scholarly journals The Price equation and the unity of social evolution theory

2020 ◽  
Vol 375 (1797) ◽  
pp. 20190362 ◽  
Author(s):  
Jussi Lehtonen
Keyword(s):  
Group Selection ◽  
Social Evolution ◽  
Causal Structure ◽  
Mathematical Structure ◽  
Price Equation ◽  
Alternative Formulation ◽  
Evolution Theory ◽  
Weak Selection ◽  
Theme Issue ◽  
Modelling Methods

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 that 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. This article is part of the theme issue ‘Fifty years of the Price equation’.

scholarly journals The Price equation and the unity of social evolution theory

2019 ◽  
Author(s):  
Jussi Lehtonen
Keyword(s):  
Group Selection ◽  
Social Evolution ◽  
Causal Structure ◽  
Mathematical Structure ◽  
Price Equation ◽  
Alternative Formulation ◽  
Behavioural Ecology ◽  
Evolution Theory ◽  
Weak Selection ◽  
Modelling Methods

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.

scholarly journals The problem with the Price equation

2020 ◽  
Vol 375 (1797) ◽  
pp. 20190355 ◽  
Author(s):  
Matthijs van Veelen
Keyword(s):  
Group Selection ◽  
Social Evolution ◽  
Linear Models ◽  
Fitness Function ◽  
Regression Coefficients ◽  
Price Equation ◽  
Theme Issue

In this paper, I will argue that the generality of the Price equation comes at a cost, and that is that the terms in it become meaningless. There are simple linear models that can be written in a Price equation-like form, and for those the terms in them have a meaningful interpretation. There are also models for which that is not the case, and in general, when no assumptions on the shape of the fitness function are made, and all possible models are allowed for, the regression coefficients in the Price equation do not allow for a meaningful interpretation. The failure to recognize that the Price equation, although general, only has a meaningful interpretation under restrictive assumptions, has done real damage to the field of social evolution, as will be illustrated by looking at an application of the Price equation to group selection. This article is part of the theme issue ‘Fifty years of the Price equation’.

Evidence, Other Approaches, and Further Topics

2015 ◽  
Author(s):  
James A.R. Marshall
Keyword(s):  
Social Evolution ◽  
Inclusive Fitness ◽  
Kin Recognition ◽  
Replicator Dynamics ◽  
Empirical Support ◽  
Natural World ◽  
Price Equation ◽  
Evolution Theory ◽  
Inclusive Fitness Theory ◽  
The Many

This book has examined the genesis, the logic, and the generality of social evolution theory. In particular, it has presented evolutionary explanations of the many social behaviors we observe in the natural world by showing that William D. Hamilton's inclusive fitness theory provides the necessary generalization of classical Darwin–Wallace–Fisher fitness. This concluding chapter discusses the limitations of the analyses presented in this book and assesses the empirical support for inclusive fitness theory, focusing on microbial altruism, help in cooperative breeders, reproductive restraint in eusocial species, and the evolution of eusociality and cooperative breeding. It also considers more advanced topics in social evolution theory, including sex allocation, genetic kin recognition, spite, and the evolution of organismality. Finally, it reviews theoretical approaches to studying social evolution other than replicator dynamics and the Price equation, such as population genetics, class-structured populations, and maximization approaches.

scholarly journals Group and individual selection during evolutionary transitions in individuality: meanings and partitions

2020 ◽  
Vol 375 (1797) ◽  
pp. 20190364 ◽  
Author(s):  
Deborah E. Shelton ◽  
Richard E. Michod
Keyword(s):  
Group Selection ◽  
Contextual Analysis ◽  
Price Equation ◽  
Individual Selection ◽  
Evolutionary Transition ◽  
Theme Issue ◽  
Heritable Variation ◽  
Selection Models ◽  
Evolutionary Transitions ◽  
Multi Level

The Price equation embodies the ‘conditions approach’ to evolution in which the Darwinian conditions of heritable variation in fitness are represented in equation form. The equation can be applied recursively, leading to a partition of selection at the group and individual levels. After reviewing the well-known issues with the Price partition, as well as issues with a partition based on contextual analysis, we summarize a partition of group and individual selection based on counterfactual fitness, the fitness that grouped cells would have were they solitary. To understand ‘group selection’ in multi-level selection models, we assume that only group selection can make cells suboptimal when they are removed from the group. Our analyses suggest that there are at least three kinds of selection that can be occurring at the same time: group-specific selection along with two kinds of individual selection, within-group selection and global individual selection. Analyses based on counterfactual fitness allow us to specify how close a group is to being a pseudo-group, and this can be a basis for quantifying progression through an evolutionary transition in individuality (ETI). During an ETI, fitnesses at the two levels, group and individual, become decoupled, in the sense that fitness in a group may be quite high, even as counterfactual fitness goes to zero. This article is part of the theme issue ‘Fifty years of the Price equation’.

scholarly journals The Price equation and the causal analysis of evolutionary change

2020 ◽  
Vol 375 (1797) ◽  
pp. 20190365 ◽  
Author(s):  
Samir Okasha ◽  
Jun Otsuka
Keyword(s):  
Natural Selection ◽  
Causal Model ◽  
Causal Structure ◽  
Causal Analysis ◽  
Evolutionary Change ◽  
Price Equation ◽  
Causal Interpretation ◽  
Theme Issue ◽  
Causal Processes ◽  
The Difference

Though the Price equation in itself is simply a statistical identity, biologists have often adopted a ‘causal interpretation’ of the equation, in the sense that its component terms have been supposed to correspond to distinct causal processes in evolution, such as natural selection and transmission bias. In this paper, we bring the issue of causal interpretation to the fore, by studying the conditions under which it is legitimate to read causal meaning into the Price equation. We argue that only if substantive assumptions about causal structure are made, which can be represented in the form of a causal model, can the component terms of the Price equation be interpreted as causally meaningful. We conclude with a reflection on the epistemic uses of the Price equation, emphasizing the difference between the description, explanation and prediction of evolutionary change. This article is part of the theme issue ‘Fifty years of the Price equation’.

scholarly journals Identifying causes of social evolution: The Price approach, contextual analysis, and multilevel selection

2020 ◽  
Author(s):  
Christoph Thies ◽  
Richard A. Watson
Keyword(s):  
Kin Selection ◽  
Group Selection ◽  
Causal Structure ◽  
Multilevel Selection ◽  
Contextual Analysis ◽  
Price Equation ◽  
Selection Theory ◽  
Individual Fitness ◽  
Multilevel Selection Theory ◽  
The Individual

AbstractKin selection theory and multilevel selection theory are different approaches to explaining the evolution of social traits. The latter claims that it is useful to regard selection as a process that can occur on multiple levels of organisation such as the level of individuals and the level of groups. This is reflected in a decomposition of fitness into an individual component and a group component. However, the two major statistical tools to determine the coefficients of such a decomposition, the multilevel Price equation and contextual analysis, are inconsistent and may disagree on whether group selection is present. Here we show that the reason for the discrepancies is that underlying the multilevel Price equation and contextual analysis are two nonequivalent causal models for the generation of individual fitness effects (thus leaving different ‘remainders’ explained by group effects). While the multilevel Price equation assumes that the individual effect of a trait determines an individual’s relative success within a group, contextual analysis posits that the individual effect is context-independent. Since these different assumptions reflect claims about the causal structure of the system, the correct approach cannot be determined on general theoretical or statistical grounds but must be identified by experimental intervention. We outline interventions that reveal the underlying causal structure and thus facilitate choosing the appropriate approach. We note that the reductionist viewpoint of kin selection theory with its focus on the individual is immune to such inconsistency because it does not address causal structure with respect to levels of organisation. In contrast, our analysis of the two approaches to measuring group selection demonstrates that multilevel selection theory adds meaningful (falsifiable) causal structure to explain the sources of individual fitness and thereby constitutes a proper refinement of kin selection theory.

scholarly journals Price's equation made clear

2020 ◽  
Vol 375 (1797) ◽  
pp. 20190361 ◽  
Author(s):  
Andy Gardner
Keyword(s):  
General Theory ◽  
Evolutionary Biology ◽  
Social Evolution ◽  
Evolutionary Change ◽  
Price Equation ◽  
Theme Issue ◽  
Price’S Equation ◽  
Scientific Disciplines ◽  
Wide Range ◽  
Mathematical Foundations

Price's equation provides a very simple—and very general—encapsulation of evolutionary change. It forms the mathematical foundations of several topics in evolutionary biology, and has also been applied outwith evolutionary biology to a wide range of other scientific disciplines. However, the equation's combination of simplicity and generality has led to a number of misapprehensions as to what it is saying and how it is supposed to be used. Here, I give a simple account of what Price's equation is, how it is derived, what it is saying and why this is useful. In particular, I suggest that Price's equation is useful not primarily as a predictor of evolutionary change but because it provides a general theory of selection. As an illustration, I discuss some of the insights Price's equation has brought to the study of social evolution. This article is part of the theme issue ‘Fifty years of the Price equation’.

scholarly journals The dissipative approach to quantum field theory: conceptual foundations and ontological implications

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Andrea Oldofredi ◽  
Hans Christian Öttinger
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Nonequilibrium Thermodynamics ◽  
Particle Creation ◽  
Mathematical Structure ◽  
Alternative Formulation ◽  
Quantum Field ◽  
Conceptual Foundations ◽  
Particle Creation And Annihilation

AbstractMany attempts have been made to provide Quantum Field Theory with conceptually clear and mathematically rigorous foundations; remarkable examples are the Bohmian and the algebraic perspectives respectively. In this essay we introduce the dissipative approach to QFT, a new alternative formulation of the theory explaining the phenomena of particle creation and annihilation starting from nonequilibrium thermodynamics. It is shown that DQFT presents a rigorous mathematical structure, and a clear particle ontology, taking the best from the mentioned perspectives. Finally, after the discussion of its principal implications and consequences, we compare it with the main Bohmian QFTs implementing a particle ontology.

scholarly journals The Social Evolution of Language, and the Language of Social Evolution

2007 ◽  
Vol 5 (4) ◽  
pp. 147470490700500 ◽  
Author(s):  
Thomas C. Scott-Phillips
Keyword(s):  
Social Evolution ◽  
Language Evolution ◽  
Reciprocal Altruism ◽  
Honest Signaling ◽  
Evolution Theory ◽  
Evolution Of Language ◽  
The Social ◽  
Human Capacity ◽  
Correct Application

Recent years have witnessed an increased interest in the evolution of the human capacity for language. Such a project is necessarily interdisciplinary. However, that interdisciplinarity brings with it a risk: terms with a technical meaning in their own field are used wrongly or too loosely by those from other backgrounds. Unfortunately, this risk has been realized in the case of language evolution, where many of the terms of social evolution theory (reciprocal altruism, honest signaling, etc.) are incorrectly used in a way that suggests that certain key fundamentals have been misunderstood. In particular the distinction between proximate and ultimate explanations is often lost, with the result that several claims made by those interested in language evolution are epistemically incoherent. However, the correct application of social evolution theory provides simple, clear explanations of why language most likely evolved and how the signals used in language — words — remain cheap yet arbitrary.

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’.

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