Description before prediction: evolutionary games in oncology

As I discussed towards the end of an old post on cross-validation and prediction: we don’t always want to have prediction as our primary goal, or metric of success. In fact, I think that if a discipline has not found a vocabulary for its basic terms, a grammar for combining those terms, and a framework for collecting, interpreting, and/or translating experimental practice into those terms then focusing on prediction can actually slow us down or push us in the wrong direction. To adapt Knuth: I suspect that premature optimization of predictive potential is the root of all evil.

We need to first have a good framework for describing and summarizing phenomena before we set out to build theories within that framework for predicting phenomena.

In this brief post, I want to ask if evolutionary games in oncology are ready for building predictive models. Or if they are still in need of establishing themselves as a good descriptive framework.


To some extent, it is silly to even consider that EGT is not a good descriptive framework in oncology. Mostly because it is already being used for this purpose! There are many many papers — some of them even by me — that use the language of evolutionary game theory to reason about problems in cancer.

But these are largely descriptions not of empirical aspects of cancer but rather a formalization of our mental models. In other words, evolutionary games have established themselves for describing theoretical puzzles in oncology. And sometimes even for resolving those theoretical puzzles.

But, to a large extent, this process is data-free or data-light. When some sort of data is used, it is often as an illustration. A way to motivate or justify the model. It is often collected besides the model — not through the model. In this way, most work seems to operate on parallel tracks of theory and experiment.

My feeling is that there is not much work already out there to use evolutionary games to describe experiments or to make empirical observations directly in oncology. So in the context of experimental oncology, I don’t think that EGT has a proven track record as a useful descriptive framework, yet.

In particular, I believe that mathematical oncology, or at least the part of it focused on evolutionary forces within the patient, is in a position where we have not found the right vocabulary, grammar, and framework for our basic terms for engaging directly with experiment more generally. We do use a language, but much of it is borrowed from physics with justifications line (1) the absorption of physicists into mathematical oncology, (2) the past success of reductionist languages in other disciplines, and (3) its coherence with our physical intuition. But all the justification feel external to oncology, like this language has not been built up for its own purposes. It has simply been borrowed. We are trying to use the language of physics to make sense of cancer. And sometimes it can be awkward.

If we wanted to better justify physics-speak for talking about experiments in cancer: I think that it is important to consider seriously an alternative choice of X-speak. Then we can contrast physics-speak with X-speak to show that physics-speak is in some way better. Or maybe we will learn something else from X-speak altogether.

Unsurprisingly, evolutionary game theory is the alternative language that I focus on. With the project of operationalization being the construction of a dictionary between the basic terms of EGT and the basic terms of the more established language of experimental practice. This is why I obsess so much about seemingly pedantic distinction between token vs type fitness and reductive vs effective games.

As in any effort of translation, new basic terms might need to be invented on both sides. This is the feedback between theory and experiment.

In such a setting, early interaction with experiment becomes an exercise in description. We use our tentative dictionary to see what the experimental story reads like in the theoretical language. This is why the game assay that we developed in Kaznatcheev et al. (2019) feels so descriptive. In some sense, it is just summarizing a large dataset as a single point in game space (alongside some error propogation for error-bars).

If the fit is natural — for example, the resulting gain functions are relatively simple, and best represented in terms of proportion rather than density — then that is some evidence for a good framework. If the fit is awkward — for example, the resulting gain functions all have terms of \frac{1}{p(1 - p)} to cancel out the replicator dynamics — then that is strong evidence for a bad framework. The further hope is that if the fit is natural then some empirical regularity will emerge across stories — for example, maybe most signalling settings are well described by quadratic gain functions — then these regularities can be transformed into theories — which we can aim to falsify with future experiments — within the framework.

Or maybe an awkwardness in the fit between EGT and experiment will make us rethink some of our worok on EGT and mental models. For example, when less studied games like Deadlock and Leader pop-out of the game assay. This can be used to justify new exploration for pure EGT, like Archetti et al. (2015) using their experiments to reinforce Archetti’s (2013; 2014) theoretical push for nonlinear payoff functions in public good games.

Either way, the short term focus becomes doing simple and clear experiments and describing their procedures and outcomes precisely from within evolutionary game theory. Or taking existing data, and interpreting it through this framework. For example, that is why I focused attention on showing how the experiments of Li et al. (2015) can be represented in an equivalent and just as natural a way with replicator dynamics as with the authors’ choice of Lotka-Volterra equations. If that could not be done, or if the replicator equation representation was significantly more awkward, then that would be evidence against it as a good language.

This doesn’t mean that I necessarily think EGT-language is better than physics-language or Lotka-Volterra-language. It is just the language that I have chosen to focus on building into a useful descriptive framework, and I hope others do the same with the languages that they are the most proficient in. It would be very exciting, for example, to take the same experiments and design and run them in such a way that we have several different descriptive languages in mind.

In the process, we’ll probably end up with an exciting creole language that can become the natural language for describing experimental cancer biology. We might all currently speak about cancer with our various accents, dialects, and awkwardness. But the next generation will hopefully have overcome our early attempts at description and build the right framework for describing cancer.

Once that is done, we can start focusing on building models in that framework to predict cancer.

At least if we want to have prediction with understanding. Of course, this isn’t always required. Sometimes we might just want prediction without understanding. In fact, areas where such phenomenological theories are successful might be the place where we should first start looking — as long as we’re willing to throw away any ontological baggage of the successful effective theories.

References

Archetti, M. (2013). Evolutionary game theory of growth factor production: implications for tumour heterogeneity and resistance to therapies. British Journal of Cancer, 109(4): 1056-1062.

Archetti, M. (2014). Evolutionary dynamics of the Warburg effect: glycolysis as a collective action problem among cancer cells. Journal of Theoretical Biology, 341, 1-8 PMID: 24075895.

Archetti, M., Ferraro, D.A., & Christofori, G. (2015). Heterogeneity for IGF-II production maintained by public goods dynamics in neuroendocrine pancreatic cancer. Proceedings of the National Academy of Sciences, 112(6), 1833-8 PMID: 25624490.

Kaznatcheev, A. (2017). Two conceptions of evolutionary games: reductive vs effective. bioRxiv: 231993.

Kaznatcheev, A. (2018). Effective games and the confusion over spatial structure. Proceedings of the National Academy of Sciences: 201719031.

Kaznatcheev, A., Peacock, J., Basanta, D., Marusyk, A., & Scott, J. G. (2019). Fibroblasts and alectinib switch the evolutionary games played by non-small cell lung cancer. Nature Ecology & Evolution, 3(3): 450-456.

Li, X.-Y., Pietschke, C., Fraune, S., Altrock, P.M., Bosch, T.C., & Traulsen, A. (2015). Which games are growing bacterial populations playing? Journal of the Royal Society Interface, 12 (108) PMID: 26236827.

About Artem Kaznatcheev
From the Department of Computer Science at Oxford University and Department of Translational Hematology & Oncology Research at Cleveland Clinic, I marvel at the world through algorithmic lenses. My mind is drawn to evolutionary dynamics, theoretical computer science, mathematical oncology, computational learning theory, and philosophy of science. Previously I was at the Department of Integrated Mathematical Oncology at Moffitt Cancer Center, and the School of Computer Science and Department of Psychology at McGill University. In a past life, I worried about quantum queries at the Institute for Quantum Computing and Department of Combinatorics & Optimization at University of Waterloo and as a visitor to the Centre for Quantum Technologies at National University of Singapore. Meander with me on Google+ and Twitter.

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