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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 EXPECT critizes for these definitions. What is the definition of fitness?

In the following, to make things easier I will consider only one bi-allelic locus. As I said I don't want to talk practical issues but theoretical ones, therefore we will assume to work on a panmictic population of inifinite size evenly distributed into class age.

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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What's wrong with "ability to survive and reproduce?" –  Amory Nov 2 '13 at 15:08
    
Over what time amount of time should one measure this ability? One generation? His measure would suffer from drift! And not everybody has the same generation time. Over 10 years? It does not give the same result if you make this measure over 5 years. It seems rather arbitrary the time one should consider, isn't it? –  Remi.b Nov 2 '13 at 15:15
    
fitness has no definition if the selection criteria are not specified. Having specified it, the fitness is a measure of reproductive potential. –  WYSIWYG Nov 4 '13 at 16:44
    
@WYSIWYG Could you develop your comment? –  Remi.b Nov 4 '13 at 22:32
    
@Remi.b.. I meant that something is said to be fit for some condition. Therefore fitness is conditional. There is nothing like absolutely fit. Unless you know what the selection pressure is you cannot measure fitness. –  WYSIWYG Nov 7 '13 at 12:55

2 Answers 2

The concept of fitness is very general. An adequate definition of fitness is hard to specify in the same way that a definition of "species" is hard to give. To be useful, scientific or technical definition of such broad concepets will often need to be so narrow that more than one is needed. A uselessly broad definition of fitness might be:

"Fitness is modeled as a utility function, where higher fitness is indicated by a higher score"

Here every important detail about whatever's fitness is being tested, how that fitness is measured, and the environment in which that fitness is determined are simply wadded up together and transformed into a different question that is no easier to answer.

The hypothetical problems you raise with various definitions are not (in essence) problems with the definitions, but problems with the definitions not being applicable to the domain in which such problems matter. You have to define your criteria for success, and then these constraints can be translated into a "fitness" function that allows the desired predictions.

Some issues that might matter are:

  • Are predictions about populations, or individuals.
  • Are predictions about dynamic fitness (snapshot at some time) or long-run steady state fitness.
  • Are predictions about quantitative values (like heights) or discrete values (like sex).
  • How do you want to present error in your predictions - p value, sensitivity/specificity, confidence interval, etc.

I'm sure this is not the kind of answer you were looking for, but I think part of your question revolves around a confusion that there is "one" technical definition for fitness. Part of the process of learning is comparing different presentations of the same concept, and realizing where they are different. A full walk over all the different ways one could evaluate and apply fitness would be a book, not a short answer. Perhaps some other people can provide good links to more detailed information.

I just found a blog posting, by Dr. John S. Wilkins, which says some of the same things. His perspective comes with a good pedigree; his PhD work was on trying to define "species" and he has authored a couple of books on the subject.

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As I see it, your question is also encompassing an inquiry for a theory of fitness.

In recent years the inclusive fitness theory has seen its share of interest, which can be applied to social entities.

Freely citing from wikipedia here:

An organism is judged by the number of offspring it has, how they support them, and how their offspring could support others

As for the mathematics and informatics this paper

JY Wakanoa et al. "A mathematical description of the inclusive fitness theory", Theoretical Population Biology, Vol84. March 2013. pg 46–55

explains:

Recent developments in the inclusive fitness theory have revealed that the direction of evolution can be analytically predicted in a wider class of models than previously thought, such as those models dealing with network structure. ...

It takes a Markov chain approach.

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