How domain growth is implemented determines the long term behaviour of a cell population through its effect on spatial correlations

Robert J. H. Ross; R. E. Baker; C. A. Yates

Spatial correlations are often observed in biological systems [19] [20] [21] [22] [23] [24] . For instance, in cell populations spatial correlations can be established by cell proliferation, as a new cell is naturally close to its parent cell following division. Individual-based models (IBMs) are able to recapitulate these spatial correlations, whereas models that employ certain mean-field approximations (MFAs), such as the logistic model [25] , and, in a spatially-extended context, the diffusion equation, cannot [26] [27] [28] [29] [30] . Accurate continuum models are important tools for understanding the behaviour of biological systems as, in contrast to IBMs, they generally allow for greater mathematical analysis. This analysis can be crucial in forming a mechanistic understanding of biological systems, which is not always apparent from simply studying the results of a large number of repeats of an IBM. Therefore, in order to derive accurate continuum approximations of IBMs that include cell proliferation it is often necessary to account for the effects of spatial correlations [25, [31] [32] [33] [34] [35] [36] [37] [38] [39] . cells), discrete random-walk model on a two-dimensional square lattice with volume-exclusion.