Tuesday, March 18, 2008

Backwards in Time   posted by gcochran @ 3/18/2008 11:32:00 AM

It's hard to have a recessive lethal hang around for a long time without some kind of heterozygote advantage: selection reduces its frequency. If the population is even moderately large, more than a few thousand, changes in allele frequency over time are very predictable: deterministic.

That also means that one can calculate past frequencies, as long as as these assumptions hold (i.e. as long as there was no tight bottleneck & selection coefficients were the same).

Going forward in time , the frequency of a recessive lethal with no het advantage declines more and more slowly, since the ratio of homozygotes to heterozygotes declines as the allele frequency declines. But if you go backward in time, the frequency grows, and it grows more and more rapidly as you go further and further back in time. This doesn't continue indefinitely: the frequency can't go above 100%. Project the frequency of such a recessive lethal back in time and you hit a singularity.

Today, lethal cystic fibrosis alleles have a frequency of 2% in northern Europeans. Unless I'm wrong, it takes 50 generations for a recessive lethal to go from almost 100% to 2%, and another 50 to go from 2% to 1%, assuming no reproductive compensation. 'Reproductive compensation' means that parents have another kid when one dies young and thus end up with the same number of children raised to adulthood. This effect weakens, but does not eliminate, selection against lethal recessives. With full reproductive compensation, it takes 80 generations for a recessive lethal to go from 99.5% to 2%, and another 75 to go from 2% to 1%.

If the frequency of lethal CF alleles is 2% today, there must have either been a selective advantage in heterogygotes over most the of the past two thousand years, or the population of northern Europe must have crashed down to a few hundred or less sometime during that period.

There was no such crash, which would have been worse than a nuclear war. Indeed, there was no bottleneck of any kind in that time period: we know this from the historical record. Events like the Black Death do not a bottleneck make: you need to get the population down into the low thousands or less. The Black Death left tens of millions.

So lethal CF mutants had some kind of selective advantage, or were closely linked to some allele that did.

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