Spatial correlation models for cell populations - Markham, D (2014)
Determining the emergent behaviour of a population from the interactions of its individuals is an ongoing challenge in the modelling of biological phenomena. Many classical models assume that the spatial location of each individual is independent of the locations of all other individuals. This mean-field assumption is not always realistic; in biological systems we frequently see clusters of individuals develop from uniform initial conditions. In this thesis, we explore situations in which the mean-field approximation is no longer valid for volume-excluding processes on a regular lattice. We provide methods which take into account the spatial correlations between lattice sites, thus more accurately reflecting the system's behaviour, and discuss methods which can provide information as to the validity of mean-field and other approximations.