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The Statistical Physics of Fixation and Equilibration in Individual-Based Models

  • Book
  • © 2016

Overview

Authors:
  1. Peter Ashcroft

    1. Institute for Integrative Biology, ETH Zürich, ZÜRICH, Switzerland

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  • Nominated as an outstanding Ph.D. thesis by the University of Manchester, UK
  • Features a clear introduction to birth-death processes and how to calculate fixation probabilities and mean fixation times
  • Considers a diverse set of applications, including evolutionary game theory and cancer dynamics
  • Provides a pedagogical account of the WentzeI-Kramers-Brillouin (WKB) method, which is illustrated with numerous examples
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Theses (Springer Theses)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xv
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  2. Introduction

    • Peter Ashcroft
    Pages 1-9

  3. Technical Background

    • Peter Ashcroft
    Pages 11-37

  4. Finite Populations in Switching Environments

    • Peter Ashcroft
    Pages 39-62

  5. Fixation Time Distributions in Birth–Death Processes

    • Peter Ashcroft
    Pages 63-89

  6. Metastable States in a Model of Cancer Initiation

    • Peter Ashcroft
    Pages 91-126

  7. The WKB Method: A User-Guide

    • Peter Ashcroft
    Pages 127-158

  8. Conclusions

    • Peter Ashcroft
    Pages 159-164
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Keywords

About this book

This thesis explores several interdisciplinary topics at the border of theoretical physics and biology, presenting results that demonstrate the power of methods from statistical physics when applied to neighbouring disciplines. From birth-death processes in switching environments to discussions on the meaning of quasi-potential landscapes in high-dimensional spaces, this thesis is a shining example of the efficacy of interdisciplinary research. The fields advanced in this work include game theory, the dynamics of cancer, and invasion of mutants in resident populations, as well as general contributions to the theory of stochastic processes.
 
The background material provides an intuitive introduction to the theory and applications of stochastic population dynamics, and the use of techniques from statistical physics in their analysis. The thesis then builds on these foundations to address problems motivated by biological phenomena.

Authors and Affiliations

  • Institute for Integrative Biology, ETH Zürich, ZÜRICH, Switzerland

    Peter Ashcroft

About the author

Peter Ashcroft graduated as a Master of Mathematics and Physics from the Univerisity of Manchester in 2012. He then studied for his PhD in Theoretical Physics in Manchester under the supervision of Dr Tobias Galla. This was completed in 2015. Peter is now a postdoc in theoretical biology at ETH Zürich where, amongst other projects, he is investigating the dynamics of blood formation and disease. 

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