Regarding a potential conceptual duality in the definition of fitness, I take the contrary view that it's important to use the same term because all definitions rely on the same underlying fundamental concept. Here's a longish thread explaining what I mean. https://twitter.com/PetrovADmitri/status/1303563440808583168

This is basically how I teach the concept in my Evolutionary Genetics course, and I use it to emphasize the conceptual unity between quantitative genetics and population genetics.

First, fitness is the contribution to the next generation by a reproducing entity, usually an individual organism.

On a raw scale, (usually called absolute fitness) it is expressed in units of numbers of entities in the next generation that are direct descendants of a given entity in the current generation (number of offspring).

Given certain assumptions, absolute fitness can be operationally defined as lifetime reproductive success. This breaks down under some conditions (e.g. when generations overlap), but a reasonable proxy can often be identified.

All equations for evolutionary change in population genetics and quantitative genetics use relative fitness, which is defined as absolute fitness divided by population mean fitness.

All these equations can be derived from the Price Equation, which in its simplest form says that change in the population mean is equal to the covariance between an individual genetic value and relative fitness.

This concept unites all of evolutionary genetics because it works for allele frequencies, additive genetic values, and phenotypes.

In other words, you can use the Price equation to show how change at one level depends on change at another, e.g. how phenotypic selection drives changes in allele frequencies.

This second definition, fitness as a statistical expectation, I would not call a separate concept. It’s just a statistical summary of fitnesses of a class of entities taken in a certain context, and I believe the best name for it is expected fitness. https://twitter.com/wc_ratcliff/status/1303431299353448448?s=20

Where this comes into play is in deterministic equations for allele frequency change. Each genotype has an expected fitness operationally defined as the mean fitness of the individuals with that genotype (defined in some context).

Expected fitness is usually normalized by dividing by the value of the best or worst genotype such that one genotype has a value of 1. This is what Wright called “selective value.”

Normalization makes it appear that we are not dealing in the currency of numbers of reproducing entities anymore, but we really are. It’s just done to simplify calculations or derivations.

All equations for evolutionary change contain mean fitness in the denominator to convert to relative fitness, so any normalization we apply cancels out.

Where expected fitness becomes important is when we want to partition deterministic and stochastic change, i.e. selection and drift. Change due to selection is driven by covariance between expected fitness and individual allele frequency.

The variance around this expectation is due to drift, and the actual observed change in allele frequency is due to a combination of selection and drift.

Both, however, involve variance in contribution to the next generation, i.e. variance in the production of offspring, i.e. variance in fitness.

All of that was a long way of saying that fitness is the same concept throughout—contribution to the next generation—but what differs is how it’s being summarized statistically.

Thus, I think the best way of dealing with it terminologically is to apply different adjectives (absolute, relative, expected, or normalized) to the word fitness. This emphasizes the conceptual unity but allows for different perspectives depending on the situation.

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