# The "theorem of evolution by natural selection"

An interesting thing happened today. I’ve finally gotten around to trying to google “theorem of evolution by natural selection” to try and get some outside information about what the notion is all about - turns out all I can find is a few links right back to Donald Hoffman’s “Case Against Reality” cottage industry.

I’m curious has anyone out there ever heard of it. No, not talking “Theory” - I’m referring to “Theorem” of evolution by natural selection.

What would a THEOREM of natural selection look like?

After all, “natural selection” is such a slippery term.

Survival of the fittest is about weeding out the weak. But there’s so much outside of the routines of our food gathering and shelter building capabilities that impact the course of survival and evolution. How would contingencies be woven into a “theorem” that depends upon mathematical proofs building up one upon another and eventually producing a conclusion that’s supposed to PROVE said claim?

Silly me. After posting this I went to Google Scholar.

“Fisher’s fundamental theorem of natural selection” garners the most attention and it dates back to the 1930’s

Fisher’s fundamental theorem of inclusive fitness and the change in fitness due to natural selection when conspecifics interact P. BIJMA First published: 14 December 2009 https://doi.org/10.1111/j.1420-9101.2009.01895.x Citations: 25 Piter Bijma, Animal Breeding and Genomics Centre, Wageningen University,

Natural selection systematically shapes life on earth. The impact of natural selection on the evolution of mean fitness of populations largely determines their evolutionary fate. Understanding the mechanisms that determine the impact of natural selection on the evolution of fitness, therefore, is critical to understanding evolutionary success. In his fundamental theorem of natural selection (FTNS), Fisher (1930) proposed that natural selection increases mean fitness at a rate equal to the additive genetic variance in fitness, which suggests that natural selection works to increase fitness. This statement has generated tremendous scientific debate, until Price (1972b) and others showed that it refers to the part of the response in fitness caused by changes in allele frequency keeping all other factors constant, including genetic factors such as the average effects of alleles (Fisher, 1941; Ewens, 1989; Frank & Slatkin, 1992; Edwards, 1994; Frank, 1997; Michod, 1999). In this interpretation, Fisher’s FTNS is a true mathematical theorem, i.e. an exact identity (Price, 1972b; Frank, 1997; Lessard, 1997; Rice, 2004) (Table 1).

Table 1

FTNS Fisher’s fundamental theorem of natural selection
IF Inclusive fitness
IGE Indirect genetic effect
i, j Focal individual, conspecifics of i
k, l Components of fitness, k, l = 1 denote direct genetic effects, k, l > 1 IGEs
g k,i Additive genetic merit of i for fitness component k
, Variance of gk, covariance between gk and gl
r Additive genetic relatedness among interacting individuals
w i , Personal fitness of i, population mean personal fitness
_ Response in mean fitness due to response in mean g‐values
_ Response in fitness predicted from the FTNS
IFi Inclusive fitness of individual i
_ Total breeding value of i, heritable impact of i on population mean fitness
G α,i Classical breeding value of i, expected fitness of i given alleles in i
_ Total heritable variance available for response to selection
var(Gα,i) Classical additive genetic variance in fitness
j(k) Individual contributing component k of fitness of focal individual (eqn. 20)
r k Relatedness between focal individual and individual j(k)

The symbol are demolished in the translation, but the meanings aren’t and as I suspected I’m not seeing anything about the environment. Or chance Acts of Providence, that can not be ignored when studying evolution, but are too challenging to incorporate into snug mathematical formulas.

Theoretical Population Biology Volume 36, Issue 2, October 1989, Pages 167-180

An interpretation and proof of the fundamental theorem of natural selection
W.J.Ewens

Abstract
Fisher’s Fundamental Theorem of natural selection is one of the most widely cited theories in evolutionary biology. Yet it has been argued that the standard interpretation of the theorem is very different from what Fisher meant to say. What Fisher really meant can be illustrated by looking in a new way at a recent model for the evolution of clutch size. Why Fisher was misunderstood depends, in part, on the contrasting views of evolution promoted by Fisher and Wright.

Well I’ve gotten to meatier papers and it’s making a little bit more sense - but now I’m left with a growing impression that Hoffman is claiming way the heck more for his highbred, that the theorem actually delivers. Surprise, surprise!

Theoretical Population Biology

An interpretation and proof of the fundamental theorem of natural selection

Volume 36, Issue 2, October 1989, Pages 167-180

W.J.Ewens

https://www.sciencedirect.com/science/article/pii/0040580989900282?via%3Dihub

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Indirect genetic effects: a key component of the genetic architecture of behaviour

Francesca Santostefano, Alastair J. Wilson, Petri T. Niemelä &amp; Niels J. Dingemanse
31 August 2017 - volume  7, Article number: 10235 (2017)

https://www.nature.com/articles/s41598-017-08258-6\

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THE FUNDAMENTAL THEOREM OF NATURAL SELECTION

BY A. W. F. EDWARDS

Biological Reviews, vol. 69, n° 4, November 1994

Department of Community Medicine, University of Cambridge

http://digamoo.free.fr/edwards1994.pdf

Sure would be fun to find someone who actually understands it and would be into discussing it a little - I even tried a hail mary pass in an email to our local college’s biology department yesterday evening, see if I can buy a tutorial session or two, who knows.

First, I believe there are two distinct forms of Natural Selection.

1. Darwinian evolution via natural selection is the meaning we are all familiar with.
2. Physical evolution via natural selection as described in Chaos theory, i.e self-assembly and the ability to maintain integrity under stress.

Maybe humans were not the most intelligent but were the most aggressive of the species .Neanderthals had bigger brains than humans maybe it cause them to be less aggressive and causing their extinction being killed off by a more aggressive species . If evolution is the truth and I believe it is intelligence was put in the equation so life could escape the planet without intelligence it would not be possible. Is man the right species to achieve it only time will tell. Nature may have to restart the whole process if we fail.

[quote=“bigbill11, post:5, topic:7560”]
If evolution is the truth and I believe it is intelligence was put in the equation so life could escape the planet without intelligence it would not be possible. Is man the right species to achieve it only time will tell. Nature may have to restart the whole process if we fail.
[/quote] You may be right in the observation that man is the only tool making species smart enough to escape the planet after we have ruined it. But I would not bet on it.

Nature did not endow man with intelligence for a purpose. The fusion of chromosome 2 was a lucky (perhaps premature) mutation and may never occur again.

There is no natural selection necessary for man’s intelligence. All other species are doing just fine. They live within the natural limits and are intellectually perfectly adapted to their lifestyle.

If it weren’t for man and his toys, many species would be doing just fine instead of being “endangered”

So for you evolution ends at the planetary level the only purpose for intelligence is to make shiny gadgets to carry around - monkeys with suits and shinny gadgets. I think we are caught in a hold pattern admiring ourselves and wasting our technology on individualism which is our whole consumer system. It won’t last were explorers its in our blood hopefully we don’t destroy ourselves before we can put our tech to good use unlike what we do today in how we waste it in the supplier consumer world. Its one of the faults of capitalism.

Humans have no purpose, other than trying to stay alive, just like every other organism on earth.

I think we are caught in a hold pattern admiring ourselves and wasting our technology on individualism which is our whole consumer system. It won’t last were explorers its in our blood hopefully we don’t destroy ourselves before we can put our tech to good use unlike what we do today in how we waste it in the supplier consumer world. Its one of the faults of capitalism.

It is GREED, an extension of hoarding for lean times. Human greed is not designed for lean times but for creating luxuries, while behaving as a parasitic “invasive species”, bent on destroying the host than gives them life.

There is nothing to discuss you have already decided your right and everyone else is wrong it would not matter what I say there is no more discussion to be had.

[quote=“bigbill11, post:9, topic:7560, full:true”]

There is nothing to discuss you have already decided your right and everyone else is wrong it would not matter what I say there is no more discussion to be had.

Do you agree or are you saying I am wrong and you are right? If so where do we differ in perspectives?

I remember having read papers explaining that there was 2 differences between men and any other specie:

1. capacity of men to abstract thinking
2. capacity of men to create ideologies with the consequence that men can cooperate at a large scale, involving thousands of individuals.

And that was the big difference with any other specie in terms of evolution as it gives man a decisive advantage.

https://en.wikipedia.org/wiki/Elephant_cognition

They still are the most aggressive species, including to each other.