Spatial Moran models I. Stochastic tunneling in the neutral case

TL;DR

This paper analyzes the timing of neutral mutations in a spatial cancer model arranged on a lattice, extending previous one-dimensional results to higher dimensions and providing insights into mutation accumulation.

Contribution

It extends the understanding of mutation accumulation timing from one-dimensional to multi-dimensional spatial models in cancer research.

Findings

Derived distribution results for mutation accumulation times in higher dimensions.

Extended previous one-dimensional models to multi-dimensional lattice structures.

Provided mathematical proofs for the distribution of the first double mutation event.

Abstract

We consider a multistage cancer model in which cells are arranged in a $d$-dimensional integer lattice. Starting with all wild-type cells, we prove results about the distribution of the first time when two neutral mutations have accumulated in some cell in dimensions $d\ge 2$, extending work done by Komarova [Genetics 166 (2004) 1571-1579] for $d=1$.