Limitations are important in understanding DNA studies, and often are not stated in popular reporting.
MtDNA is the energy producing part of the cell, directly transmitted from mothers to offspring w/o recombination. If you analyze mtDNA, you know your maternal lineage, mother's mother, etc. You carry half the mtDNA of you parent generation, that of 1 of 4 of your grandparents, 1/8th of your great-grandparents, 1/16th. 1/32nd. 1/64th, etc. It can readily happen that your apparent physiognomy does not match that of 1/16th or less ancestry ('existence of races' is merely our mental/cultural category/perception, and not real).
So, for 1,000 years ago, 40 plus generations back, mtDNA still evidences only one female's mtDNA, only 1 of your "1,099 TRILLION" possible maternal ancestors during that time. While we each have mtDNA from a single lineage from that long ago, and much longer of course, the range of inferences that can be drawn is very limited because of the very high number of possibilities.
Likewise with y-chromosone study in males, for each generation going back in time the sample size is half unless you only have one grandfather, ie. cousins having offspring!
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