Space and stochasticity in evolutionary games

Two of my goals for TheEGG this year are to expand the line up of contributors and to extend the blog into a publicly accessible venue for active debate about preliminary, in-progress, and published projects; a window into the everyday challenges and miracles of research. Toward the first goal, we have new contributions from Jill Gallaher late last year and Alexander Yartsev this year with more posts taking shape as drafts from Alex, Marcel Montrey, Dan Nichol, Sergio Graziosi, Milo Johnson, and others. For the second goal, we have an exciting debate unfolding that was started when my overview of Archetti (2013,2014) prompted an objection from Philip Gerlee in the comments and Philipp Altrock on twitter. Subsequently, Philip and Philipp combined their objections into a guest post that begat an exciting comment thread with thoughtful discussion between David Basanta, Robert Vander Velde, Marc Harper, and Philip. Last Thursday, I wrote about how my on-going project with Robert, David, and Jacob Scott is expanding on Archetti’s work and was surprised to learn that Philip has responded on twitter with the same criticism as before. I was a little flabbergast by this because I thought that I had already addressed Philip’s critique in my original comment response and that he was reiterating the same exact text in his guest post simply for completeness and record, not because he thought it was still a fool-proof objection.

My biggest concern now is the possibility that Philip and I are talking past each other instead of engaging in a mutually beneficial dialogue. As such, I will use this post to restate (my understand of the relevant parts of) Philip and Philipp’s argument and extend it further, providing a massive bibliography for readers interested in delving deeper into this. In a future post, I will offer a more careful statement of my response. Hopefully Philip or other readers will clarify any misunderstandings or misrepresentations in my summary or extension. Since this discussion started in the context of mathematical oncology, I will occasionally reference cancer, but the primary point at issue is one that should be of interest to all evolutionary game theorists (maybe even most mathematical modelers): the model complexity versus simplicity tension that arises from the stochastic to deterministic transition and the discrete to continuous transition.

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