Modeling changes in genetic heterogeneity using games with resources.

Background And Objective: This study explores an extension of the classic Hawk and Dove evolutionary game model by considering the influence of environmental or external resources on the players' fitness. This allows us to model the resulting heterogeneous population dynamics, which is of great importance for simulating cancer population growth and optimizing anti-cancer therapies.

Methods: To model population heterogeneity, we are using an extension of classical spatial evolutionary game theory by introducing multidimensional spatial evolutionary games (MSEG). This allows for the study of genetic heterogeneity on a multidimensional lattice. The classic Hawk and Dove model is modified to reflect the impact of external resources. Various types and shapes of resource functions were included in the payoff matrix and then simulated to examine their impact on the model's dynamics and population heterogeneity.

Results: The results are presented in time-dependent plots for both mean-field and spatial models. Additionally, spatial 2D and 3D matrices are presented to show the spatial distribution of both phenotypes analyzed in the extended Hawk and Dove model. The results reveal significant differences between the mean-field and spatial models for the same parameter values. Furthermore, differences are observed when comparing models with different resource functions.

Conclusion: The two-phenotype model was used to show the influence of external, time- and phenotype-specific resource functions on the dynamics of the game's phenotypes. Moreover, the study highlights that spatial models, which provide more accurate information about population heterogeneity, can yield significantly different results compared to mean-field models.