Ults of the proposed technique of modeling have only qualitative value. Moreover, new types of reproduction proposed in the paper open new possibilities of understanding some `altruistic’ behavior observed in some experimental studies on tumor cells. Unfortunately, all these prospective applications are not discussed in the paper. Such discussion may significantly improve its quality. Authors’ response: We wish to thank the reviewer for bringing to our attention some advantages of our approach. Frankly speaking, some of them has been “discovered” by us due to the reviewer’s comment. We have extended the discussion session to include some of them. On the other hand, just recently, our publication [30] prepared in collaboration with biologists from our institution, has appeared in which we reported our successful attempt to mimic results of biological experiment using MSEG.Reviewer’s report 3: Jacek BanasiakReviewer comments: Having read the paper carefully, I realized that I should not have accepted invitation to review it as Varlitinib molecular weight evolutionary games is not my field of interest and also I am a mathematician and the appear does not contain much mathematics in the conventional style. Nevertheless, let me try to provide some comments. Evolutionary game theory has been used with some success to simulate tumour development. Spatial evolutionary games allows to model somewierniak and Krzelak Biology Direct (2016) 11:Page 15 ofspatial heterogeneity of cells. The main contribution of the paper is to extend the existing results of simulating tumour processes that have been limited to two or three phenotypes, to four phenotypes. Moreover, what the authors call mixed (or multilayer) spatial evolutionary games, allow each cell to play different strategy (out of these four). Different mixes of strategies are treated as different phenotypes. An important feature of the paper is bringing some parallel between the PubMed ID:https://www.ncbi.nlm.nih.gov/pubmed/25679764 spatial evolutionary games and the replicator dynamics approach that looks at the `meanfield’ description of the game. According to the authors, extending the number of strategies to four, bringing the dimension of the mean-field model to three, allows the replicator dynamics (described by an ODE system) to exhibit more complex dynamics, including chaos (strange attractors). However, the authors have not pursued this comment. In general, the paper offers a description of the mixed spatial evolutionary game theory approach to cancer modelling in which not only heterogeneity in space but also at a given point, in the sense of possibility of having different phenotypes at any give site, can be modelled. This is illustrated by performing in two sets of simulations varying two out of four parameters in each one. Some comparison with results obtained by the mean-field approach for the same values of parameters as before. There are some statements in the paper that should be re-considered. ?For instance, on p. 2, in Conclusions, the authors write: Despite complex analysis….., the model gives finite number of diverse results (meaning, I believe, few different results). On the other hand, on p. 16, line 35, they state: Due to immense amount of different results…., we discuss only the case when the population is quadromorphic. So, do we have just few different results, or an immense amount of them? ?The first sentence of the last paragraph on p. 7 would be more clear if a colon was used. The second sentence in that paragraph should be re-written { it is t.
