# Fisher’s Fundamental Theorem of Natural Selection

Fisher’s Fundamental Theorem of Natural Selection has done a lot to convince many professional academics of the truth of Darwinian evolution.

The theorem states that the rate of increase in fitness of any organism at any time is equal to its variance in fitness at that time. In other words, fitness must go up! Because it is a mathematical equation, many are convinced that selection must be effective.

However, it turns out that Fisher’s theorem actually says very little about fitness, or even biology. While this has been pointed out before, a recent paper shows (a) the limitations of the theorem to tell us anything helpful about selection, (b) the limitations of the theorem to tell us anything about evolution, and even (c) the limitations of the theorem to tell us anything about biology.

Fisher’s theorem has been lauded as “biology’s central theorem” because it describes why biologists expect fitness to increase. However, the meaning of “fitness” in this sense is so weak as to not be helpful in any way to describe biological expectations.

Fisher’s Fundamental Theorem of Natural Selection Isn’t Fundamental After All

## 4 Replies to “Fisher’s Fundamental Theorem of Natural Selection”

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ET says:

LoL! An “increase of fitness” is a relative term. And it all comes down to contingent serendipity. It could be the fastest, slowest or anywhere in between. It could be the biggest, smallest or anywhere in between. It could be the best sight, no sight or anywhere in between. That goes for ALL traits. And that is but one reason why natural selection is impotent with respect to macroevolution and universal common descent.

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PaV says:

Fisher’s Theorem is used finds uses in statistical mechanics–think of gas molecules bumping into one another. So, the “fundamental” theorem of how life “evolves” also describes now inert, life-less molecules of gas interact. How can both be simultaneously true?

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Fasteddious says:

I think this “theorem” is easily disproven by so called “living fossils”; that is species that remain unchanged over long periods of fossil history, such as the horseshoe crab or the coelacanth fish. These are essentially identical today to their fossil ancestors, in some cases 100 million years ago. These disprove Darwinian evolution for two reasons:
1. Given that the environment around them has changed significantly over those millions of years, Darwin would have expected them to change in response, either to adapt to changing conditions, or just by evolutionary “drift”. Yet at least from an external view, they have not changed significantly. The fossils may be given different species names, but they are recognizably almost identical.
2. More to the point of this article, if these species remained unchanged, how is it that they were not outcompeted by younger species which were supposedly more “fit” to survive and reproduce? If Darwinian evolution is a constant battle for survival in an ever more competitive environment, then why did these unchanging species not become driven to extinction by their “superior” and “fitter” younger neighbours?
I expect Darwinists have some hand waving “explanation” for this, but they can’t have it both ways: dynamic survival of the fittest vs. stasis despite a changing environment.

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johnnyb says:

Fasteddious –

I think this is a good example of why much in evolutionary theory is problematic. There is a *huge* disconnect between what the theorem *shows* and what people *think* it shows. The theorem itself is actually best *demonstrated* by identical ancestors.

When you look at the theorem, what it says is that the most successful variant will tend to dominate the population, driving the other variants to zero. That seems to be precisely what happened with living fossils.

The problem is that the theorem was thought to be proof that evolution can *build* something or make it *better*. This is due to an equivocation between what might be termed “relative” and “absolute” fitnesses. Even those terms are misleading, because the two have almost nothing to do with each other. The theorem is about relative fitness, which is only defined as the member of the population that is most successful (even if it is not very successful).

Anyway, like many ideas in evolution, they tell you something, but not always what it seems like they are telling you. I’m convinced that a lot of people hold to evolutionary theory because they don’t know what the theory actually says well enough.