Abstract
BackgroundEvolutionary game theory (EGT) has been widely used to simulate tumour processes. In almost all studies on EGT models analysis is limited to two or three phenotypes. Our model contains four main phenotypes. Moreover, in a standard approach only heterogeneity of populations is studied, while cancer cells remain homogeneous. A multilayer approach proposed in this paper enables to study heterogeneity of single cells.MethodIn the extended model presented in this paper we consider four strategies (phenotypes) that can arise by mutations. We propose multilayer spatial evolutionary games (MSEG) played on multiple 2D lattices corresponding to the possible phenotypes. It enables simulation and investigation of heterogeneity on the player-level in addition to the population-level. Moreover, it allows to model interactions between arbitrary many phenotypes resulting from the mixture of basic traits.ResultsDifferent equilibrium points and scenarios (monomorphic and polymorphic populations) have been achieved depending on model parameters and the type of played game. However, there is a possibility of stable quadromorphic population in MSEG games for the same set of parameters like for the mean-field game.ConclusionThe model assumes an existence of four possible phenotypes (strategies) in the population of cells that make up tumour. Various parameters and relations between cells lead to complex analysis of this model and give diverse results. One of them is a possibility of stable coexistence of different tumour cells within the population, representing almost arbitrary mixture of the basic phenotypes.ReviewersThis article was reviewed by Tomasz Lipniacki, Urszula Ledzewicz and Jacek Banasiak.
Highlights
Evolutionary game theory (EGT) has been widely used to simulate tumour processes
The model assumes an existence of four possible phenotypes in the population of cells that make up tumour
In this paper spatial evolutionary games, proposed by Bach et al [17] have been developed further following our proposal [14]. This new approach considers that each simple player shall be treated as a more complex individual expressing different traits, which seems to be more realistic for the simulation of many biological processes considering the heterogeneity of individuals
Summary
Evolutionary game theory (EGT) has been widely used to simulate tumour processes. In almost all studies on EGT models analysis is limited to two or three phenotypes. It links mathematical tools of the game theory with Darwinian adaptation and species evolution In this case players are representatives of the population, and their strategies (phenotypes) are determined genetically. The standard example and the fundamental evolutionary model is Hawk and Dove game This game, studied by Maynard Smith [2], is a finite nonzero sum game and assumes that the population contains two phenotypes: aggressive (non-outgoing) and compliant. Population members fight for a resource V which affects the reproductive success, but they can suffer wounds C (the phenotype called Hawk that always takes a fight) This model has been developed into a number of generalizations including spatial effects, evolution in time or other strategies e.g. a legalist strategy (a phenotype can switch between strategies depending on a situation) [3]
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