Temporal and Spatial Effects Beyond Replicator Dynamics
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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] -
Interim Report IR-03-078 Evolutionary Game Dynamics
International Institute for Tel: 43 2236 807 342 Applied Systems Analysis Fax: 43 2236 71313 Schlossplatz 1 E-mail: [email protected] A-2361 Laxenburg, Austria Web: www.iiasa.ac.at Interim Report IR-03-078 Evolutionary Game Dynamics Josef Hofbauer ([email protected]) Karl Sigmund ([email protected]) Approved by Ulf Dieckmann ([email protected]) Project Leader, Adaptive Dynamics Network December 2003 Interim Reports on work of the International Institute for Applied Systems Analysis receive only limited review. Views or opinions expressed herein do not necessarily represent those of the Institute, its National Member Organizations, or other organizations supporting the work. IIASA STUDIES IN ADAPTIVE DYNAMICS NO. 76 The Adaptive Dynamics Network at IIASA fosters the develop- ment of new mathematical and conceptual techniques for under- standing the evolution of complex adaptive systems. Focusing on these long-term implications of adaptive processes in systems of limited growth, the Adaptive Dynamics Network brings together scientists and institutions from around the world with IIASA acting as the central node. Scientific progress within the network is collected in the IIASA ADN Studies in Adaptive Dynamics series. No. 1 Metz JAJ, Geritz SAH, Meszéna G, Jacobs FJA, van No. 11 Geritz SAH, Metz JAJ, Kisdi É, Meszéna G: The Dy- Heerwaarden JS: Adaptive Dynamics: A Geometrical Study namics of Adaptation and Evolutionary Branching. IIASA of the Consequences of Nearly Faithful Reproduction. IIASA Working Paper WP-96-077 (1996). Physical Review Letters Working Paper WP-95-099 (1995). van Strien SJ, Verduyn 78:2024-2027 (1997). Lunel SM (eds): Stochastic and Spatial Structures of Dynami- cal Systems, Proceedings of the Royal Dutch Academy of Sci- No. -
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. -
Evolutionary Game Theory: ESS, Convergence Stability, and NIS
Evolutionary Ecology Research, 2009, 11: 489–515 Evolutionary game theory: ESS, convergence stability, and NIS Joseph Apaloo1, Joel S. Brown2 and Thomas L. Vincent3 1Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, Nova Scotia, Canada, 2Department of Biological Sciences, University of Illinois, Chicago, Illinois, USA and 3Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, Arizona, USA ABSTRACT Question: How are the three main stability concepts from evolutionary game theory – evolutionarily stable strategy (ESS), convergence stability, and neighbourhood invader strategy (NIS) – related to each other? Do they form a basis for the many other definitions proposed in the literature? Mathematical methods: Ecological and evolutionary dynamics of population sizes and heritable strategies respectively, and adaptive and NIS landscapes. Results: Only six of the eight combinations of ESS, convergence stability, and NIS are possible. An ESS that is NIS must also be convergence stable; and a non-ESS, non-NIS cannot be convergence stable. A simple example shows how a single model can easily generate solutions with all six combinations of stability properties and explains in part the proliferation of jargon, terminology, and apparent complexity that has appeared in the literature. A tabulation of most of the evolutionary stability acronyms, definitions, and terminologies is provided for comparison. Key conclusions: The tabulated list of definitions related to evolutionary stability are variants or combinations of the three main stability concepts. Keywords: adaptive landscape, convergence stability, Darwinian dynamics, evolutionary game stabilities, evolutionarily stable strategy, neighbourhood invader strategy, strategy dynamics. INTRODUCTION Evolutionary game theory has and continues to make great strides. -
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. -
2.4 Mixed-Strategy Nash Equilibrium
Game Theoretic Analysis and Agent-Based Simulation of Electricity Markets by Teruo Ono Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2005 ( Massachusetts Institute of Technology 2005. All rights reserved. Author............................. ......--.. ., ............... Department of Electrical Engineering and Computer Science May 6, 2005 Certifiedby.................... ......... T...... ... .·..·.........· George C. Verghese Professor Thesis Supervisor ... / ., I·; Accepted by ( .............. ........1.-..... Q .--. .. ....-.. .......... .. Arthur C. Smith Chairman, Department Committee on Graduate Students MASSACHUSETTS INSTilRE OF TECHNOLOGY . I ARCHIVES I OCT 21 2005 1 LIBRARIES Game Theoretic Analysis and Agent-Based Simulation of Electricity Markets by Teruo Ono Submitted to the Department of Electrical Engineering and Computer Science on May 6, 2005, in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science Abstract In power system analysis, uncertainties in the supplier side are often difficult to esti- mate and have a substantial impact on the result of the analysis. This thesis includes preliminary work to approach the difficulties. In the first part, a specific electricity auction mechanism based on a Japanese power market is investigated analytically from several game theoretic viewpoints. In the second part, electricity auctions are simulated using agent-based modeling. Thesis Supervisor: George C. Verghese Title: Professor 3 Acknowledgments First of all, I would like to thank to my research advisor Prof. George C. Verghese. This thesis cannot be done without his suggestion, guidance and encouragement. I really appreciate his dedicating time for me while dealing with important works as a professor and an educational officer. -
Econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible
A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Banerjee, Abhijit; Weibull, Jörgen W. Working Paper Evolution and Rationality: Some Recent Game- Theoretic Results IUI Working Paper, No. 345 Provided in Cooperation with: Research Institute of Industrial Economics (IFN), Stockholm Suggested Citation: Banerjee, Abhijit; Weibull, Jörgen W. (1992) : Evolution and Rationality: Some Recent Game-Theoretic Results, IUI Working Paper, No. 345, The Research Institute of Industrial Economics (IUI), Stockholm This Version is available at: http://hdl.handle.net/10419/95198 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative Commons Licences), you genannten Lizenz gewährten Nutzungsrechte. may exercise further usage rights as specified in the indicated licence. www.econstor.eu Ind ustriens Utred n i ngsi nstitut THE INDUSTRIAL INSTITUTE FOR ECONOMIC AND SOCIAL RESEARCH A list of Working Papers on the last pages No. -
The Replicator Dynamics with Players and Population Structure Matthijs Van Veelen
The replicator dynamics with players and population structure Matthijs van Veelen To cite this version: Matthijs van Veelen. The replicator dynamics with players and population structure. Journal of Theoretical Biology, Elsevier, 2011, 276 (1), pp.78. 10.1016/j.jtbi.2011.01.044. hal-00682408 HAL Id: hal-00682408 https://hal.archives-ouvertes.fr/hal-00682408 Submitted on 26 Mar 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Author’s Accepted Manuscript The replicator dynamics with n players and population structure Matthijs van Veelen PII: S0022-5193(11)00070-1 DOI: doi:10.1016/j.jtbi.2011.01.044 Reference: YJTBI6356 To appear in: Journal of Theoretical Biology www.elsevier.com/locate/yjtbi Received date: 30 August 2010 Revised date: 27 January 2011 Accepted date: 27 January 2011 Cite this article as: Matthijs van Veelen, The replicator dynamics with n players and population structure, Journal of Theoretical Biology, doi:10.1016/j.jtbi.2011.01.044 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. -
The Replicator Equation on Graphs
The Replicator Equation on Graphs The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Ohtsuki Hisashi, Martin A. Nowak. 2006. The replicator equation on graphs. Journal of Theoretical Biology 243(1): 86-97. Published Version doi:10.1016/j.jtbi.2006.06.004 Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:4063696 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA The Replicator Equation on Graphs Hisashi Ohtsuki1;2;¤ & Martin A. Nowak2;3 1Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan 2Program for Evolutionary Dynamics, Harvard University, Cambridge MA 02138, USA 3Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge MA 02138, USA ¤The author to whom correspondence should be addressed. ([email protected]) tel: +81-92-642-2638 fax: +81-92-642-2645 Abstract : We study evolutionary games on graphs. Each player is represented by a vertex of the graph. The edges denote who meets whom. A player can use any one of n strategies. Players obtain a payo® from interaction with all their immediate neighbors. We consider three di®erent update rules, called `birth-death', `death-birth' and `imitation'. A fourth update rule, `pairwise comparison', is shown to be equivalent to birth-death updating in our model. -
Thesis This Thesis Must Be Used in Accordance with the Provisions of the Copyright Act 1968
COPYRIGHT AND USE OF THIS THESIS This thesis must be used in accordance with the provisions of the Copyright Act 1968. Reproduction of material protected by copyright may be an infringement of copyright and copyright owners may be entitled to take legal action against persons who infringe their copyright. Section 51 (2) of the Copyright Act permits an authorized officer of a university library or archives to provide a copy (by communication or otherwise) of an unpublished thesis kept in the library or archives, to a person who satisfies the authorized officer that he or she requires the reproduction for the purposes of research or study. The Copyright Act grants the creator of a work a number of moral rights, specifically the right of attribution, the right against false attribution and the right of integrity. You may infringe the author’s moral rights if you: - fail to acknowledge the author of this thesis if you quote sections from the work - attribute this thesis to another author - subject this thesis to derogatory treatment which may prejudice the author’s reputation For further information contact the University’s Director of Copyright Services sydney.edu.au/copyright The influence of topology and information diffusion on networked game dynamics Dharshana Kasthurirathna A thesis submitted in fulfillment of the requirements for the degree of Doctor of Philosophy Complex Systems Research Group Faculty of Engineering and IT The University of Sydney March 2016 Declaration I hereby declare that this submission is my own work and that, to the best of my knowledge and belief, it contains no material previously published or written by another person nor material which to a substantial extent has been accepted for the award of any other degree or diploma of the University or other institute of higher learning, except where due acknowledgement has been made in the text.