These first two sentences are essentially WRONG.
This is how it should be worded:
Genealogical ancestry is able to investigate the “ancestry” of individuals (or an entire population), without examining any specific or general GENOME. The impact of a single male, (e.g., Genghas Khan) is NOT on the genome, but on the legal, cultural or traditional status of individuals known to be his descendants, rather than on the genetic contents of their cells.
^^^ The re-written statements, based on yours, reflect Genealogical affects on individuals or populations without any recourse to genes, genetics or genomes.