Dynamics of Advantageous Mutant Spread in Spatial Death-Birth and Birth-Death Moran Models

Jasmine Foo, Einar Bjarki Gunnarsson, Kevin Leder, David Sivakoff

Research output: Contribution to journalArticlepeer-review


The spread of an advantageous mutation through a population is of fundamental interest in population genetics. While the classical Moran model is formulated for a well-mixed population, it has long been recognized that in real-world applications, the population usually has an explicit spatial structure which can significantly influence the dynamics. In the context of cancer initiation in epithelial tissue, several recent works have analyzed the dynamics of advantageous mutant spread on integer lattices, using the biased voter model from particle systems theory. In this spatial version of the Moran model, individuals first reproduce according to their fitness and then replace a neighboring individual. From a biological standpoint, the opposite dynamics, where individuals first die and are then replaced by a neighboring individual according to its fitness, are equally relevant. Here, we investigate this death-birth analogue of the biased voter model. We construct the process mathematically, derive the associated dual process, establish bounds on the survival probability of a single mutant, and prove that the process has an asymptotic shape. We also briefly discuss alternative birth-death and death-birth dynamics, depending on how the mutant fitness advantage affects the dynamics. We show that birth-death and death-birth formulations of the biased voter model are equivalent when fitness affects the former event of each update of the model, whereas the birth-death model is fundamentally different from the death-birth model when fitness affects the latter event.

Original languageEnglish (US)
Pages (from-to)576-604
Number of pages29
JournalCommunications on Applied Mathematics and Computation
Issue number1
StatePublished - Mar 2024

Bibliographical note

Publisher Copyright:
© Shanghai University 2023.


  • 60G50
  • 60J27
  • 60K35
  • 92B05
  • 92D25
  • Biased voter model
  • Dual process
  • Evolutionary graph theory
  • Fixation probability
  • Shape theorem
  • Spatial birth-death models
  • Spatial cancer models
  • Spatial death-birth models
  • Spatial evolutionary models
  • Stochastic processes


Dive into the research topics of 'Dynamics of Advantageous Mutant Spread in Spatial Death-Birth and Birth-Death Moran Models'. Together they form a unique fingerprint.

Cite this