title: Cancer heterogeneity and multilayer spatial evolutionary games.
abstract: 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. 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.
  
  
  
  In 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.
  
  
  
  Different 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.
  
  
  
  The 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.
  
  
  
  This article was reviewed by Tomasz Lipniacki, Urszula Ledzewicz and Jacek Banasiak.
authors.affiliation: Department of Automatic Control, Silesian University of Technology, ul. Akademicka 16, 44-100, Gliwice, Poland.
authors.forename: Andrzej
authors.initials: A
authors.lastname: Świerniak
authors.affiliation: Department of Automatic Control, Silesian University of Technology, ul. Akademicka 16, 44-100, Gliwice, Poland. krzeslak.michal@gmail.com.
authors.forename: Michał
authors.initials: M
authors.lastname: Krześlak
mesh_terms: D005075:Biological Evolution; D005716:Game Theory; D018740:Genetic Heterogeneity; D006801:Humans; D008957:Models, Genetic; D009369:Neoplasms / Q000235:genetics*; D010641:Phenotype
keywords: Biomathematical modelling; Cancer; Evolutionary games; Heterogeneity; Sensitivity; Spatial effects