Abstract
Cooperation is prevalent in nature, not only in the context of social interactions within the animal kingdom but also on the cellular level. In cancer, for example, tumour cells can cooperate by producing growth factors. The evolution of cooperation has traditionally been studied for well-mixed populations under the framework of evolutionary game theory, and more recently for structured populations using evolutionary graph theory (EGT). The population structures arising due to cellular arrangement in tissues, however, are dynamic and thus cannot be accurately represented by either of these frameworks. In this work, we compare the conditions for cooperative success in an epithelium modelled using EGT, to those in a mechanical model of an epithelium—the Voronoi tessellation (VT) model. Crucially, in this latter model, cells are able to move, and birth and death are not spatially coupled. We calculate fixation probabilities in the VT model through simulation and an approximate analytic technique and show that this leads to stronger promotion of cooperation in comparison with the EGT model.
Highlights
Tumour development is an evolutionary process whereby cells undergo a series of genetic changes leading to acquired capabilities that confer some growth advantage
In order to analyse the dynamics of evolutionary games on a more realistic population structure, we will use the Voronoi tessellation (VT) model [42,43] developed for the colonic crypt epithelium
evolutionary graph theory (EGT) has become the accepted framework for modelling the evolution of cooperation on structured populations, ranging from complex social networks to collective cellular behaviour organized in tissues
Summary
Tumour development is an evolutionary process whereby cells undergo a series of genetic changes leading to acquired capabilities that confer some growth advantage. Models of the evolution of cooperation for diffusible growth factors [5,6,7] have been developed using the framework of evolutionary game theory for well-mixed populations These models have been extended to consider spatial effects by placing cells on a lattice [8,9,10] or a fixed graph [11,12]. In order to elucidate what impact, if any, the dynamic nature of cell populations and spatial decoupling of birth and death has on the evolution of cooperation, we will consider evolutionary games on a mechanical model of an epithelium— the Voronoi tessellation (VT) model [42,43]. By running further simulations, implementing an explicit death–birth update in the VT model and a migration analogue into the EGT model, we identify the decoupling of birth and death to be the primary mechanism for the discrepancy
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