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The fundamental theorem of natural selection with mutations
Remarkably, Fisher’s theorem by itself illustrates a self-limiting process – once all the bad alleles are eliminated, and once all the individuals carry only good alleles, then there is nothing left to select, and so selective progress must stop. The end result is that the population improves slightly and then becomes locked in stasis (no further change). It is astounding that Fisher’s Theorem does not explicitly address this profound problem! Newly arising mutations are not even part of Fisher’s mathematical formulation. Instead, Fisher simply added an informal corollary (which was never proven), which involved extrapolation from his simple proof. He assumed that a continuous flow of new mutations would continuously replenish the population’s genetic variability, thereby allowing continuous and unlimited fitness increase.
The authors of the new paper realized that one of Fisher’s pivotal assumptions was clearly false, and in fact was falsified many decades ago. In his informal corollary, Fisher essentially assumed that new mutations arose with a nearly normal distribution – with an equal proportion of good and bad mutations (so mutations would have a net fitness effect of zero). We now know that the vast majority of mutations in the functional genome are harmful, and that beneficial mutations are vanishingly rare. The simple fact that Fisher’s premise was wrong, falsifies Fisher’s corollary. Without Fisher’s corollary – Fisher’s Theorem proves only that selection improves a population’s fitness until selection exhausts the initial genetic variation, at which point selective progress ceases. Apart from his corollary, Fisher’s Theorem only shows that within an initial population with variant genetic alleles, there is limited selective progress followed by terminal stasis.
Remarkably, Fisher’s theorem by itself illustrates a self-limiting process – once all the bad alleles are eliminated, and once all the individuals carry only good alleles, then there is nothing left to select, and so selective progress must stop. The end result is that the population improves slightly and then becomes locked in stasis (no further change). It is astounding that Fisher’s Theorem does not explicitly address this profound problem! Newly arising mutations are not even part of Fisher’s mathematical formulation. Instead, Fisher simply added an informal corollary (which was never proven), which involved extrapolation from his simple proof. He assumed that a continuous flow of new mutations would continuously replenish the population’s genetic variability, thereby allowing continuous and unlimited fitness increase.
The authors of the new paper realized that one of Fisher’s pivotal assumptions was clearly false, and in fact was falsified many decades ago. In his informal corollary, Fisher essentially assumed that new mutations arose with a nearly normal distribution – with an equal proportion of good and bad mutations (so mutations would have a net fitness effect of zero). We now know that the vast majority of mutations in the functional genome are harmful, and that beneficial mutations are vanishingly rare. The simple fact that Fisher’s premise was wrong, falsifies Fisher’s corollary. Without Fisher’s corollary – Fisher’s Theorem proves only that selection improves a population’s fitness until selection exhausts the initial genetic variation, at which point selective progress ceases. Apart from his corollary, Fisher’s Theorem only shows that within an initial population with variant genetic alleles, there is limited selective progress followed by terminal stasis.
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