Evolutionary dynamics of cancer in the bone

I don’t know about you, dear reader, but when I was a senior in highschool, I was busy skipping class to play CounterStrike. And I wasn’t even any good at it. Pranav Warman, however, is busy spending his senior year curing cancer. Or at least modeling it. On Friday, David Basanta, Pranav, and I spent much of the evening trying to understand prostate cancer after it has metastasized to the bone. Below, you can see us trying to make sense of some Mathematica calculations.[1]


In this post, I want to sketch some of the ideas that we fooled around with. First is a model of healthy bone. Second is an introduction of the tumour into the system. Third, we will consider a model of a simple chemotherapy as treatment. You might notice some similarities to Warman et al. (2015) and my old discussions of the Basanta et al. (2012) model of tumour-stroma interaction. This is not accidental.

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Short history of iterated prisoner’s dilemma tournaments

Nineteen Eighty — if I had to pick the year that computational modeling invaded evolutionary game theory then that would be it. In March, 1980 — exactly thirty-five years ago — was when Robert Axelrod, a professor of political science at University of Michigan, published the results of his first tournament for iterated prisoner’s dilemma in the Journal of Conflict Resolution. Game theory experts, especially those specializing in Prisoner’s dilemma, from the disciplines of psychology, political science, economics, sociology, and mathematics submitted 14 FORTRAN programs to compete in a round-robin tournament coded by Axelrod and his research assistant Jeff Pynnonen. If you want to relive these early days of evolutionary game theory but have forgotten FORTRAN and only speak Python then I recommend submitting a strategy to an analogous tournament by Vincent Knight on GitHub. But before I tell you more about submitting, dear reader, I want to celebrate the anniversary of Axelrod’s paper by sharing more about the original tournament.

Maybe it will give you some ideas for strategies.
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Helicobacter pylori and stem cells in the gastric crypt


Last Friday, the 4th Integrated Mathematical Oncology Workshop finished here at Moffitt. The event drew a variety of internal and external participants — you can see a blurry photo of many of them above — and was structured as a competition between four teams specializing in four different domains: Microbiome, Hepatitis C, Human papillomavirus, and Helicobacter pylori. The goal of each team was to build mathematical models of a specific problem in their domain that were well integrated with existing clinical and biological resources, the reward was a start-up grant to the project that seemed most promising to the team of judges. As I mentioned earlier in the week, I was on team H. Pylori — lead by Heiko Enderling with clinical insights from Domenico Coppola and Jose M. Pimiento. To get a feeling for the atmosphere of this workshop, I recommend a video summary of 2013’s workshop made by Parmvir Bahia, David Basanta, and Arturo Araujo:

I want to use this post to summarize some of the modeling that we did for the interaction of H. Pylori and gastric cancer. This is a brief outline — a reminder of sorts — and concentrates only on the parts that I was closely involved in. Unfortunately, this means that I won’t cover all the perspectives that our team offered, nor all the great work that they did. I apologize for the content I omitted. Hopefully, I can convince some other team members to blog about their experience to give a more balanced perspective.

This post also won’t cover all that you might want to know about bacteria and gastric cancer. As we saw earlier, fun questions about H. Pylori span many length and temporal scales and it was difficult to pick one to focus on. Domenico pointed us toward Houghton et al.’s (2004) work on the effect of H. Pylori on stem cell recruitment (for a recent survey, see Bessede et al., 2014), and suggested we aim our modeling at a level where we can discuss stem cells quantitatively. The hope is to use the abundance of stem cells as a new marker for disease progression. In the few days of the workshop, we ended up building and partially integrating two complimentary models; one agent-based and one based purely on ODEs. In the future, we hope to refine and parametrize these models based on patient data from Moffitt for the non-H. Pylori related gastric cancers, and from our partners in Cali, Colombia for H. Pylori related disease.
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Predicting the risk of relapse after stopping imatinib in chronic myeloid leukemia

IMODay1To escape the Montreal cold, I am visiting the Sunshine State this week. I’m in Tampa for Moffitt’s 3rd annual integrated mathematical oncology workshop. The goal of the workshop is to lock clinicians, biologists, and mathematicians in the same room for a week to develop and implement mathematical models focussed on personalizing treatment for a range of different cancers. The event is structured as a competition between four teams of ten to twelve people focused on specific cancer types. I am on Javier Pinilla-Ibarz, Kendra Sweet, and David Basanta‘s team working on chronic myeloid leukemia. We have a nice mix of three clinicians, one theoretical biologist, one machine learning scientist, and five mathematical modelers from different backgrounds. The first day was focused on getting modelers up to speed on the relevant biology and defining a question to tackle over the next three days.
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Liquidity hoarding and systemic failure in the ecology of banks

As you might have guessed from my recent posts, I am cautious in trying to use mathematics to build insilications for predicting, profiting from, or controlling financial markets. However, I realize the wealth of data available on financial networks and interactions (compared to similar resources in ecology, for example) and the myriad of interesting questions about both economics and humans (and their institutions) more generally that understanding finance can answer. As such, I am more than happy to look at heuristics and other toy models in order to learn about financial systems. I am particularly interested in understanding the interplay between individual versus systemic risk because of analogies to social dilemmas in evolutionary game theory (and the related discussions of individual vs. inclusive vs. group fitness) and recently developed connections with modeling in ecology.

Three-month Libor-overnight Interest Swap based on data from Bloomberg and figure 1 of Domanski & Turner (2011). The vertical line marks 15 September 2008 -- the day Lehman Brothers filed for bankruptcy.

Three-month Libor-overnight Interest Swap based on data from Bloomberg and figure 1 of Domanski & Turner (2011). The vertical line marks 15 September 2008 — the day Lehman Brothers filed for bankruptcy.

A particular interesting phenomenon to understand is the sudden liquidity freeze during the recent financial crisis — interbank lending beyond very short maturities virtually disappeared, three-month Libor (a key benchmarks for interest rates on interbank loans) skyrocketed, and the world banking system ground to a halt. The proximate cause for this phase transition was the bankruptcy of Lehman Brothers — the fourth largest investment bank in the US — at 1:45 am on 15 September 2008, but the real culprit lay in build up of unchecked systemic risk (Ivashina & Scharfstein, 2010; Domanski & Turner, 2011; Gorton & Metrick, 2012). Since I am no economist, banker, or trader, the connections and simple mathematical models that Robert May has been advocating (e.g. May, Levin, & Sugihara (2008)) serve as my window into this foreign land. The idea of a good heuristic model is to cut away all non-essential features and try to capture the essence of the complicated phenomena needed for our insight. In this case, we need to keep around an idealized version of banks, their loan network, some external assets with which to trigger an initial failure, and a way to represent confidence. The question then becomes: under what conditions is the initial failure contained to one or a few banks, and when does it paralyze or — without intervention — destroy the whole financial system?
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Cooperation through useful delusions: quasi-magical thinking and subjective utility

GoBoardEconomists that take bounded rationality seriously treat their research like a chess game and follow the reductive approach: start with all the pieces — a fully rational agent — and kill/capture/remove pieces until the game ends, i.e. see what sort of restrictions can be placed on the agents to deviate from rationality and better reflect human behavior. Sometimes these restrictions can be linked to evolution, but usually the models are independent of evolutionary arguments. In contrast, evolutionary game theory has traditionally played Go and concerned itself with the simplest agents that are only capable of behaving according to a fixed strategy specified by their genes — no learning, no reasoning, no built in rationality. If egtheorists want to approximate human behavior then they have to play new stones and take a constructuve approach: start with genetically predetermined agents and build them up to better reflect the richness and variety of human (or even other animal) behaviors (McNamara, 2013). I’ve always preferred Go over chess, and so I am partial to the constructive approach toward rationality. I like to start with replicator dynamics and work my way up, add agency, perception and deception, ethnocentrism, or emotional profiles and general condition behavior.

Most recently, my colleagues and I have been interested in the relationship between evolution and learning, both individual and social. A key realization has been that evolution takes cues from an external reality, while learning is guided by a subjective utility, and there is no a priori reason for those two incentives to align. As such, we can have agents acting rationally on their genetically specified subjective perception of the objective game. To avoid making assumptions about how agents might deal with risk, we want them to know a probability that others will cooperate with them. However, this depends on the agent’s history and local environment, so each agent should learn these probabilities for itself. In our previous presentation of results we concentrated on the case where the agents were rational Bayesian learners, but we know that this is an assumption not justified by evolutionary models or observations of human behavior. Hence, in this post we will explore the possibility that agents can have learning peculiarities like quasi-magical thinking, and how these peculiarities can co-evolve with subjective utilities.
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Hunger Games themed semi-iterated prisoner’s dilemma tournament

hungerGamesCodeWith all the talk surrounding it, crowdsourcing science might seem like a new concept and it might be true for citizen science efforts, but it is definitely an old trick to source your research to other researchers. In fact, evolutionary game theory was born (or at least popularized) by one such crowdsourcing exercise; in 1980, Robert Axelrod wanted to find out the best strategy for iterated prisoner’s dilemma and reached out to prominent researchers for strategy submissions to a round-robin tournmanet. Tit-for-tat was the winning strategy, but the real victor was Axelrod. His 1981 paper with Hamilton analyzing the result went on to become a standard reference in applications of game theory to social questions (at least outside of economics), agent-based modeling, and — of course — evolutionary game theory. Of Axelrod’s sizeable 47,222 (at time of writing) citations, almost half (23,370) come from this single paper. The tradition of tournaments continues among researchers, I’ve even discussed an imitation tournament on imitation previously.

The cynical moral of the tale: if you want to be noticed then run a game theory tournament. The folks at Brilliant.org — a website offering weekly olympiad-style challange problems in math and physics — took this message to heart, coupled it to the tried-and-true marketing technique of linking to a popular movie/book franchise, and decided to run a Hunger Games themed semi-iterated Prisoner’s dillema tournament. Submit a quick explanation of your strategy and Python script to play the game, and you could be one of the 5 winners of the $1,000 grand prize. Hooray! The submission deadline is August 18th, 2013 and all you need is a Brilliant account and it seems that these are free. If you are a reader of TheEGG blog then I recommend submitting a strategy, and discussing it in the comments (either before or after the deadline); I am interested to see what you come up with.
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Evolve ethnocentrism in your spare time

Running an agent based simulation really isn’t that complex. While there’s no shortage of ready-made software packages for ABM (like Repast and NetLogo), all you really need is a good, high-level programming language and a code editor.

As you may have noticed from other blog posts, we have spent quite a bit of time studying agent based models of ethnocentric evolution. To coincide with the publication of our paper (Hartshorn, Kaznatcheev & Shultz, 2013) on the evolution of ethnocentrism in the Journal of Artificial Societies and Social Simulation (JASSS), we thought it would be fun to provide a hands-on tutorial so you can replicate the model yourself. There’s a lot to cover here, so we won’t get into the scientific description of the model itself, but you can read a good synopsis in my executive summary, or Artem’s general overview.

This post assumes no programming background, just a computer, patience, and some curiosity. That being said, you will be compiling a small Java program and modifying its source code, so if words like “compile,” “source code,” and “Java” strike terror in your heart, consider yourself forewarned. It’s actually not that scary. In Estonia they’re teaching kids to program in first grade, and you’re smarter than a first grader…right?!
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How ethnocentrism evolves: a simulation of evolutionary dynamics

tumblr_lcuael7Jyx1qeodf5Cooperation is a paradox—it just doesn’t make sense. Why should I help you when there’s no direct benefit for me? Artem, Professor Tom Shultz, and I have been working for quite some time on a paper about cooperation, and we’re psyched to announce that it’s finally been published in The Journal of Artificial Societies and Social Simulation (JASSS). JASSS is an open web journal, so you can view the full text of our article for free on their website. Or you could skip the 8000 or so words and check out this summary post. Read more of this post

Conditional cooperation and emotional profiles

I haven’t been delving into evolutionary game theory and agent-based modeling for very long, and yet I find that in that little time something quite eerie happens once I’m immersed in these models and simulations: I find myself oscillating between two diametrically opposed points of view. As I watch all of these little agents play their games using some all-too-simplistic strategy, I feel like a small God*. I watch cooperators cooperate, and defectors defect oblivious to what’s in their best interest at the moment. Of course, in the end, my heart goes out to the cooperators, who unfortunately can’t understand that they are being exploited by the defectors. That is what pushes me at the other end of the spectrum of omniscience, and with a nudge of empathy I find myself trying to be a simpleton agent in my over-simplified world.

In that state of mind, I begin to wonder what information exists in the environment, in particular information about the agents I am going to play against. I suppose I’m able to access it and use it to condition my move. Admittedly, that makes me a bit more complex than my original simpleton, and that complexity is likely to come at a cost, but I leave it to evolution to figure out whether the trade-off is worthwhile.
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