I claim that I am a researcher in mathematical biology. By this I mostly understand studying biological problems by using the mathematical modeling method. Additionally, I am interested in analyzing properties of mathematical models arising in mathematical biology. I strongly believe that extra knowledge about these models is enough to claim that a new and publishable result is obtained. However, a lot of editors and reviewers think differently. Here is an extract from the review section a recent paper “Parabolic replicator dynamics and the principle of minimum Tsallis information gain” by my dear collaborators Georgy Karev and Eugene Koonin, published in Biology Direct (I already discussed the unusual review process in this journal: Both the reviews and answers are published after the main text).
Reviewer 2: Puushottam Dixit (nominated by Sergei Maslov. Brookhaven National Laboratory)
In this work, the authors generalize their previous result on the relationship between the Gibbs-Boltzmann-Shannon entropy and the exponential growth replicator equation by analyzing parabolic and hyperbolic growth models. They show that the frequency distribution of species growing with a modified exponential dynamics is best described by a Tsallis q-exponential distribution. I find the mathematical results of the work interesting but I think that the physical conclusions are not clearly delineated. I would like the authors to considerably extend their discussion about the biological implications of their results before I can recommend the article to be published in Biology Direct.Response: we certainly realize the value of biological implications. However, this paper primarily aims at presenting mathematical/information-theoretical results that apply to a biologically most realistic replicator system, that is a parabolically growing one. Hence the biological relevance. We do discuss what we think is an interesting biological implication, namely the applicability of this non-additive formalism to cooperative behavior of prebiotic replicators; this part was reworded in the revision to clarify. We tend to believe that further biological speculation would be excessive at this stage.
This is a very good point that new mathematical results about mathematical model of a biological system do have biological relevance. Unfortunately, I do not think that I can use similar arguments for my reviewers.
Mathematical Biology 
I am very fearful of these sort of critiques. Like you, I think that understanding models deeply for the sake of understanding the model itself and not necessarily the biology it seeks to reflect is extremely important. I am pursuing this strategy right now by bringing tools from theoretical computer science to evolutionary modeling. Unfortunately, I’ve found it hard to explain to biologists that I am looking at what logical conclusions we can rigorously draw from models or not, and not trying to make a statement about the ’empirical reality’ that those models purport to represent. I.e. I am studying models of biology, not biology. Do you have any advice on how to explain studying models in a way that is interesting to orthodox biologists? Or is it a matter of selecting friendly venues?
I wish I knew how to answer your question 🙂 Anyway, I would not recommend to state that you study “models of biology, not biology”.