguistic and mono-religious nature at present. This has to do with linguistic, religious, and cultural replacement more than anything else.
Modern Turks carry ancestry from Central Asian nomads, Greeks, Pelasgians, Asia Minor aborigines, Hittites, Iranian groups such as the Medes; Jews, Armenians, Galatians, Bulgars, Gypsies, and Romans, besides Slavs, Albanians, Arabs, Kurds, Caucasus peoples, and even Germans. There are communities of Afro-Turks as well.
Modern nationalism, as it formed, caused lots of people to forget their origins due to economic/social necessity. As Catholic Austria conquered into the Ottoman Empire, it was not comfortable with Islamized Balkan people, and many of these moved toward Asia Minor. Likewise, in Turkey to have full civil rights you need to speak Turkish and identify as a Turk. This has resulted in more ethnic groups remaining in Turkey than leaving over the centuries; partly due to geography as Turkey is a large peninsula, with the land approaches hard to cross, making the place attractive to migrants who then saw little reason to leave.
Political realities, impelling people to join the greater tribe, have erased from view many of the old cultures. Many of today's Turks have Romans in their ancestry, though this would not be practical to trace as many linguistic/religious transformations caused the loss of information.