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Effective population size

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BottleNeck
Superintelligence 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.

bottleneck.eqn4 (1)51lNaQt3ZDL._AA160_ 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.

400px-Concept_Mars_colonyNow, 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

Number Generations Of Bottleneck
Bottleneck 1 5 10 20 50
10 0.9500 0.7738 0.5987 0.3585 0.0769
100 0.9950 0.9752 0.9511 0.9046 0.7783
200 0.9975 0.9876 0.9753 0.9512 0.8824
300 0.9983 0.9917 0.9835 0.9672 0.9200
400 0.9988 0.9938 0.9876 0.9753 0.9394
500 0.9990 0.9950 0.9900 0.9802 0.9512
600 0.9992 0.9958 0.9917 0.9835 0.9592
700 0.9993 0.9964 0.9929 0.9858 0.9649
800 0.9994 0.9969 0.9938 0.9876 0.9692
900 0.9994 0.9972 0.9945 0.9889 0.9726
1000 0.9995 0.9975 0.9950 0.9900 0.9753
 
• Category: Science • Tags: Effective population size 
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The Black Death

I noticed during Peter Ralph and Graham Coop’s Ask Me Anything about their new paper, The Geography of Recent Genetic Ancestry across Europe, someone brought up the effects of plague. Recall that ~1/3 of Europe’s population died during the Black Death. And population size reductions on the order of ~50% due to epidemics are not unknown in human history. Surely this would have a major genetic effect? Well, in fact it would have a genetic effect due to possible adaptations to disease (see CCR5). But there would be little overall impact on genetic diversity, at least in the short term. That is because for bottlenecks to produce major change in the genetic character of a population they have to be rather extreme in magnitude.

This issue came to mind for me in 2009 when I watched Stark Trek. If you haven’t watched the J. J. Abrams reboot, and are a spoilerphobe, read no more! Now, with that out of the way you may recall that during this film the Vulcans suffered a genocidal attack. Out of billions of Vulcans only ~10,000 survived. Here’s some commentary on the possible consequences, New Star Trek Movie: A Vulcan Holocaust?:

Yes, there is a remnant of ten thousand Vulcans left. At the end of the movie, we are told that they have found a new planet to settle on. Still, we must ask: If we are now in a new timeline and all we have left are a few thousand survivors, will the Vulcans have any political influence at all? Or will they just become a relic on a museum planet? Spock even refers to his people as an endangered species.

It would seem the Vulcans will have no other choice but to accept “converts” if they want to survive, because 10,000 is not really a very big gene pool in the long haul. The Amish, who do not accept converts or newcomers, have become very inbred and are now facing problems with genetic diseases. European Jews, who lived in isolated communities for many centuries, also carry certain genetic diseases. However, the recent influx of Jews by Choice is bringing new DNA patterns into the community, so that Jews have fewer such problems than the Amish.

3.5% growth per year

First things first. Vulcans would have no problem reestablishing their population on a virgin planet. It’s simply the power of exponential growth. The nation of East Timor has a growth rate of 3.5% per year (total fertility rate ~6 per woman). This is not an outlandish value. The Puritans of New England maintained higher fertility for several generations. The key here is that humans (or humanoids) are like any organism when faced with a Malthusian surfeit: they breed. Though Vulcans live longer than humans, and have some life history quirks, I’m rather confident that Vulcans could reproduce at least as fast as humans. The reality is that they’re superior to humankind in almost every way possible (their lack of emotions is a testament to culture, not biology). Some quick computations tell me that it would take 400 years for Vulcans to get back to a population of 10 billion. Since some Vulcans can live longer than two centuries, this seems like a rather short window of time.

But what about the second clause? Vulcan genetic diversity. Vulcans are logical, so I’m rather confident that they would have sampled diverse populations when evacuating. And to my knowledge I am not aware of an ethnic skew of Vulcans who were resident across the Federation. So with concerns of representativeness addressed, what would such a crash in population entail?

First you need to become familiar with the concept of an effective population, Ne. Consider that in any given generation some individuals shall breed and some shall not. Though the count of population may be x, the count of those who contribute to the next generation is invariably (x – those who do not breed). And it is this inter-generational transfer which is relevant to population genetics. Also, for the purposes of genetics deep history matters a great deal. Bottlenecks have an inordinate impact on the long term effective population. Intuitively, consider the case of a large population which goes through an extreme bottleneck, and then expands again. The average census size over that time might be rather substantial. But for genetic purposes the lineages are likely to coalesce back to a few common ancestors at the bottleneck. The impact of the pre-bottleneck period is attenuated, because much of the population was simply not genetically sampled. It may as well have not existed!

To make it concrete, below is a toy example. Imagine an island with 10,000 individuals which undergoes population crashes. You see the results below.

 

The total number of individuals over the 30 generations across the three scenarios is about the same. But the long term effective population in the scenario where the size dropped to 10 is 30 times smaller than the case where the size was reduced to 10% of the prior value.

But what does this do to genetics? There are complicated ways to model this, because populations may be in mutation/drift/selection equilibrium, with the bottleneck being a temporary perturbation. But one way to think about the issue is that a bottleneck can drop heterozygosity by about a factor of 1-1/(2Ne). As Ne → ∞ there is no change. But 1-1/(2Ne), where Ne is 1,000 to 10,000 (assuming that Ne is smaller than the census size of 10,000), is not implying a great change in heterozygosity. Of course many rare alleles, or alleles private to families, will be lost. But so long as the Vulcan population was reasonably representative (not inbred), then I think they don’t have much to fret about in terms of genetic health.

The purpose of this post was not to answer a question of deep interest to Trekkies. Rather, it was to encourage people to establish some intuitions about these sorts of demographic processes and their effect upon genetics.

References:

Hartl, Daniel L., and Andrew G. Clark. Principles of population genetics. Vol. 116. Sunderland: Sinauer associates, 1997.

Nei, Masatoshi, Takeo Maruyama, and Ranajit Chakraborty. “The bottleneck effect and genetic variability in populations.” Evolution (1975): 1-10.

(Republished from Discover/GNXP by permission of author or representative)
 
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Nathaniel Pearson has an eminently readable post up on human effective population sizes. If you don’t know the importance of harmonic means in this domain, worth a read. He finishes though with an issue of practical importance, the proliferation of individually deleterious alleles at the large census sizes we see us today:

Along the way, our changing population size may shape public health in complex ways. In particular, a key question will be what happens to the likely sizable subset of newly arisen rare variants that pose health risks to people who carry them. As our population continues to skyrocket, more such variants will come into our midst.

At the same time, continued population growth should ultimately help natural selection purge such variants more efficiently than it can in a small population (where chance dominates the fate of variants, harmful or not).

But, to the extent that our future population growth itself depends on further advances in healthcare, we’ll also be altering the regime of such natural selection, ideally relaxing it in ways that help people live healthier lives no matter what variants they carry in their genomes.

As Mark Ridley observed in The Cooperative Gene natural operates in utero as well. Even assuming that natural selection is not purging deleterious alleles with great efficiency today, high human miscarriage rates are going to serve as a counterbalance to better healthcare for the genetically less fit.*

* On the order of ~50% of pregnancies miscarry, with the majority being cryptic, as women may not have known that fertilization occurred due to failure of implantation or problems in the first month).

(Republished from Discover/GNXP by permission of author or representative)
 
• Category: Science • Tags: Effective population size, Genetics, Genomics 
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Razib Khan
About Razib Khan

"I have degrees in biology and biochemistry, a passion for genetics, history, and philosophy, and shrimp is my favorite food. If you want to know more, see the links at http://www.razib.com"