Fisher's ‘fundamental theorem’ made clear

Price, George R.

doi:10.1111/j.1469-1809.1972.tb00764.x

Cited by 347 publications

(339 citation statements)

References 8 publications

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“…Price never connected these abstract ideas about mapping and about separating frequency and property directly to his formulation of the Price equation, although one can see hints of this in Price (1972a). In other work (Price, 1972b), Price clarified one of the great puzzles in the history of evolutionary theory. In 1930, Fisher stated his fundamental theorem of natural selection as: “The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time.”…”

Section: Natural Selectionmentioning

confidence: 99%

“…Fisher is regarded as perhaps the greatest mathematical biologist ever. So the mismatch between Fisher's strong claim and the seemingly obvious failure of the theorem was hard to reconcile.Price (1972b) solved the puzzle. In the language of the present article, Fisher meant that the rate of increase in fitness equals the variance in fitness when evaluated with respect to the fixed frame of reference of the population's initial state.…”

Section: Natural Selectionmentioning

confidence: 99%

“…Selection acts as a direct force, with consequences of the direct force evaluated by holding constant the context. Any changes to the population that alter the fitnesses of individuals are regarded as consequences of inertial forces that alter the frame of reference.Price (1972b) did not use the language of direct and inertial forces, but he clearly understood Fisher's partition of total change into two components. Later work clarified a variety of early theories about natural selection within the context of the Fisher's partition (Ewens, 1989, 1992; Frank & Slatkin, 1992).…”

Section: Natural Selectionmentioning

confidence: 99%

“…Price (1972b) solved the puzzle. In the language of the present article, Fisher meant that the rate of increase in fitness equals the variance in fitness when evaluated with respect to the fixed frame of reference of the population's initial state.…”

Section: Natural Selectionmentioning

confidence: 99%

“…Price (1972b) did not use the language of direct and inertial forces, but he clearly understood Fisher's partition of total change into two components. Later work clarified a variety of early theories about natural selection within the context of the Fisher's partition (Ewens, 1989, 1992; Frank & Slatkin, 1992).…”

Section: Natural Selectionmentioning

confidence: 99%

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Universal expressions of population change by the Price equation: Natural selection, information, and maximum entropy production

Frank

2017

Ecology and Evolution

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The Price equation shows the unity between the fundamental expressions of change in biology, in information and entropy descriptions of populations, and in aspects of thermodynamics. The Price equation partitions the change in the average value of a metric between two populations. A population may be composed of organisms or particles or any members of a set to which we can assign probabilities. A metric may be biological fitness or physical energy or the output of an arbitrarily complicated function that assigns quantitative values to members of the population. The first part of the Price equation describes how directly applied forces change the probabilities assigned to members of the population when holding constant the metrical values of the members—a fixed metrical frame of reference. The second part describes how the metrical values change, altering the metrical frame of reference. In canonical examples, the direct forces balance the changing metrical frame of reference, leaving the average or total metrical values unchanged. In biology, relative reproductive success (fitness) remains invariant as a simple consequence of the conservation of total probability. In physics, systems often conserve total energy. Nonconservative metrics can be described by starting with conserved metrics, and then studying how coordinate transformations between conserved and nonconserved metrics alter the geometry of the dynamics and the aggregate values of populations. From this abstract perspective, key results from different subjects appear more simply as universal geometric principles for the dynamics of populations subject to the constraints of particular conserved quantities.

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Section: Natural Selectionmentioning

confidence: 99%

Section: Natural Selectionmentioning

confidence: 99%

Section: Natural Selectionmentioning

confidence: 99%

Section: Natural Selectionmentioning

confidence: 99%

Section: Natural Selectionmentioning

confidence: 99%

See 3 more Smart Citations

Universal expressions of population change by the Price equation: Natural selection, information, and maximum entropy production

Frank

2017

Ecology and Evolution

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Evolutionary Quantitative Genetics

Walsh

2003

Handbook of Statistical Genetics

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Evolutionary quantitative genetics is the study of how complex traits evolve over time. While this field builds on traditional concepts from quantitative genetics widely used by applied breeders and human geneticists (in particular, the inheritance of complex traits), its unique feature is in examining the role of natural selection in changing the population distribution of a complex trait over time. Our review focuses on this role of selection, starting with response under the standard infinitesimal model, in which trait variation is determined by a very large number of loci, each of small effect. We then turn to issues of measuring fitness (and hence natural selection) on both univariate and multivariate traits. We conclude by examining models that treat fitness itself as a complex trait.

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Evolutionary Quantitative Genetics

Walsh

2007

Handbook of Statistical Genetics

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Fisher's ‘fundamental theorem’ made clear

Cited by 347 publications

References 8 publications

Universal expressions of population change by the Price equation: Natural selection, information, and maximum entropy production

Universal expressions of population change by the Price equation: Natural selection, information, and maximum entropy production

Evolutionary Quantitative Genetics

Evolutionary Quantitative Genetics

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