Evolutionary game theory without interactions

When I am working on evolutionary game theory, I usually treat the models I build as heuristics to guide intuitions and push the imagination. But working on something as practical as cancer, and being in a department with many physics-trained colleagues puts pressure on me to think of moving more towards insilications or abductions. Now, Philip Gerlee and Philipp Altrock are even pushing me in that direction with their post on TheEGG. So this entry might seem a bit uncharacteristic, I will describe an experiment — at least as a theorist like me imagines them.

Consider the following idealized protocol that is loosely inspired by Archetti et al. (2015) and the E. coli Long-term evolution experiment (Lenski et al., 1991; Wiser et al., 2013; Ribeck & Lenski, 2014). We will (E1) take a new petri dish or plate; (E2) fill it with a fixed mix of nutritional medium like fetal bovine serum; (E3) put a known number N of two different cell types A and B on the medium (on the first plate we will also know the proportion of A and B in the mixture); (E4) let them grow for a fixed amount of time T which will be on the order of a cell cycle (or two); (E5) scrape the cells off the medium; and (E6) return to step (E1) while selecting N cells at random from the ones we got in step (E5) to seed step (E3). Usually, you would use this procedure to see how A-cells and B-cells compete with each other, as Archetti et al. (2015). However, what would it look like if the cells don’t compete with each other? What if they produce no signalling molecules — in fact, if they excrete nothing into the environment, to avoid cross-feeding interactions — and don’t touch each other? What if they just sit there independently eating their very plentiful nutrient broth?[1]

Would you expect to see evolutionary game dynamics between A and B? Obviously, since I am asking, I expect some people to answer ‘no’ and then be surprised when I derive some math to show that the answer can be ‘yes’. So, dear reader, humour me by being surprised.
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