This simulator will help you to visualize how frequently human lineages go extinct. Select a fertility rate and click "Go" a few times.
Current Fertility Rates: Rates have plummeted throughout the developed world. Current estimates are 1.9 for the US, 1.8 for the UK, 1.35 for Italy, 1.45 for Japan, and an astonishing 1.17 for South Korea. See Wikipedia for details. Try these rates with the simulator to see how soon we can expect major extinctions of Y chromosomal and mtDNA lines and surnames.
Historic Rates: Humankind lived on the thin edge of extinction for millennia: in Paleolithic times the fertility rate was about 2.0003. Things took off with the advent of agriculture in the Neolithic with a rate of 2.04. From the Bronze Age until recently our numbers grew steadily with a rate of 2.1, and for a generation we've rocketed at a rate of 2.9. Very recently it's now down to about 2.4 globally and much lower in the developed world, as noted above.
Implications: We do not need natural disasters or wars to create population extinctions and bottlenecks. Run the simulator at rates of 2.04 (Neolithic Era, 5000 BC - 1000 BC) or 2.1 (Historic Era, 1000 BC - 1850 AD) and you will see surviving lines (in blue) that touch the x-axis after 10+ generations (300+ years) and then climb again. These are natural founder events: the diversity of descendants' DNA is reset to zero; that one survivor is a new Adam or Eve as far as their Y or mtDNA is concerned. This natural occurrence has a profound effect on STR patterns that we can see today.
Yes, extinctions and founder events are more likely when there are plagues and wars, and Y DNA patterns are more likely to flourish when a founder has many sons and grandsons. But such events only amplify what is already a natural stochastic process.