Congratulations to Debbie on passing her viva on Wednesday!
Spatial correlation models for cell populations
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 In this thesis, we explore situations in which the mean-field approximation is no longer valid for volume-excluding processes on a regular lattice.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-eld and other approximations.
You can check out the papers arising from her work here:
- D. C. Markham, M. J. Simpson and R. E. Baker (2013). Simplified method for including spatial correlations in mean-field approximations. Phys. Rev. E 87(6):062702. DOI
- D. C. Markham, M. J. Simpson, P. K. Maini, E. A. Gaffney and R. E. Baker (2013). Incorporating spatial correlations into multispecies mean-field models. Phys. Rev. E 88(5):052713. DOI
- D. C. Markham, M. J. Simpson, P. K. Maini, E. A. Gaffney and R. E. Baker (2014). Comparing methods for modelling spreading cell fronts. J. Theor. Biol. 353:95-103. DOI
- D. C. Markham, M. J. Simpson and R. E. Baker (2014). Choosing an appropriate framework for analysing multispecies co-culture experiments. Available on bioRxiv. DOI