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J R Soc Interface. 2017 Sep;14(134). pii: 20170342. doi: 10.1098/rsif.2017.0342.

Extinction rates in tumour public goods games.

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Department of Mathematical Sciences, Chalmers University of Technology, 41296 Gothenburg, Sweden
Department of Mathematical Sciences, University of Gothenburg, 40530 Gothenburg, Sweden.
Department of Integrated Mathematical Oncology, Moffitt Cancer Center and Research Institute, Tampa, FL 33612, USA
University of South Florida Morsani College of Medicine, Tampa, FL 33612, USA.


Cancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumour cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the time scales, in particular, in coevolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell-type-specific rates have to be accounted for explicitly.


cancer evolution; evolutionary game theory; fixation times; logistic growth; replicator equation

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