Is the diversity in modern Turkish appearance today due to the early Turkish sultans marrying European women, mixing Turkic and European genes, and the mass migration of Muslims from all over the world and basically anyone that converted to Islam just assimilated into the culture during that era ?

Is the diversity in modern Turkish appearance today due to the early Turkish sultans marrying European women, mixing Turkic and European genes, and the mass migration of Muslims from all over the world or basically anyone that converted to Islam just assimilated into the culture?