Fitness is certainly the most important concept in the theory of evolution. My question does not have to do with practical measures of fitness but with the theoretical definition of it.
I am a bit lost with the concept of fitness. Below I give some possible definitions of fitness and I am hoping to get critics for these definitions. The broad question is What is the definition of fitness?
In the following, to make things easier I will consider only one bi-allelic locus. For simplicity, I will assume a panmictic population of infinite size evenly distributed into age classes.
1) Let the variable $M$ be the mean time of a generation in the species of interest. Measure the allele frequency $p(t)$ and measure the frequency $p(t+M)$. By comparing the two you get the ratio of fitness of the two different genotypes. Obviously it does not work if we have sexual reproduction or diploid selection.
2) Genotype the individuals and wait until they die by counting the number of offspring they had and take the mean per genotype ($W_{AA}$, $W_{Aa}$, $W_{aa}$). This method would not work if they have different lifespan. One individual might make two babies in 8 years and the other would make two babies in 2 years but they would have he same fitness.
3) Do the same that at 2) but don't wait until they die, wait 1 month, Or 2 years?, or $M$?, or $2\cdot M$?, or...? What is the right decision? The more you wait, the closest you will be to the long term effect of natural selection. The less you wait, the more probable you will suffer of genetic drift.
4) Fitness is just a measure of natural selection that is not perfectly accurate because it is measured at short-term. In some circumstances, our measure on this short term is representative (Wright-Fisher equation) enough of what will happen on the long term.
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