scholarly journals A simple completion of Fisher’s fundamental theorem of natural selection

2020 ◽  
Author(s):  
Alan Grafen
Keyword(s):  
Natural Selection ◽  
Fundamental Theorem ◽  
Fisher’S Fundamental Theorem

Adding Dynamical Sufficiency to Fisher’s Fundamental Theorem of Natural Selection

2011 ◽  
Author(s):  
Philip J. Gerrish ◽  
Paul D. Sniegowski ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
...  
Keyword(s):  
Natural Selection ◽  
Fundamental Theorem ◽  
Fisher’S Fundamental Theorem

scholarly journals The Price equation and reproductive value

2020 ◽  
Vol 375 (1797) ◽  
pp. 20190356 ◽  
Author(s):  
Alan Grafen
Keyword(s):  
Natural Selection ◽  
Fundamental Theorem ◽  
Structured Populations ◽  
Reproductive Value ◽  
Price Equation ◽  
Class Structure ◽  
Theme Issue ◽  
Starting Point ◽  
Important Idea ◽  
Fisher’S Fundamental Theorem

The Price equation is widely recognized as capturing conceptually important properties of natural selection, and is often used to derive versions of Fisher’s fundamental theorem of natural selection, the secondary theorems of natural selection and other significant results. However, class structure is not usually incorporated into these arguments. From the starting point of Fisher’s original connection between fitness and reproductive value, a principled way of incorporating reproductive value and structured populations into the Price equation is explained, with its implications for precise meanings of (two distinct kinds of) reproductive value and of fitness. Once the Price equation applies to structured populations, then the other equations follow. The fundamental theorem itself has a special place among these equations, not only because it always incorporated class structure (and its method is followed for general class structures), but also because that is the result that justifies the important idea that these equations identify the effect of natural selection. The precise definitions of reproductive value and fitness have striking and unexpected features. However, a theoretical challenge emerges from the articulation of Fisher’s structure: is it possible to retain the ecological properties of fitness as well as its evolutionary out-of-equilibrium properties? This article is part of the theme issue ‘Fifty years of the Price equation’.

scholarly journals The Fundamental Theorem of Natural Selection

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1436
Author(s):  
John C. Baez
Keyword(s):  
Natural Selection ◽  
Continuous Function ◽  
Fundamental Theorem ◽  
Time Dependent ◽  
Original Result ◽  
Fisher Information Metric ◽  
Different Types ◽  
Information Metric ◽  
Fisher’S Fundamental Theorem ◽  
Dependent Probability

Suppose we have n different types of self-replicating entity, with the population Pi of the ith type changing at a rate equal to Pi times the fitness fi of that type. Suppose the fitness fi is any continuous function of all the populations P1,⋯,Pn. Let pi be the fraction of replicators that are of the ith type. Then p=(p1,⋯,pn) is a time-dependent probability distribution, and we prove that its speed as measured by the Fisher information metric equals the variance in fitness. In rough terms, this says that the speed at which information is updated through natural selection equals the variance in fitness. This result can be seen as a modified version of Fisher’s fundamental theorem of natural selection. We compare it to Fisher’s original result as interpreted by Price, Ewens and Edwards.

Ecological versions of Fisher's fundamental theorem of natural selection

1976 ◽  
Vol 8 (4) ◽  
pp. 639-641
Author(s):  
Jesús Alberto León ◽  
B. Charlesworth
Keyword(s):  
Natural Selection ◽  
Fundamental Theorem ◽  
Fisher’S Fundamental Theorem

Some general conclusions on Fisher's fundamental theorem of natural selection

1978 ◽  
Vol 20 (7-8) ◽  
pp. 675-678
Author(s):  
E. Ya. Frisman
Keyword(s):  
Natural Selection ◽  
Fundamental Theorem ◽  
Fisher’S Fundamental Theorem

scholarly journals The purpose of adaptation

2017 ◽  
Vol 7 (5) ◽  
pp. 20170005 ◽  
Author(s):  
Andy Gardner
Keyword(s):  
Natural Selection ◽  
Fundamental Theorem ◽  
Social Evolution ◽  
Inclusive Fitness ◽  
Central Feature ◽  
Biological Adaptation ◽  
Fisher’S Fundamental Theorem

A central feature of Darwin's theory of natural selection is that it explains the purpose of biological adaptation. Here, I: emphasize the scientific importance of understanding what adaptations are for, in terms of facilitating the derivation of empirically testable predictions; discuss the population genetical basis for Darwin's theory of the purpose of adaptation, with reference to Fisher's ‘fundamental theorem of natural selection'; and show that a deeper understanding of the purpose of adaptation is achieved in the context of social evolution, with reference to inclusive fitness and superorganisms.

scholarly journals Indirect genetic effects clarify how traits can evolve even when fitness does not

2018 ◽  
Author(s):  
David N. Fisher ◽  
Andrew G. McAdam
Keyword(s):  
Natural Selection ◽  
Fundamental Theorem ◽  
Genetic Effects ◽  
Social Effects ◽  
Indirect Genetic Effects ◽  
The Social ◽  
Mean Fitness ◽  
Related Individuals ◽  
Fundamental Theorems ◽  
Fisher’S Fundamental Theorem

AbstractThere are many situations in nature where we expect traits to evolve but not necessarily for mean fitness to increase. However, these scenarios are hard to reconcile simultaneously with Fisher’s Fundamental Theorem of Natural Selection and the Price identity. The consideration of indirect genetic effects on fitness reconciles these fundamental theorems with the observation that traits sometimes evolve without any adaptation, by explicitly considering the correlated evolution of the social environment, which is a form of transmission bias. While transmission bias in the Price identity is often assumed to be absent, here we show that explicitly considering indirect genetic effects as a form of transmission bias for fitness has several benefits: 1) it makes clear how traits can evolve while mean fitness remains stationary, 2) it reconciles the fundamental theorem of natural selection with the evolution of maladaptation, 3) it explicitly includes density-dependent fitness through negative social effects that depend on the number of interacting conspecifics, and 4) its allows mean fitness to evolve even when direct genetic variance in fitness is zero, if related individuals interact and/or if there is multilevel selection. In summary, considering fitness in the context of indirect genetic effects aligns important theorems of natural selection with many situations observed in nature and provides a useful lens through which we might better understand evolution and adaptation.

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

2020 ◽  
Vol 2 (2) ◽  
pp. 25-34
Author(s):  
Salvador Cordova
Keyword(s):  
Natural Selection ◽  
Population Growth ◽  
Fundamental Theorem ◽  
Biological Evolution ◽  
Memorial Lecture ◽  
Population Growth Rates ◽  
Biology Textbook ◽  
The Common ◽  
Definition Of ◽  
Fisher’S Fundamental Theorem

Fisher’s Fundamental Theorem of Natural Selection (FTNS) was called “biology’s central theorem” (Fisher, 1930, pgs. 36–37; Brockman, 2011; Royal Society, 2020). FTNS might possibly have been accorded this status for decades because Fisher himself declared his own theorem to be fundamental to biology (Fisher, 1930, pgs. 36–37). However, the idea that Fisher’s theorem is biology’s central theorem is by-and-large a myth promoted by popu- lar science writers like Richard Dawkins (Brockman, 2011). Joseph Felsenstein, when delivering the 2018 Fisher Memorial Lecture declared that FTNS was “alas, not so fundamental” (Felsenstein, 2018; Felsenstein, 2017, pg. 94. One may be hard-pressed to find a biology textbook or biology student who can explain how FTNS helps them understand biology. Even the meaning and proof of the FTNS have re- mained contentious even to this day (Price, 1972; Basener and Sanford, 2018). Not only does FTNS do little to nothing to explain biological evolution, but like most population genetic and evolutionary literature, FTNS relies on a definition of fit- ness in terms of population growth rates rather than the biophysical notions of fitness which are more in line with the common-sense intuitions of the medical and engineering communities. From the perspective of the biophysical (rather than the population growth) notion of fitness, natural selection might be more accurately described as an agent against the increase of complexity rather than an agent for it. Thus, metaphorically speaking, some sort of anti-Weasel model of natural selection might better describe how selection actu- ally works in nature rather than Dawkins’ Weasel or other man-made genetic algorithms. However, the main focus of this communication is to pro- vide some pedagogical insights through simple numerical illustrations of Fisher’s Theorem. The hope is that this will show the general irrelevance of FTNS to the question of the evolution of complexity by means of natural selection, and thus show that Fisher’s Theorem is not so fundamental after all.

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