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.