Stochasticity and variability in the dynamics and genetics of populations Perez de Vladar, Harold

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1 University of Groningen Stochasticity and variability in the dynamics and genetics of populations Perez de Vladar, Harold IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 2009 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Perez de Vladar, H. (2009). Stochasticity and variability in the dynamics and genetics of populations Groningen: s.n. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date:

2 RIJKSUNIVERSITEIT GRONINGEN Stochasticity and Variability in the Dynamics and Genetics of Populations Proefschrift ter verkrijging van het doctoraat in de Wiskunde en Natuurwetenschappen aan de Rijksuniversiteit Groningen op gezag van de Rector Magnificus, dr F. ZWAR TS, in het openbaar te verdedigen op vrijdag 25 september 2009 om 13:15 uur door HAROLD P. DE VLADAR geboren op 18 september 1976 te Caracas, Venezuela

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4 Promotores: Prof. dr Prof. dr IDO PEN FRANZ J. WEISSING Beoordelingscommissie: Prof. dr Prof. dr Prof. dr REINHARD BÜRGER JOHAN A.J. METZ EÖRS SZATHMÁRY

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6 To Leonardo Mateu To the Organic Intellectuals To the Sewer Poets.

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8 Contents List of Figures Samenvatting (NL) Summary (EN) Resumen (ES) Acknowledgements xiii xv xvi xviii xx General Introduction 1 I Population Dynamics 19 1 Density Dependence as a Size-Independent Regulatory Mechanism INTRODUCTION MECHANICS OF SIZE REGULATION GENERALIZED RATES OF GROWTH STABILITY ANALYSES SCALING LAWS DISCUSSION vii

9 1.7 CONCLUDING REMARKS Determinism, Noise, and Spurious Estimations in a Generalized Model of Population Growth INTRODUCTION DISTRIBUTION OF THE GROWTH RATES DENSITY REGULATION BY NOISE ESTIMATIONS OF GROWTH PATTERNS CONCLUDING REMARKS II Population Genetics 75 3 Statistical Mechanics and the Evolution of Polygenic Quantitative Traits INTRODUCTION GENERAL ANALYSIS DIRECTIONAL SELECTION, MUTATION, AND DRIFT LOW MUTATION RATES: 4Nµ < DISCUSSION G spotted in Rana temporaria! INTRODUCTION THEORETICAL BACKGROUND MATERIALS AND METHODS RESULTS DISCUSSION Evolution of Polygenic Traits: Adaptation at Maximal Entropy INTRODUCTION MECHANISMS OF QUANTITATIVE EVOLUTION ENTROPY MAXIMIZING THEORY

10 5.4 CONCLUDING REMARKS Perspectives: Pleiotropic effects on the G-matrix STANDING AND MUTATIONAL VARIATION SOME CONSEQUENCES OF PLEIOTROPY MOVING ON WITH THE G MATRIX CONCLUDING REMARKS Perspectives: The evolution of quantitative characters under stabilizing selection, mutation, and drift INTRODUCTION MAX-ENTROPIC APPROACH SINGLE LOCUS DYNAMICS FORMULATING POLYGENIC DYNAMICS POSTSCRIPT ON STABILIZING SELECTION III Synthesis Synthesis AN OVERVIEW OF THE CONCLUSIONS FURTHER EVOLUTIONARY IMPLICATIONS RESEARCH PERSPECTIVES Bibliography 253 A Maximization of entropy or of mean fitness? 283 A.1 MAXIMUM ENTROPY A.2 MAXIMUM FITNESS B Notes on the analogy with Statistical Mechanics in Physics 291

11 C Estimations of the genetic architecture of Rana temporaria 297 C.1 GENETIC EFFECTS AND EFFECTIVE NUMBER OF LOCI C.2 GENETIC ARCHITECTURE AND M.S.D. EQUILIBRIUM C.3 PLEIOTROPIC STRUCTURES AND FITNESS DIFFERENTIALS (β) C.4 EIGENSTRUCTURES OF THE G MATRICES D Formulas for the quantitative variables 311 D.1 DIRECTIONAL SELECTION D.2 STABILIZING SELECTION