Effects of Heterogeneity on Cancer: A Game Theory Perspective

Abstract

In this study, we explore interactions between cancer cells by using the hawk–dove game. We analyze the heterogeneity of tumors by considering games with populations composed of 2 or 3 types of cell. We determine what strategies are evolutionarily stable in the 2-type and 3-type population games and what the corresponding expected payoffs are. Our results show that the payoff of the best-off cell in the 2-type population game is higher than that of the best-off cell in the 3-type population game. When these mathematical findings are transferred to the field of oncology they suggest that a tumor with low intratumor heterogeneity pursues a more aggressive course than one with high intratumor heterogeneity. Some histological and genomic data on clear cell renal cell carcinomas is consistent with these results. We underline the importance of identifying intratumor heterogeneity in routine practice and suggest that therapeutic strategies that preserve heterogeneity may be promising as they may slow down cancer growth.

Early Evolution in Cancer: A Mathematical Support for Pathological and Genomic Evidence in Clear Cell Renal Cell Carcinoma

“…The conclusion at this point of tumor evolution is that high ITH is linked to an attenuated evolutive course and longer survival than with low ITH tumors. This evidence is supported by a recent mathematical approach using the hawk-dove game [9].…”

“…Many examples of this interdisciplinary cooperation can be found in the literature. In particular, we have recently analyzed the clinical consequences of ITH in CCRCC using the hawk-dove game, showing that the math supports the clinical evidence [9]. Thus, mathematics, histopathology, and genomics come together to demonstrate that tumor aggressiveness is linked to low ITH in the late temporal periods of CCRCC [10].…”

“…The comparison of the payoffs in the ESS of the different population games yields the following results (see [9,13,15] and Appendix A for the proofs).…”

“…The three temporal scenarios depicted in Figure 1 establish early and late eco-evolutionary periods occurring in many CCRCCs, which correspond roughly to linear, branching, and punctuated temporal models. The late period, i.e., how a CCRCC with high ITH (three cell types, branching model) evolves towards a neoplasm with low ITH (two cell types, punctuated model), has also recently been modeled using the hawk-dove game [9]. Here, however, we focus on modeling the early period, i.e., how homogeneous tumors (one cell type, linear model) evolve into CCRCCs with high ITH (three cell types, branching model).…”

“…Laruelle et al [9] demonstrate that in heterogeneous populations with three types, there is (under some conditions) an ESS in which each type of cell receives a different treatment.…”