In a recent blog post at theEGG me and Philipp Altrock argued for caution when applying game theoretic models to cancer. One of our concerns was the difficulty of measuring selective advantage, which is not constant, but changes with the frequency of the genotype. This problem has been partially addressed in a new paper by Ribeck & Lenski. I have one reservation though: they only consider frequency dependence in one of two competing clones, which means that their approach cannot be applied to a general two-player game which has two free parameters. Also as a mathematician I would like to see a more rigorous comparison between the Monod model for cross-feeding and the proposed model for frequency dependence, but this paper is at least showing us the way forward.
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