Adaptive dynamics of unstable cancer populations: the canonical equation

Abstract

In most instances of tumour development, genetic instability plays a role in allowing cancer cell populations to respond to selection barriers, such as physical constraints or immune responses, and rapidly adapt to an always changing environment. Modelling instability is a nontrivial task, since by definition evolving changing instability leads to changes in the underlying landscape. In this paper we explore mathematically a simple version of unstable tumor progression using the formalism of Adaptive Dynamics (AD) where selection and mutation are explicitly coupled. Using a set of basic fitness landscapes, the so called canonical equation for the evolution of genetic instability on a minimal scenario associated to a population of unstable cells is derived. The implications and potential extensions of this model are discussed.