

It’s not a big secret that I’m a fan of Elon Musk. I’ve never met the man, but I have met people who have met him, and he’s the type of visionary that nerds would march to the gates of hell for. If you want to know what he’s not reputedly like, watch this pitch from the 1990s, Bill Gates, Future Vision: A Microsoft Plus Program from 1994. Gates’ “vision” has made him rich, and has changed the lives of everyone. He’s succeeded. But he doesn’t inspire in the way that Steve Jobs did. Musk differs even from Jobs. Apple makes beautiful and functional products which integrate seamlessly with our lives and improve them. Musk’s aspires to transform civilization. It’s no surprise that he read and endorsed Nick Bostrom’s Superintelligence (His friend Peter Thiel’s interest in these topics is well known). With that sort of fact in mind the recent piece for Aeon Magazine, Exodus: Elon Musk argues that we must put a million people on Mars if we are to ensure that humanity has a future, is not too surprising. Throughout the piece it’s obvious that Musk is haunted by Fermi paradox.

But there is one aspect, in the subhead itself, where I think Musk errs. He states: “Some individuals might be able to endure these conditions for decades, or longer, but Musk told me he would need a million people to form a sustainable, genetically diverse civilisation.” This just strikes me as wrong. My impression is that most people have incorrect intuitions as to the effect of a population bottleneck on genetic diversity. For example, the Black Death in Europe was not a bottleneck, because not enough of the population died off. A die off on the order of 30% is a tragedy, but it isn’t really a population bottleneck. What matters for genetic diversity is who reproduces, and it might not be implausible that in many organisms 30% of individuals within a given generation do not reproduce (this is why effective population which predicts the variation you actually have is always smaller than census population). Second, because mutation would take a long time to build variation back up after it is lost long term effective population is very sensitive to a bottleneck event. This is why despite our census size of 7 billion long term effective population for humans is closer to the range of 1,000 to 10,000. We went through bottlenecks in our relatively recent past.

One way to measure this genetic diversity that is rather straightforward is to look at heterozygosity. Basically it is the proportion of genotypes which are heterozygotes, that is, alleles are of different state at a locus. Heterozygosity is not the only measure of genetic diversity, nor the most informative, but it is a reasonable one to use for this sort of coarse question. At a single locus heterozygosity peaks when you have a random mating population with alleles segregating at comparable frequencies. So you have two alleles at 50% frequency (this for a diallelic SNP, obviously microsatellites are going to be different), and as per Hardy-Weinberg 50% of the genotypes will be heterozygotes. Because random genetic drift tends to shift the allele frequencies from these mid-points, and result in the extinction of particular variants, populations subject to more drift tend to be less heterozygous. And the power of drift is inversely proportional to population size. Small populations are subject to a lot of drift. So they lose heterozygosity.

The equation to the left can formalize this relation in the context of bottlenecks, where N is the population size, and t is the number of generations. The chart at the top illustrates some results plugging in some values. Basically you can see how a population crash of varying magnitudes and lengths impacts reduction in heterozygosity. Not only does the size of the bottleneck matter, but how long it lasts is also something we need to keep in mind. I don’t think a 50 generation bottleneck is realistic, but I wanted to include that to show you the effect. For the purposes of genetic diversity it seems that ~1,000 humans would be more than enough. Note that this assumes a random sampling from the total human population. On the one hand this means they are unlikely to be related. But it also means you wouldn’t “optimize” for genetic diversity. There’s no reason that Musk would need to sample randomly, and it seems unlikely for many reasons that he would.

Now, it could be that Musk is thinking of such huge population sizes because he wants a lot of variation from which one could select personality types that could flourish on Mars. Even then 1 million is definitely overkill. More plausibly you could select particular personality types, combined with the likely self-selection that would occur. Of course diversity does not matter just for genetics, it matters for culture. There are models which suggest that too small a population can result in cultural poverty, as ideas and skills are lost over time. I think the key to this is that the long term population needs to start growing soon so that more than one individual is the repository for a particular skill. Additionally, literacy and record keeping can allow for the preservation of certain types of knowledge. There’s going to be a lot of “trial and error” on Mars if human existence is sustainable, so I suspect organic growth from a small base will be critical. It isn’t as if we don’t have precedents for small founding groups. Apparently the millions of French Canadians in North America descend overwhelmingly from less than 3,000 founders. The founding stock for Mars is likely to be somewhat more diverse that this group to begin with.

Addendum: Also, I have a hard time believing that a Mars colony wouldn’t have super-advanced CRISPR-like technology, as well as extra sperm and eggs from un-sampled populations, if diversity is needed.

Raw results under the fold

