© 2016

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

  • 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


Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Peter Ashcroft
    Pages 1-9
  3. Peter Ashcroft
    Pages 11-37
  4. Peter Ashcroft
    Pages 127-158
  5. Peter Ashcroft
    Pages 159-164

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.


Evolutionary Game Theory Moran Process Fixation Probability Fixation Time Distribution Mixing Time Stochastic Tunnelling Cancer Initiation WKB Method Quasi-stationary Distribution Quasi-potential Landscapes

Authors and affiliations

  1. 1.Institute for Integrative BiologyETH ZürichZÜRICHSwitzerland

About the authors

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. 

Bibliographic information