Journal of Theoretical Medicine
Volume 5 (2003), Issue 1, Pages 47-58
Spatial Evolutionary Games of Interaction among Generic Cancer Cells
1EVALife Group, Institute of Computer Science, University of Aarhus, Building 540, Ny Munkegade, DK-8000 Aarhus C, Denmark
2Department of Ecology and Genetics, University of Aarhus, Building 540, Ny Munkegade, DK-8000 Aarhus C, Denmark
3Mathematics Department, Umeå University, SE-901 87 Umeå, Sweden
4Centre for Mathematical Biology, Mathematical Institute, Oxford University, 24-29 St Giles', Oxford OX1 3LB, UK
5Department of Experimental Clinical Oncology, Aarhus University Hospital, Aarhus, Denmark
Received 1 November 2002; Revised 31 July 2003; Accepted 14 August 2003
Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Evolutionary game models of cellular interactions have shown that heterogeneity in the cellular genotypic composition is maintained through evolution to stable coexistence of growth-promoting and non-promoting cell types. We generalise these mean-field models and relax the assumption of perfect mixing of cells by instead implementing an individual-based model that includes the stochastic and spatial effects likely to occur in tumours. The scope for coexistence of genotypic strategies changed with the inclusion of explicit space and stochasticity. The spatial models show some interesting deviations from their mean-field counterparts, for example the possibility of altruistic (paracrine) cell strategies to thrive. Such effects can however, be highly sensitive to model implementation and the more realistic models with semi-synchronous and stochastic updating do not show evolution of altruism. We do find some important and consistent differences between the spatial and mean-field models, in particular that the parameter regime for coexistence of growth-promoting and nonpromoting cell types is narrowed. For certain parameters in the model a selective collapse of a generic growth promoter occurs, hence the evolutionary dynamics mimics observable in vivo tumour phenomena such as (therapy induced) relapse behaviour. Our modelling approach differs from many of those previously applied in understanding growth of cancerous tumours in that it attempts to account for natural selection at a cellular level. This study thus points a new direction towards more plausible spatial tumour modelling and the understanding of cancerous growth.