Wright’s Adaptive Landscape, Fisher’s Fundamental Theorem

2018 ◽  
Author(s):  
Samir Okasha
Keyword(s):  
Natural Selection ◽  
Fundamental Theorem ◽  
Evolutionary Biology ◽  
Weak Sense ◽  
Hill Climbing ◽  
Adaptive Landscape ◽  
Classical Formulation ◽  
The Hill ◽  
Fisher’S Fundamental Theorem ◽  
Fitness Maximization

Fitness maximization, or optimization, is a controversial idea in evolutionary biology. One classical formulation of this idea is that natural selection will tend to push a population up a peak in an adaptive landscape, as Sewall Wright first proposed. However, the hill-climbing property only obtains under particular conditions, and even then the ascent is not usually by the steepest route; this shows why it is misleading to assimilate the process of natural selection to a process of goal-directed choice. A different formulation of the idea of fitness-maximization is R. A. Fisher’s ‘fundamental theorem of natural selection’. However, the theorem points only to a weak sense in which selection is an optimizing process, for it requires that ‘environmental constancy’ be understood in a highly specific way. It does not vindicate the claim that natural selection has an intrinsic tendency to produce adaptation.

scholarly journals Adaptive fitness landscape for replicator systems: to maximize or not to maximize

2018 ◽  
Vol 13 (3) ◽  
pp. 25 ◽  
Author(s):  
Alexander S. Bratus ◽  
Yuri S. Semenov ◽  
Artem S. Novozhilov
Keyword(s):  
Natural Selection ◽  
Fitness Landscape ◽  
Evolutionary Process ◽  
Hill Climbing ◽  
Adaptive Landscape ◽  
Basic Model ◽  
Mean Fitness ◽  
The Mean ◽  
The Hill ◽  
Fisher’S Fundamental Theorem

Sewall Wright’s adaptive landscape metaphor penetrates a significant part of evolutionary thinking. Supplemented with Fisher’s fundamental theorem of natural selection and Kimura’s maximum principle, it provides a unifying and intuitive representation of the evolutionary process under the influence of natural selection as the hill climbing on the surface of mean population fitness. On the other hand, it is also well known that for many more or less realistic mathematical models this picture is a severe misrepresentation of what actually occurs. Therefore, we are faced with two questions. First, it is important to identify the cases in which adaptive landscape metaphor actually holds exactly in the models, that is, to identify the conditions under which system’s dynamics coincides with the process of searching for a (local) fitness maximum. Second, even if the mean fitness is not maximized in the process of evolution, it is still important to understand the structure of the mean fitness manifold and see the implications of this structure on the system’s dynamics. Using as a basic model the classical replicator equation, in this note we attempt to answer these two questions and illustrate our results with simple well studied systems.

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.

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.

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