A mother passes on her mitochondrial DNA to her daughter, who then passes it on to her daughter, _________.
Some phrases that come to mind are
and so on/fourth and
et cetera, but these aren't specific enough (they can be used for non-iterative lists e.g. "I like fruits like apples, bananas, and so on").
Another phrase I can think of is
ad infinitum, but that emphasizes length rather than repetitiveness.