One Equation to Rule Them All
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The Mirror of Physics: on How the Price Equation Can Unify Evolutionary Biology
Synthese https://doi.org/10.1007/s11229-021-03339-6 ORIGINAL RESEARCH The mirror of physics: on how the Price equation can unify evolutionary biology Victor J. Luque1 · Lorenzo Baravalle2 Received: 30 September 2020 / Accepted: 26 July 2021 © The Author(s) 2021 Abstract Due to its high degree of complexity and its historical nature, evolutionary biol‑ ogy has been traditionally portrayed as a messy science. According to the supporters of such a view, evolutionary biology would be unable to formulate laws and robust theories, instead just delivering coherent narratives and local models. In this article, our aim is to challenge this view by showing how the Price equation can work as the core of a general theoretical framework for evolutionary phenomena. To support this claim, we outline some unnoticed structural similarities between physical theo‑ ries (in particular, classical mechanics) and evolutionary biology. More specifcally, we shall argue that the Price equation, in the same way as fundamental formalisms in physics, can serve as a heuristic principle to formulate and systematise diferent theories and models in evolutionary biology. Keywords Evolutionary biology · Price equation · Complexity · Metatheoretical structuralism · Guiding principle · Classical mechanics This article belongs to the topical collection “Simplicity out of Complexity? Physics and the Aims of Science,” Edited by Florian J. Boge, Martin King, Paul Grünke and Miguel Ángel Carretero Sahuquillo. * Victor J. Luque [email protected] Lorenzo Baravalle [email protected] -
The 'Algebra of Evolution': the Robertson–Price Identity and Viability Selection for Body Mass in a Wild Bird Population
Edinburgh Research Explorer The ‘algebra of evolution’: the Robertson–Price identity and viability selection for body mass in a wild bird population Citation for published version: Hajduk, GK, Walling, CA, Cockburn, A & Kruuk, LEB 2020, 'The ‘algebra of evolution’: the Robertson–Price identity and viability selection for body mass in a wild bird population', Philosophical Transactions of the Royal Society B: Biological Sciences, vol. 375, no. 1797, 20190359. https://doi.org/10.1098/rstb.2019.0359 Digital Object Identifier (DOI): 10.1098/rstb.2019.0359 Link: Link to publication record in Edinburgh Research Explorer Document Version: Publisher's PDF, also known as Version of record Published In: Philosophical Transactions of the Royal Society B: Biological Sciences General rights Copyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer content complies with UK legislation. If you believe that the public display of this file breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Download date: 26. Sep. 2021 The ‘algebra of evolution’: the Robertson–Price identity and royalsocietypublishing.org/journal/rstb viability selection for body mass in a wild bird population Research G. K. Hajduk1, C. A. Walling1, A. Cockburn2 and L. E. B. Kruuk2 1 Cite this article: Hajduk GK, Walling CA, Institute of Evolutionary Biology, University of Edinburgh, Edinburgh EH9 3FL, UK 2Research School of Biology, Australian National University, Canberra, ACT 2601, Australia Cockburn A, Kruuk LEB. -
Multilevel Selection and Population Genetics in Structured
Multilevel Selection, Population Genetics and Cooperation in Structured Populations NIMBioS Tutorial: Game Theoretical Modeling of Evolution in Structured Populations Jeremy Van Cleve University of Kentucky 26 April 2016 Multilevel selection, pop gen and games in structured pops UNIVERSITY OF KENTUCKY How do cooperative behaviors evolve? Cooperation occurs when: focal: cost to improve state of its partner partner: beneft from improved state Food improves state ⟶ higher ftness Multilevel selection, pop gen and games in structured pops UNIVERSITY OF KENTUCKY trate into a tightWhen form they known cease as moving,and the a when cells Mexican there ofenvironment hat. is the lacks Then, either slug electrolytes, concen- directional when light it orimmune is system, no before they very are light. shed at moist, thefunctioning rear of simultaneously the slug. asthe liver, slug from kidney, front and toered back innate class picking up of toxins cells and calledand bacteria, ultimately sentinel become cells the stalk. that There is sweep athe through recently discov- constituent cells. Those atthe slug the lacks a front nervous system, direct there are movement differencesmove: among an important advantage to themore quickly social and farther stage. than Though any individual amoebaeffectively could recovering the solitaryrear, stage. and these The cells slug can feed moves sheath on any largely bacteria made they discover, upfrom of it cellulose, it in drops some cells important at ways. the Astoward light and heat it and away from ammonia crawls ( throughwhich a then elongatesAfter slightly a few and hours, beginsa this center to center concentrates into crawl in aconcentrate around a mound, in great process streams of calledhighest dicty cells, aggregation concentration. -
The Purpose of Adaptation
Downloaded from http://rsfs.royalsocietypublishing.org/ on February 1, 2018 The purpose of adaptation Andy Gardner rsfs.royalsocietypublishing.org School of Biology, University of St Andrews, Dyers Brae, St Andrews KY16 9TH, UK AG, 0000-0002-1304-3734 A central feature of Darwin’s theory of natural selection is that it explains the purpose of biological adaptation. Here, I: emphasize the scientific impor- tance of understanding what adaptations are for, in terms of facilitating Research the derivation of empirically testable predictions; discuss the population genetical basis for Darwin’s theory of the purpose of adaptation, with refer- Cite this article: Gardner A. 2017 The ence to Fisher’s ‘fundamental theorem of natural selection’; and show that a purpose of adaptation. Interface Focus 7: deeper understanding of the purpose of adaptation is achieved in the context 20170005. of social evolution, with reference to inclusive fitness and superorganisms. http://dx.doi.org/10.1098/rsfs.2017.0005 One contribution of 20 to a theme issue ‘New 1. The purpose of adaptation trends in evolutionary biology: biological, Darwinism is a theory of the process of adaptation, i.e. the appearance of design philosophical and social science perspectives’. in the biological world. The problem of how to explain adaptation is an ancient one, and it famously provided the basis for William Paley’s [1] argument for Subject Areas: the existence of an intelligent, divine designer. This problem was decisively solved by Charles Darwin [2], whose theory of evolution by natural selec- biomathematics tion—in which heritable variations associated with greater survival and reproductive success are identified as being more likely to accumulate in natural Keywords: populations—explained the adaptation of organisms in purely naturalistic, natural selection, fundamental theorem, mechanical terms. -
Struggle for Existence: the Models for Darwinian and Non-Darwinian Selection
Struggle for Existence: the models for Darwinian and non-Darwinian selection G. Karev1, F. Berezovskaya2 1National Center for Biotechnology Information, Bethesda, MD 20894, USA. Email: [email protected] 2 Howard University, Washington, DC 20059, USA e-mail: [email protected] Abstract Classical understanding of the outcome of the struggle for existence results in the Darwinian “survival of the fittest”. Here we show that the situation may be different, more complex and arguably more interesting. Specifically, we show that different versions of inhomogeneous logistic-like models with a distributed Malthusian parameter imply non-Darwinian “survival of everybody”. In contrast, the inhomogeneous logistic equation with distributed carrying capacity shows Darwinian “survival of the fittest”. We also consider an inhomogeneous birth-and-death equation and give a simple proof that this equation results in the “survival of the fittest”. In addition to this known result, we find an exact limit distribution of the parameters of this equation. We also consider “frequency-dependent” inhomogeneous models and show that although some of these models show Darwinian “survival of the fittest”, there is not enough time for selection of the fittest species. We discuss the well-known Gauze’s Competitive exclusion principle that states that “Complete competitors cannot coexist”. While this principle is often considered as a direct consequence of the Darwinian “survival of the fittest”, we show that from the point of view of developed mathematical theory complete competitors can in fact coexist indefinitely. 1. Introduction. Darwinian evolution and Competitive Exclusion principle In his 1934 book, G.F. Gause described his experiments where he cultivated two types of yeast, S. -
George Price's Contributions to Evolutionary Genetics
J. theor. Biol. (1995) 175, 373–388 George Price’s Contributions to Evolutionary Genetics S A. F Department of Ecology and Evolutionary Biology, University of California, Irvine, CA 92717, U.S.A. (Received on 9 November 1994, Accepted in revised form on 14 February 1995) George Price studied evolutionary genetics for approximately seven years between 1967 and 1974. During that brief period Price made three lasting contributions to evolutionary theory; these were: (i) the Price Equation, a profound insight into the nature of selection and the basis for the modern theories of kin and group selection; (ii) the theory of games and animal behavior, based on the concept of the evolutionarily stable strategy; and (iii) the modern interpretation of Fisher’s fundamental theorem of natural selection, Fisher’s theorem being perhaps the most cited and least understood idea in the history of evolutionary genetics. This paper summarizes Price’s contributions and briefly outlines why, toward the end of his painful intellectual journey, he chose to focus his deep humanistic feelings and sharp, analytical mind on abstract problems in evolutionary theory. 7 1995 Academic Press Limited Introduction (iii) Price (1972b) was the first to crack the most obscure and misunderstood of R. A. Fisher’s many At the age of 44, George Price quit his engineering job oracles: the fundamental theorem of natural selection. at IBM and took up evolutionary genetics. Price This theorem is perhaps the most widely quoted result moved to the Galton Laboratories at London in 1967, in evolutionary theory, yet Price demonstrated where C. A. B. Smith, Weldon Professor of Biometry, convincingly that the consensus interpretation of the provided him with space and encouragement. -
Ecological and Evolutionary Dynamics of Interconnectedness and Modularity
Ecological and evolutionary dynamics of interconnectedness and modularity Jan M. Nordbottena,b, Simon A. Levinc, Eörs Szathmáryd,e,f, and Nils C. Stensethg,1 aDepartment of Mathematics, University of Bergen, N-5020 Bergen, Norway; bDepartment of Civil and Environmental Engineering, Princeton University, Princeton, NJ 08544; cDepartment of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ 08544; dParmenides Center for the Conceptual Foundations of Science, D-82049 Pullach, Germany; eMTA-ELTE (Hungarian Academy of Sciences—Eötvös University), Theoretical Biology and Evolutionary Ecology Research Group, Department of Plant Systematics, Ecology and Theoretical Biology, Eötvös University, Budapest, H-1117 Hungary; fEvolutionary Systems Research Group, MTA (Hungarian Academy of Sciences) Ecological Research Centre, Tihany, H-8237 Hungary; and gCentre for Ecological and Evolutionary Synthesis (CEES), Department of Biosciences, University of Oslo, N-0316 Oslo, Norway Contributed by Nils C. Stenseth, December 1, 2017 (sent for review September 12, 2017; reviewed by David C. Krakauer and Günter P. Wagner) In this contribution, we develop a theoretical framework for linking refinement of this inquiry is to look for compartmentalization (i.e., microprocesses (i.e., population dynamics and evolution through modularity) in ecosystems. In food webs, for example, compartments natural selection) with macrophenomena (such as interconnectedness (which are subgroups of taxa with many strong interactions in each and modularity within an -
What Genomic Data Can Reveal About Eco-Evolutionary Dynamics
PERSPECTIVE https://doi.org/10.1038/s41559-017-0385-2 What genomic data can reveal about eco-evolutionary dynamics Seth M. Rudman 1*, Matthew A. Barbour2, Katalin Csilléry3, Phillip Gienapp4, Frederic Guillaume2, Nelson G. Hairston Jr5, Andrew P. Hendry6, Jesse R. Lasky7, Marina Rafajlović8,9, Katja Räsänen10, Paul S. Schmidt1, Ole Seehausen 11,12, Nina O. Therkildsen13, Martin M. Turcotte3,14 and Jonathan M. Levine15 Recognition that evolution operates on the same timescale as ecological processes has motivated growing interest in eco-evo- lutionary dynamics. Nonetheless, generating sufficient data to test predictions about eco-evolutionary dynamics has proved challenging, particularly in natural contexts. Here we argue that genomic data can be integrated into the study of eco-evo- lutionary dynamics in ways that deepen our understanding of the interplay between ecology and evolution. Specifically, we outline five major questions in the study of eco-evolutionary dynamics for which genomic data may provide answers. Although genomic data alone will not be sufficient to resolve these challenges, integrating genomic data can provide a more mechanistic understanding of the causes of phenotypic change, help elucidate the mechanisms driving eco-evolutionary dynamics, and lead to more accurate evolutionary predictions of eco-evolutionary dynamics in nature. vidence that the ways in which organisms interact with their evolution plays a central role in regulating such dynamics. environment can evolve fast enough to alter ecological dynam- Particularly relevant is information gleaned from efforts to under- Eics has forged a new link between ecology and evolution1–5. A stand the genomic basis of adaptation, a burgeoning field in evolu- growing area of study, termed eco-evolutionary dynamics, centres tionary biology that investigates the specific genomic underpinnings on understanding when rapid evolutionary change is a meaningful of phenotypic variation, its response to natural selection and effects driver of ecological dynamics in natural ecosystems6–8. -
Martin A. Nowak
EVOLUTIONARY DYNAMICS EXPLORING THE EQUATIONS OF LIFE MARTIN A. NOWAK THE BELKNAP PRESS OF HARVARD UNIVERSITY PRESS CAMBRIDGE, MASSACHUSETTS, AND LONDON, ENGLAND 2006 Copyright © 2006 by the President and Fellows of Harvard College All rights reserved Printed in Canada Library of Congress Cataloging-in-Publication Data Nowak, M. A. (Martin A.) Evolutionary dynamics : exploring the equations of life / Martin A. Nowak. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-674-02338-3 (alk. paper) ISBN-10: 0-674-02338-2 (alk. paper) 1. Evolution (Biology)—Mathematical models. I. Title. QH371.3.M37N69 2006 576.8015118—dc22 2006042693 Designed by Gwen Nefsky Frankfeldt CONTENTS Preface ix 1 Introduction 1 2 What Evolution Is 9 3 Fitness Landscapes and Sequence Spaces 27 4 Evolutionary Games 45 5 Prisoners of the Dilemma 71 6 Finite Populations 93 7 Games in Finite Populations 107 8 Evolutionary Graph Theory 123 9 Spatial Games 145 10 HIV Infection 167 11 Evolution of Virulence 189 12 Evolutionary Dynamics of Cancer 209 13 Language Evolution 249 14 Conclusion 287 Further Reading 295 References 311 Index 349 PREFACE Evolutionary Dynamics presents those mathematical principles according to which life has evolved and continues to evolve. Since the 1950s biology, and with it the study of evolution, has grown enormously, driven by the quest to understand the world we live in and the stuff we are made of. Evolution is the one theory that transcends all of biology. Any observation of a living system must ultimately be interpreted in the context of its evolution. Because of the tremendous advances over the last half century, evolution has become a dis- cipline that is based on precise mathematical foundations. -
The Place of Development in Mathematical Evolutionary Theory SEAN H
COMMENTARY AND PERSPECTIVE The Place of Development in Mathematical Evolutionary Theory SEAN H. RICEÃ Department of Biological Sciences, Texas Tech University, Lubbock, Texas ABSTRACT Development plays a critical role in structuring the joint offspring–parent phenotype distribution. It thus must be part of any truly general evolutionary theory. Historically, the offspring–parent distribution has often been treated in such a way as to bury the contribution of development, by distilling from it a single term, either heritability or additive genetic variance, and then working only with this term. I discuss two reasons why this approach is no longer satisfactory. First, the regression of expected offspring phenotype on parent phenotype can easily be nonlinear, and this nonlinearity can have a pronounced impact on the response to selection. Second, even when the offspring–parent regression is linear, it is nearly always a function of the environment, and the precise way that heritability covaries with the environment can have a substantial effect on adaptive evolution. Understanding these complexities of the offspring–parent distribution will require understanding of the developmental processes underlying the traits of interest. I briefly discuss how we can incorporate such complexity into formal evolutionary theory, and why it is likely to be important even for traits that are not traditionally the focus of evo–devo research. Finally, I briefly discuss a topic that is widely seen as being squarely in the domain of evo–devo: novelty. I argue that the same conceptual and mathematical framework that allows us to incorporate developmental complexity into simple models of trait evolution also yields insight into the evolution of novel traits. -
The Price Equation, Fisher's Fundamental Theorem, Kin Selection, and Causal Analysis
Evolution, 51(6), 1997, pp. 1712-1729 THE PRICE EQUATION, FISHER'S FUNDAMENTAL THEOREM, KIN SELECTION, AND CAUSAL ANALYSIS STEVEN A. FRANK Department of Ecology and Evolutionary Biology, University of California, Irvine, California 92697-2525 E-mail: [email protected] Abstract.--A general framework is presented to unify diverse models of natural selection. This framework is based on the Price Equation, with two additional steps. First, characters are described by their multiple regression on a set of predictor variables. The most common predictors in genetics are alleles and their interactions, but any predictor may be used. The second step is to describe fitness by multiple regression on characters. Once again, characters may be chosen arbitrarily. This expanded Price Equation provides an exact description of total evolutionary change under all conditions, and for all systems of inheritance and selection. The model is first used for a new proof of Fisher's fundamental theorem of natural selection. The relations are then made clear among Fisher's theorem, Robertson's covariance theorem for quantitative genetics, the Lande-Arnold model for the causal analysis of natural selection, and Hamilton's rule for kin selection. Each of these models is a partial analysis of total evolutionary change. The Price Equation extends each model to an exact, total analysis of evolutionary change for any system of inheritance and selection. This exact analysis is used to develop an expanded Hamilton's rule for total change. The expanded rule clarifies the distinction between two types of kin selection coefficients. The first measures components of selection caused by correlated phenotypes of social partners. -
Joint Phenotypes, Evolutionary Conflict and the Fundamental Theorem of Natural Selection David C
Washington University in St. Louis Washington University Open Scholarship Biology Faculty Publications & Presentations Biology 5-19-2014 Joint phenotypes, evolutionary conflict and the fundamental theorem of natural selection David C. Queller Washington University in St Louis, [email protected] Follow this and additional works at: https://openscholarship.wustl.edu/bio_facpubs Part of the Biology Commons, Evolution Commons, and the Population Biology Commons Recommended Citation Queller, David C., "Joint phenotypes, evolutionary conflict and the fundamental theorem of natural selection" (2014). Biology Faculty Publications & Presentations. 57. https://openscholarship.wustl.edu/bio_facpubs/57 This Article is brought to you for free and open access by the Biology at Washington University Open Scholarship. It has been accepted for inclusion in Biology Faculty Publications & Presentations by an authorized administrator of Washington University Open Scholarship. For more information, please contact [email protected]. Joint phenotypes, evolutionary conflict, and the fundamental theorem of natural selection David C. Queller Department of Biology Washington University in St. Louis St. Louis, MO 63130 USA Email: [email protected] Prepublication version. Pulbished in Phil. Trans. Roy. Soc. B 369:20130423 doi:10.1098/rstb.2013.0423. 1 Abstract Multiple organisms can sometimes affect a common phenotype. For example the portion of a leaf eaten by an insect is a joint phenotype of the plant and the insect and the amount of food obtained by an offspring can be joint trait with its mother. Here I describe the evolution of joint phenotypes in quantitative genetic terms. A joint phenotype for multiple species evolves as the sum of additive genetic variances in each species, weighted by the selection on each species.