Abstract
In this work we study the effect of domain growth on spatial correlations in agent populations containing multiple species. This is important as heterogenous cell populations are ubiquitous during the embryonic development of many species. We have previously shown that the long term behaviour of an agent population depends on the way in which domain growth is implemented. We extend this work to show that, depending on the way in which domain growth is implemented, different species dominate in multispecies simulations. Continuum approximations of the lattice-based model that ignore spatial correlations cannot capture this behaviour, while those that explicitly account for spatial correlations can. The results presented here show that the precise mechanism of domain growth can determine the long term behaviour of multispecies populations, and in certain circumstances, establish spatially varying species densities.
Footnotes
↵* ross{at}maths.ox.ac.uk
↵† c.yates{at}bath.ac.uk
↵‡ baker{at}maths.ox.ac.uk
↵7 To compute the average relative error we proceed as follows: we initialise a domain of length Nx = 100, Ny = 100, with Pgx = 0.1 and Pgy = 0 (i.e. no growth in the y direction), 500 initial agents (assigned uniformly at random to lattice sites) and Pp = 1 and Pm = 1. We calculate the relative error associated with the closure for all domain sizes, for example c109×100(t) = (110/109)c110×100(t), for the duration of the simulation sampling at equally spaced time intervals. We then sum the absolute values of the relative error for each domain length closure for each time point, and divide by the number of samples (time points) to generate the average relative error associated with this closure over the time course of the simulation.