Ronald Fisher discovered what he, with humility, called the Fundamental Theorem
ID: 36977 • Letter: R
Question
Ronald Fisher discovered what he, with humility, called the Fundamental Theorem of Natural Selection. This theorem says (in its modern terminology):
The rate of increase in the mean fitness of any organism at any time ascribable to natural selection acting through changes in gene frequencies is exactly equal to its genetic variance in fitness at that time.
As I understand it, it sounds alike the standard equation that we learn in the first class of Introduction to evolutionary biology
In words: the response to selection equals the selection differential times the genetic variance of the trait under consideration divided by the total phenotypic variance of the trait under consideration
But how can we prove/demonstrate that Fisher's fundamental theorem of natural selection holds true?
I don't ask for empirical evidences that support this claim but for a theoretical/mathematical proof/demonstration of this claim.
Ronald Fisher discovered what he, with humility, called the Fundamental Theorem of Natural Selection. This theorem says (in its modern terminology): The rate of increase in the mean fitness of any organism at any time ascribable to natural selection acting through changes in gene frequencies is exactly equal to its genetic variance in fitness at that time. As I understand it, it sounds alike the standard equation that we learn in the first class of Introduction to evolutionary biology R = S. VG/Vp In words: the response to selection equals the selection differential times the genetic variance of the trait under consideration divided by the total phenotypic variance of the trait under consideration But how can we prove/demonstrate that Fisher's fundamental theorem of natural selection holds true? I don't ask for empirical evidences that support this claim but for a theoretical/mathematical proof/demonstration of this claim.Explanation / Answer
Here's a paper with an historical bibliography of mathematical analyses in the introduction.
As you can see when you demand a mathematical treatment of something as poorly understood as the genetic inheritance of traits, the word proof is to be used in a qualified way. In this case a multilocus fitness with variation in the population with no linkage between the alleles. Its probably a case that shows up frequently enough, but how many alleles are we talking about? With large numbers of alleles which are scrambled randomly at each generation (zero linkage) I would imagine that the number of individuals that contain a lot of diversity.
Most GWAS studies show lots of less probable variants may contribute to many genetic traits (like height, diabetes, etc). So this is quite a reasonable number of the cases.
The fundamental theorem is true for any number of variants involved though, so hopefully this helps.
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