Natural Genocide

One of the worst crimes we can imagine is genocide – erasing an entire lineage from the universe forevermore.  Sadly, nature is so cruel that the usual ups and downs in lineage success mean genocide is the natural long-term result for most every lineage!  Let me explain.

Lineages fluctuate on all scales.  Og falls off a cliff, while Ok does not.  A surprise attack wipes out half of a tribe.  A virus kills off half of those in connected community.  A drought kills off half of those in a region.  Or one lineage finds a mutation useful in the current environment while another does not. 

These usual ups and downs can be modeled via a "lineage swap."  To swap a population, divide it into halves, pick one at random and delete a random half of it, replacing with copies of random selections from the other half.  When the total population size stays constant (and when the halves-lineage correlation has half the max effect) then after ten swaps the median outcome is for a lineage to contain about half as many individuals as before.  (The mean number is of course unchanged.)  So after one hundred swaps a lineage that started with one thousand individuals is probably extinct. 

For our hunter-gather ancestors (and our animal ancestors before that) this was clearly the usual outcome.  Even though the hunter-gatherer population doubled about every quarter million years, twenty five thousand years was plenty of time for the equivalent of several swaps.  Our farming ancestors had a better chance – for lineages whose swap rate was less than one per century, the overall population growth meant it could expect to survive indefinitely.   

Since the introduction of industry the situation looks even better.  But more changes are yet to come, which raises the key future genocide question:  Will less than ten swap equivalents continue to happen on average in the time it takes the population to double?