I just have some anecdotal evidence of a few families I know.
In one family, the parents got married in the ‘50s, and they had four children. Of those four children, only two got married. Those two who got married produced two children. Those two children today are in their late 30s, and neither has children. That family line is dying out.
In another family, the parents also got married in the ‘50s, and they had three children. Those three children all got married. Those children had 7 children among them. Of those 7, only three are married. And of the three who were married, only one has had a child. A group of 7 children are producing only 1 for the next generation.
Another family, the parents got married in the ‘70s. They have four children. Of those four only two are married. Of the two who are married, they produced two children for the next generation.
Everyone think about your own families or other friends of the family, or others in your community. And see if the current generations or having children at the same rate as their parents and grandparents did.
Definitely the case in my own family. I was one of six children born from 1951 to 1961. The six of us all married but had only five children in total from 1982 to 1995. Of those five, so far just two have one child each.
It might depend on where we start counting. If I count from one set of grandparents, that family tree might live on forever, even though each subsequent generation had children at a lower rate. Those grandparents had eight children, 20 grandchildren, 37 great-grandchildren, and at last count, about 35 great-great grandchildren with more to come. That last generation will probably end up closer to 45, and they have begun having children of their own. But, if you started counting from my generation, some branches might come to an end.