4 papers
Branching stable processes and motion by mean curvature flow
Kimberly Becker, Alison Etheridge, Ian Letter
We prove a new result relating solutions of the scaled fractional Allen--Cahn equation to motion by mean curvature flow, motivated by the motion of hybrid zones in populations that…
Looking forwards and backwards: dynamics and genealogies of locally regulated populations
Alison M. Etheridge, Thomas G. Kurtz, Ian Letter +2
We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure,…
On the effects of a wide opening in the domain of the (stochastic) Allen-Cahn equation and the motion of hybrid zones
Alison M. Etheridge, Mitchell D. Gooding, Ian Letter
We are concerned with a special form of the (stochastic) Allen-Cahn equation, which can be seen as a model of hybrid zones in population genetics. Individuals in the population can…
A probabilistic analysis of a continuous-time evolution in recombination
Ian Letter, Servet Martínez
We study the continuous-time evolution of the recombination equation of population genetics. This evolution is given by a differential equation that acts on a product probability s…