One equation to rule them all: a philosophical analysis of the Price equation

Luque, Víctor J.

doi:10.1007/s10539-016-9538-y

Cited by 40 publications

(40 citation statements)

References 73 publications

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“…At the top of the hierarchy of candidates for fundamental theorem status is Price's equation or theorem: (Price 1970(Price , 1972aGrafen 1985;Frank 1997Frank , 2012Rice 2004;Walsh and Lynch, forthcoming). Though initially derived in a somewhat limited form (Price 1970), it is a general mathematical identity that applies to any trait f of entities i that can be tracked through time, either by following i itself or by tracking from i to its descendants (Price 1972a(Price , 1995Grafen 1985;Frank 1995Frank , 1997Frank , 2012Rice 2004;Luque 2017;Walsh and Lynch, forthcoming). Though couched in statistical terms, the basic Price equation is concerned not primarily with estimation but rather with the population parameters and causal interpretation (Frank 2012).…”

Section: The Fundamental Theorem Of Evolutionmentioning

confidence: 99%

“…It is not my goal to review the many applications of the Price equation, which has been done better elsewhere (Rice 2004;Luque 2017), but to trace its relations to other funda- mental selection theorems. The derivations shown below reflect logical relationships but not historical ones-all of the fundamental theorems considered below actually predated the Price equation and were initially derived by other means.…”

Section: The Fundamental Theorem Of Evolutionmentioning

confidence: 99%

“…The derivations shown below reflect logical relationships but not historical ones-all of the fundamental theorems considered below actually predated the Price equation and were initially derived by other means. The Price equation helps show how to unify them and what their assumptions are (Luque 2017). The other fundamental theorems follow from Price's equation using three kinds of steps ( fig.…”

Section: The Fundamental Theorem Of Evolutionmentioning

confidence: 99%

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Fundamental Theorems of Evolution

Queller

2017

The American Naturalist

109

112

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Evolutionary biology is undergirded by an extensive and impressive set of mathematical models. Yet only one result, Fisher's theorem about selection and fitness, is generally accorded the status of a fundamental theorem. I argue that although its fundamental status is justified by its simplicity and scope, there are additional results that seem similarly fundamental. I suggest that the most fundamental theorem of evolution is the Price equation, both because of its simplicity and broad scope and because it can be used to derive four other familiar results that are similarly fundamental: Fisher's average-excess equation, Robertson's secondary theorem of natural selection, the breeder's equation, and Fisher's fundamental theorem. These derivations clarify both the relationships behind these results and their assumptions. Slightly less fundamental results include those for multivariate evolution and social selection. A key feature of fundamental theorems is that they have great simplicity and scope, which are often achieved by sacrificing perfect accuracy. Quantitative genetics has been more productive of fundamental theorems than population genetics, probably because its empirical focus on unknown genotypes freed it from the tyranny of detail and allowed it to focus on general issues.

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Section: The Fundamental Theorem Of Evolutionmentioning

confidence: 99%

Section: The Fundamental Theorem Of Evolutionmentioning

confidence: 99%

Section: The Fundamental Theorem Of Evolutionmentioning

confidence: 99%

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Fundamental Theorems of Evolution

Queller

2017

The American Naturalist

109

112

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“…At the level of pure, bare-bones mathematical description of selection, there really seemed to be nothing special about altruism. Nevertheless, his derivation of what is now known as the Price equation has proven valuable for social evolution theory and beyond [6][7][8][9][10][11][12]. The Price equation can be presented in a handful of equivalent forms, with the form of equation 1 being perhaps the most common.…”

Section: The (Single-level) Price Equation and Social Evolution Theorymentioning

confidence: 99%

The Price equation and the unity of social evolution theory

Lehtonen¹

2019

Preprint

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The Price equation has been entangled with social evolution theory from the start. It has been used to derive the most general versions of kin selection theory, and Price himself produced a multilevel equation which provides an alternative formulation of social evolution theory, dividing selection into components between and within groups. In this sense, the Price equation forms a basis for both kin and group selection, so often pitted against each other in the literature. Contextual analysis and the neighbour approach are prominent alternatives for analysing group selection. I discuss these four approaches to social evolution theory and their connections to the Price equation, focusing on their similarities and common mathematical structure. Despite different notations and modelling traditions, all four approaches are ultimately linked by a common set of mathematical components, revealing their underlying unity in a transparent way. The Price equation can similarly be used in the derivation of streamlined, weak selection social evolution modelling methods. These weak selection models are practical and powerful methods for constructing models in evolutionary and behavioural ecology, they can clarify the causal structure of models, and can be easily converted between the four social evolution approaches just like their regression counterparts.

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“…We acknowledge that this does not separate fitness effects from transmission bias, should there be any. There are different decompositions of the equation that deal adequately with this separation (Luque, 2017), however, these include additional terms for which there are no empirical data. More importantly, the assumption of no transmission bias is actually a worst-case scenario, because individuals with the PCD trait die or have lower viability or reproductive potential.…”

Section: The Price Formalism and Pcdmentioning

confidence: 99%

The Nature of Programmed Cell Death

Durand

Ramsey

2018

Biol Theory

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In multicellular organisms, cells are frequently programmed to die. This makes good sense: cells that fail to, or are no longer playing important roles are eliminated. From the cell's perspective, this also makes sense, since somatic cells in multicellular organisms require the cooperation of clonal relatives. In unicellular organisms, however, programmed cell death (PCD) poses a difficult and unresolved evolutionary problem. The empirical evidence for PCD in diverse microbial taxa has spurred debates about what precisely PCD means in the case of unicellular organisms (how it should be defined). In this article, we survey the concepts of PCD in the literature and the selective pressures associated with its evolution. We show that definitions of PCD have been almost entirely mechanistic and fail to separate questions concerning what PCD fundamentally is from questions about the kinds of mechanisms that realize PCD. We conclude that an evolutionary definition is best able to This is a preprint of an article whose final and definitive form is published in Biological Theory.

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One equation to rule them all: a philosophical analysis of the Price equation

Cited by 40 publications

References 73 publications

Fundamental Theorems of Evolution

Fundamental Theorems of Evolution

The Price equation and the unity of social evolution theory

The Nature of Programmed Cell Death

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