Lots of people get bent out of shape about Fisher’s Fundamental theorem, and spend lots of pages talking about it. The problem is that people tend to see the FFT as being magical. Theoreticians promote this because, well, the basic proof is so simple that you need to add some sort of complication to justify your existence (Ok, some of the complications are interesting). So without further adieu, here is my one line proof of Fishers Fundamental Theorem
Added in edit: I completely forgot to tell you what Fisher’s Fundamental Theorem was!
Fisher (1930) stated that “The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time.”. I would strike the word “genetic” from that sentence.
First, define terms:
The frequency of the ith individual = pi (usually that will be 1/N, but the truth is general, all we need is a frequency, and in reality it should be particle, not individual in the definition)
Some math you need to know:
12=1 (not sure what to call this other than a truism)
(A*B)*C = A*(B*C) (the associative property of multiplication)
SO the one line proof:
In a recent article, Andy Gardner (1015, J. of Evol. Biol, DOI:10.1111/jeb.12566)says:
“Today, disagreement still persists as to the correct interpretation of the fundamental theorem. For example, whereas Okasha and Ewens both regard the theorem as concerning the selection of genes, I regard it as concerning the selection of individuals.”
Are you serious? I don’t think it applies to Koalas. Of course FFT applies to genes, and to phenotypes, and yes, even to Koalas. Heck it applies to anything to which relative fitness can be applied. OK, maybe I will give this to Andy: there is really no meaningful way to assign fitnesses to genes, so maybe the fundamental theorem isn’t so useful in that situation.
This actually raises an important point. Yes, the FFT is a truism, but that doesn’t mean it is meaningful in all circumstances. When people refer to it as the “not so fundamental theorem” they are not complaining about the theorem itself, but about the application of that theorem to a particular biological situation.
Koalas don’t know or care about Fisher’s Fundamental Theorem. However, just because you don’t know or care about something doesn’t mean it doesn’t apply to you. (http://en.wikipedia.org/wiki/Koala)