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? 

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  • You’re use the word “genocide” in a very unusual way, to refer to any event that kills off a “lineage”, not just human-caused events. (By the way, how is “lineage” being defined here?)

    I would say that genocide – in the ordinary sense of the word – is wrong because it involves the deliberate killing of huge numbers of people. The fact that some genes and some memes (by which I mean aspects of culture) go extinct seems like a relatively minor side effect…

    Clearly the existence of such genes and memes has some value, but I wouldn’t want to say that it was the main reason for genocide being bad.

  • Caledonian

    Sometimes taking unusual positions produces interest and a willingness to think outside normal boundaries. Other times, it’s nothing more than oblivious to the meanings of words and putting your foot in your mouth through sheer social tone deafness.

    This post is not an example of the first case, Robin.

  • Robin, I’m also unclear about how your model relates to the real world. Is each iteration supposed to represent a new generation of people? If so, it seems to assume that everyone belongs to just one “lineage”, and thus ignores the presence of mixed race people, who could keep alive several “lineages” at once.

    If your parents belonged to two different tribes, presumably you’re keeping alive two lineages. If your grandparents belonged to four different tribes, then you’re keeping alive four lineages, and so on.

    (But I would still like to see a definition of “lineage” – is a lineage any group of people who are descended from a common ancestor?)

  • spindizzy


    Personally, I think this is quite a good post. Robin obviously chose the term “genocide” for a bit of headline grabbing. Maybe I don’t understand the point, but what would be wrong with “extinction”?

    Still, I have to rush to Robin’s defense on this one because I think the content is interesting.


    Is genocide significantly worse than the untargeted killing of an equal number of people? You seem to think not, but my impression is that most people disagree.

    On the other hand, as Robin says, extinction for most (ultimately all) species is inevitable. Perhaps even appropriate? Isn’t genocide a subcategory of extinctions i.e. those with a primarily human cause. Therefore, can some genocides also be appropriate?

    Standard disclaimers: I am not taking a position on this issue.

  • Allan, people are biased I think to care far more about 3000 people killed by terrorists than 3000 people killed by nature, so we might help to overcome this bias if we talk about how nature “murdered” those people. The math I described applies to any set of individuals as a “lineage.”

    Spin, some murders are appropriate too, but most should be lamented.

  • Constant

    The math I described applies to any set of individuals as a “lineage.”

    But your math does not seem to model the mixing of lineages through sex, and yet your math apparently attempts to model a population over time (because you talk about replacing lost members – you write “replacing with copies of random selections from the other half”). The failure of your model to incorporate sex seems to render its conclusions suspect as far as trying to apply them to actual populations, because the mixing of lineages could very well be a significant offsetting effect, allowing lineages to survive much longer than your math suggests.

  • spindizzy


    I think people are biased to care about causes which they have some control over. Generally, this means human causes. However, people do care about natural disasters if they think that e.g. government mismanagement is implicated in the resultant devastation.

    For dangers which are out of our control, two strategies would be either to avoid thinking about them, or to fool ourselves that we can influence them after all.

    > some murders are appropriate too, but most should be lamented.

    Perhaps all should be lamented, although some are appropriate. The same might be said of wars. I can suggest an appropriate war (the 2nd World War?) but I’m having trouble thinking of an appropriate genocide. 🙂

  • Constant: that’s a more clearer version of what I was trying to say, thanks! 🙂

  • I’m sorry for double posting.

    The math I described applies to any set of individuals as a “lineage.”

    I assume you mean any set of individuals, plus all of their descendants? But as soon as you take descendants into account, lineages start to come together, and we get to the stage where it’s impossible to destroy (all of) one lineage without destroying (a large part of) the other.

    It seems to me that the model would only describe the actual world if the dead were replaced by clones of the living, rather than ordinary children.

  • athmwiji

    perhaps, by a lineage, you mean the set of people who have a common allele, so there is one lineage for each allele? In this case you should include mutations as creating new lineages. Also, each person belongs to exactly two lineages for each gene. Is this what you mean?

    Or do you mean just matrilineal or patrilineal descendents? Or bacteria?

    When you say any set of individuals is a lineage, this seems odd. Do you mean any subset of the population of all living things throughout history. In which case if there are N individuals in history then there are 2^N subsets and 2^N lineages? It would seem odd for example to count the set of only myself and Napoleon’s steed as a lineage.

  • Spin, some murders are appropriate too, but most should be lamented
    Reminds me of something James Q Wilson said.

    If exterminating a race is bad, is exterminating a species worse? I think I heard somewhere that the vast majority of species go extinct.

  • This analysis applies directly to discrete mutually-exclusive labels, where each short-lived individual has exactly one of the labels. Examples include main language spoken, eye color, prefers Plato or Aristotle, etc.

  • Shaun

    It could be argued that extinction is something that happens naturally, while genocide seems to be more of a term applied to humans. In which case genocide is the actual goal and not just the outcome. Extinction seems to be more along the lines or survival of the fittest, whereas genocide is straight up annihilation of a certain group. Also, forever are there to be new lineages because people and animals interbreed to the point where the original strain is just filtered/blended out.

  • Peter St. Onge

    It’ll also be interesting once we see therapeutic genetic therapy; it seems conceivable that great swathes of genetic variation could be eliminated for being unfashionable.

    Of course, if this therapy were reversible (cf cosmetic surgery today), then we may see an explosion in genetic variety (centaurs, drow elves).

    Similar phenomenon cross-species; begs the question why we bother saving species from extinction when schoolchildren in 2100 will have pet griffins and unicorns.

  • spindizzy

    > If exterminating a race is bad, is exterminating a species worse?

    Exterminating the Anopheles (malarial) mosquito would probably be a good thing.

    We can be justified in sacrificing another species for the good of our own. Therefore, I suggest the same logic can be applied to human groups / races / tribes, and of course it has been applied repeatedly throughout history.

    I guess what I’m saying is: guilt is the luxury of the victor.

    > divide it into halves, pick one at random and delete
    > a random half of it

    You mean a half of a half i.e. a quarter of the whole?

    Sorry, I’m dense about maths so you really have to spell things out.

  • Spin, repeated independent swaps gives a log normal distribution of sizes, and so the mean log change shows how the median moves. The mean log change per max correlation swap is .5*log(3/2)+ .5*(1/2).

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