To study this, I modified my code, so that rather than having a unique growth constant m, there may be multiple segments during which growth is governed by a different constant. In particular, I simulated a period of g=99 generations with m=1 or m=1.05, but in the last (100th) generation, I set m to 0.5, 0.1, 0.01, representing a bottleneck equivalent to the loss of half, nine tenths, or ninety nine hundreds of the haplogroup population; I will call these "mild", "severe", or "extreme" bottleneck.
In the following table I list the observed reduction in Y-STR variance compared to the case where there is no bottleneck. As usual, the results are averaged over 10,000 runs.
|Change in Variance (%)|
As expected, variance decreases more in an extreme bottleneck, but not as sharply as one might expect. Indeed, if the long-term trend is positive (m=1.05), the expected variance of surviving groups may even increase after a bottleneck. What gives?
During a bottleneck, two things happen:
- Y-STR variance within individual lineages decreases, as e.g. rare alleles are lost, however:
- Low-frequency lineages (which usually have lower Y-STR variance) are more likely to be lost, i.e. to become extinct during the bottleneck.
Predictably, larger groups (created at m=1.05) experience less severe effects during a bottleneck. Note, also that in this simulation, haplogroups did not even grow to very large sizes (only ~1,600 men for m=1.05 and no bottleneck); thus, real-world haplogroups will probably be even less susceptible to bottlenecks.
Bottlenecks don't seem to reduce Y-STR variance dramatically, especially for large haplogroups. So, while they are a potential mechanism for reducing the effective mutation rate, by periodically removing variance, their efficacy is limited.
Indeed, bottlenecks not only reduce Y-STR diversity but also haplogroup abundance. Thus, in order to achieve the same present-day haplogroup abundance, growth in the post-bottleneck eras must proceed even faster than if no bottleneck had occurred, with a therefore higher effective rate during those rebound periods.
In conclusion, while dramatic bottlenecks at a time when human population sizes were small, e.g., the Ice Ages during the Paleolithic, may have effectively reduced Y-STR variance of surviving lineages, this effect seems to have been unimportant in large human populations emerging from the Neolithic onwards.