Allele frequency problem in “Looper”





Looking around the internet, it appears that the world death rate is something like 0.8%, while the world birthrate is something like 1.15% (values vary dramatically by resource and will certainly change in time). This means that something like 33% of the people alive in 2043 will have been born between now and then (2.4 billion births). And thus nearly 1/3 of all of them would have to have the TK mutation! This means a ~33% chance of the same spontaneous mutation in every birth.

So what is the mutation rate in humans? The most recent high estimate sits around 1.38 mutations in 100,000,000 bases [1]. This means that any one human has a 1.38/100,000,000 chance of having the TK mutation. This is 4 million times smaller than the 33% chance required!

In other words, only 35 people born between now and 2030 would be expected to have the same mutation, in this case the TK mutation. That is a hell of  a lot fewer than 760,000,000!

Conclusion: The world in which the loopers live is a magical one. Fortunately, the existence of magic also goes a long way toward explaining the time travel paradoxes and their resolution. Alternatively, there could have been some exogenous source of the TK gene. Perhaps a mosquito-borne retrovirus?

NOTE 1: All of the values I used above are estimates based on the best information I could find, but even if I am way off on all of them, it would be impossible to find reasonable values that would give a final outcome such that anything even close to 10% of people could end up with the same new mutation in 20 years. Unless there are over twenty million sites at which this mutation would cause the TK phenotype, and in that case we ought to be seeing a heck of a lot of telekinesis right now.

NOTE 2: Maybe we should interpret this as a TK gene instead of a mutation. A mutation implies a change to an existing gene, which most of the time breaks it. Rarely, though, a mutation can give a new function to a gene. But there are fewer ways to add function, and so we wouldn’t be able to get past the probability problem described above. If it was a gene, though, then perhaps it could have come from some outside source. A retrovirus, perhaps?

[1] Scally and Durbin. “Revising the human mutation rate: implications for understanding human evolution.” Nature Reviews Genetics 13, 745-753 (October 2012) | doi:10.1038/nrg3295

For those who love code, here are the lines in R I used to get the numbers in this post:

population = 7000000000
birthrate  = .0115
deathrate  = .0087

new_people = 0
years      = 30

for( year in 1:years ){
	dead = population * deathrate
	born = population * birthrate
	new_people = new_people + born
	population = population + born - dead

fraction_new = new_people/population

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