Looking for species in cancer but finding strategies and players

Sometime before 6 August 2014, David Basanta and Tamir Epstein were discussing the increasing focus of mathematical oncology on tumour heterogeneity. An obstacle for this focus is a good definitions of heterogeneity. One path around this obstacle is to take definitions from other fields like ecology — maybe species diversity. But this path is not straightforward: we usually — with some notable and interesting examples — view cancer cells as primarily asexual and the species concept is for sexual organisms. Hence, the specific question that concerned David and Tamir: is there a concept of species that applies to cancer?

I want to consider a couple of candidate answers to this question. None of these answers will be a satisfactory definition for species in cancer. But I think the exercise is useful for understanding evolutionary game theory. With the first attempt to define species, we’ll end up using the game assay to operationalize strategies. With the second attempt, we’ll use the struggle for existence to define players. Both will be sketches that I will need to completely more carefully if there is interest.

Strategies: species as types

David and Tamir were looking for an operational definition of species. A definition they could use in the petri dish. So they proposed:

If you start a colony of cells in a petri dish starting from one single cell there will be a lot of traits where the cells will be slightly different from the original one. We can describe this with a distribution… two organisms belong to the same species if for a relevant number of traits they can lead to the same distribution [when started separately from a single cell].

I liked this definition back in 2014, although I thought we should consider turning it around. Instead of defining species based on some magic “relevant number of traits” — for any collection of traits that one might care about define a relevant species. In other words, two cells might be the same species for motility, but a different species when we look at florescence, and that should be alright.

Four years later, I would consider the above to be a definition of type (or strategy) rather than species.

The simple operationalization above is also vulnerable to cells with high phenotypic plasticity. When I place my original cell in the petri dish, the final distribution of phenotypes is a function of two different things: (1) the original cell, and (2) the phenotype selected by the evolutionary pressures of the chosen environment. It could be that the environment is so biased toward certain phenotypes that as long as the cell even rarely produces that phenotype, that phenotype will end up dominating the population (kind of like convergent evolution). In that case, even if the two cells I was testing really were different — in that one was more likely to produce a given phenotype than the other — I wouldn’t pick that up as long as they each express this highly selected phenotype slightly.

But we can account for this. Suppose we want to see if cell type A and cell type B are the same species, then (1) add some sort of heritable genetic tracer alpha to cell type A and beta to cell type B (maybe infect them with some phage or introduce some plasmid), (2) grow a Petri dish with both cell types (with tracer) present in it in equal numbers, (3) once the growth is finished, sort the cells by relevant trait phenotype (if possible), (4) sequence each batch of different trait to see that tracer alpha and tracer beta are equally represented.

In this case, we would be testing if the descendants of the two cell types are selectively neutral with respect to each other on the set of phenotypic traits of interests. A phenotypic trait that is almost always of interest is fitness itself. In this case, there would be no sorting, just counting the amount of tracer in a cross-culture experiment. And as with other cross-culture tests, we might want to generalize to many seeding proportions and thus perform an effective game assay (Kaznatcheev, 2017; Kaznatcheev et al., 2018). If the resultant gain function is zero then the above definition would call them the same species. Although a more game theoretically appropriate term would be to call them the same strategy.

Maybe strategy is the more relevant concept that species, anyways.

Players: species as populations

But let me stick with species for now but double down on the game theoretic aspects. This brings me to the reason that David’s old post recently resurfaced in mind (and prompted a long comment that became this post): I was reading Fisher’s The Genetical Theory of Natural Selection.

Fisher starts chapter 6 with a contrast between sexual and asexual reproduction. In the process, he wants to have a working definition of ‘species’ for asexual organisms. From the perspective of a game theorist, I found his definition particularly interesting and I wanted to share it with you, dear reader (pg. 121 of 1930 edition):

The groups most nearly corresponding to species would be those adapted to fill so similar a place in nature that any one individual could replace another, or more explicitly that an evolutionary improvement in any one individual threatens the existence of the descendants of all the others. Within such a group the increase in numbers of the more favoured types would be balanced by the continual extinction of lines less fitted to survive, so that, just as, looking backwards, we could trace the ancestry of the whole group back to a single individual progenitor, so, looking forward at any stage, we can foresee the time when the whole group then living will be the descendants of one particular individual of the existing population.

This definition stood out to me because unlike the reductive definitions we tried to give above, which rely heavily on observing particular phenotypes or genotypes, this one is much more closely linked to the definition of natural selection. For Fisher, two asexual organisms are part of the same species if they struggle for existence against/with each other. This is fascinating and I think a stark contrast to our approaches. It places natural selection first and everything else second. It ‘falls out’ of the abstract idea of “struggle for existence”.

The above definition of species seems almost equivalent to Millstein’s (2009) view of a population as a Ghiselin-Hull individual and it tries to cut nature at joints similar to those identified by Wells & Richmond (1995). So it is interesting to see Fisher anticipating these views, and I will have to revisit these recent papers to see if they mention his conceptions of species.

Of course, the fact that modern authors use this definition for populations rather than species, should also have us questioning if ‘species’ is the right word. After all, if we apply Fisher’s definition of species back to sexual populations then we can get awkward results. For example, we would have wolves and rabbits as the same species — since they are clearly linked by a struggle for existence. Seems like it is much better as definition of the player.

As such, two different attempts at defining species have given us two different game theoretic definitions: strategies (as types) and players (as populations).

There are other reasons why Fisher’s view as described above isn’t perfect for cancer. One big issue is understanding the requirements of the struggle for existence. If here we follow Lennox & Wilson (1994) — which I think is perfectly reasonable to do, since their arguments seem convincing to me — the ideal r-selection (i.e. an exponentially growing tumour) would not correspond to a struggle for existence and thus it would not allow us to define species. Given that in cancer we often care about rapidly growing populations, this might be an important conceptual hurdle.

A practical hurdle is that the big benefit of Fisher’s definition of species in his first sentence is the application to prediction in the second sentence. However, as game theorists, we often care about frequency (or density) dependent fitness and co-existence, thus we care about cases where two types coexist with a cancer species.

Still, I think that Fisher’s definition can be a useful one to reflect on. Although I am sure cancer biologists have already done this. What other useful definitions of species for asexual organisms do you know, dear reader? Can they also provide other new ways to think about evolutionary games?


Fisher, R. A. (1930). The genetical theory of natural selection: a complete variorum edition. Oxford: Clarendon Press.

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

Kaznatcheev, A., Peacock, J., Basanta, D., Marusyk, A., & Scott, J. G. (2018). Fibroblasts and alectinib switch the evolutionary games that non-small cell lung cancer plays. bioRxiv, 179259.

Lennox, J. G., & Wilson, B. E. (1994). Natural selection and the struggle for existence. Studies in History and Philosophy of Science Part A, 25(1): 65-80.

Millstein, R. L. (2009). Populations as individuals. Biological Theory, 4(3): 267-273.

Wells, J. V., & Richmond, M. E. (1995). Populations, metapopulations, and species populations: what are they and who should care? Wildlife Society Bulletin 23(3): 458-462.

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.

4 Responses to Looking for species in cancer but finding strategies and players

  1. Jon Awbrey says:

    I always see tumors as control systems that have grown out of control. Kind of like capitalism …

  2. Jon Awbrey says:

    A cancer is a malign narcicyst, a player who does not play well with others, whose stratagenes are short-haul winning but long-haul meta-losing since it cheats the niche, bankrupts the house, and burns up the board it preys on. Its a sociopathic subsociety.

  3. Pingback: Cataloging a year of blogging: cancer and fitness landscapes | Theory, Evolution, and Games Group

  4. Pingback: Blogging community of computational and mathematical oncologists | Theory, Evolution, and Games Group

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