Hadza hunter-gatherers, social networks, and models of cooperation

At the heart of the Great Lakes region of East Africa is Tanzania — a republic comprised of 30 mikoa, or provinces. Its border is marked off by the giant lakes Victoria, Tanganyika, and Malawi. But the lake that interests me the most is an internal one: 200 km from the border with Kenya at the junction of mikao Arusha, Manyara, Simiyu and Singed is Lake Eyasi. It is a temperamental lake that can dry up almost entirely — becoming crossable on foot — in some years and in others — like the El Nino years — flood its banks enough to attract hippos from the Serengeti.

For the Hadza, it is home.

The Hadza number around a thousand people, with around 300 living as traditional nomadic hunter-gatherers (Marlow, 2002; 2010). A life style that is believed to be a useful model of societies in our own evolutionary heritage. An empirical model of particular interest for the evolution of cooperation. But a model that requires much more effort to explore than running a few parameter settings on your computer. In the summer of 2010, Coren Apicella explored this model by traveling between Hadza camps throughout the Lake Eyasi region to gain insights into their social network and cooperative behavior.

Here is a video abstract where Coren describes her work:

The data she collected with her colleagues (Apicella et al., 2012) provides our best proxy for the social organization of early humans. In this post, I want to talk about the Hadza, the data set of their social network, and how it can inform other models of cooperation. In other words, I want to freeride on Apicella et al. (2012) and allow myself and other theorists to explore computational models informed by the empirical Hadza model without having to hike around Lake Eyasi for ourselves.

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Measuring games in the Petri dish

For the next couple of months, Jeffrey Peacock is visiting Moffitt. He’s a 4th year medical student at the University of Central Florida with a background in microbiology and genetic engineering of bacteria and yeast. Together with Andriy Marusyk and Jacob Scott, he will move to human cells and run some in vitro experiments with non-small cell lung cancer — you can read more about this on Connecting the Dots. Robert Vander Velde is also in the process of designing some experiments of his own. Both Jeff and Robert are interested in evolutionary game theory, so this is great opportunity for me to put my ideas on operationalization of replicator dynamics into practice.

In this post, I want to outline the basic process for measuring a game from in vitro experiments. Games in the Petri-dish. It won’t be as action packed as Agar.io — that’s an actual MMO cells-in-Petri-dish game; play here — but hopefully it will be more grounded in reality. I will introduce the gain function, show how to measure it, and stress the importance of quantifying the error on this measurement. Since this is part of the theoretical preliminaries for my collaborations, we don’t have our own data to share yet, so I will provide an illustrative cartoon with data from Archetti et al. (2015). Finally, I will show what sort of data would rule-out the theoretician’s favourite matrix games and discuss the ego-centric representation of two-strategy matrix games. The hope is that we can use this work to go from heuristic guesses at what sort of games microbes or cancer cells might play to actually measuring those games.
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A year in books: Neanderthals to the National Cancer Act to now

A tradition I started a couple of years ago is to read at least one non-fiction book per month and then to share my thoughts on the reading at the start of the following year. Last year, my dozen books were mostly on philosophy, psychology, and political economy. My brief comments on them ended up running a long 3.2 thousand words. This time the list had expanded to around 19 books. So I will divide the summaries into thematic sets. For the first theme, I will start with a subject that is new for my idle reading: cancer.

As a new researcher in mathematical oncology — and even though I am located in a cancer hospital — my experience with cancer has been mostly confined to the remote distance of replicator dynamics. So above all else these three books — Nelson’s (2013) Anarchy in the Organism, Mukherjee’s (2010) The Emperor of All Maladies, and Leaf’s (2014) The Truth in Small Doses — have provided me with insights into the personal experiences of the patient and doctor.

I hope that based on these reviews and the ones to follow, you can suggest more books for me to read in 2016. Better yet, maybe my comments will help you choose your next book. Much of what I read in 2015 came from suggestions made by my friends and readers, as well as articles, blogs, and reviews I’ve stumbled across.[1] In fact, each of these cancer books was picked for me by someone else.

If you’ve been to a restaurant with me then you know that I hate choosing between close-to-equivalent options. To avoid such discomfort, I outsourced the choosing of my February book to G+ and Nelson’s Anarchy in the Organism beat out Problems of the Self by a narrow margin to claim a spot on the reading list. As I was finishing up Nelson’s book — which I will review last in this post — David Basanta dropped off The Emperor of All Maladies on my desk. So I continued my reading on cancer. Finally, Leaf’s book came towards the end of the year based on a recommendation from Jacob Scott. It helped reinvigorate me after a summer away from the Moffitt Cancer Center.
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Cataloging a year of blogging

Happy Old New Year.

January 2016 is the the start of the 6th calendar year and the 41st month with updates to TheEGG. The reason for the large discrepancy between these two numbers is occasional months without activity. The past year was exceptional in this regard with the longest single silence on the blog between April 4th and October 26th. This means that the year saw only 29 new entries, 2 indexes cataloging 2014, a report on the EGT reading group, and an update on readership. This post is meant to organize the last year of activity for future reference, and to try to uncover common themes.

If you like lists and TL;DRs then this is for you.
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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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Diversity and persistence of group tags under replicator dynamics

Everyday I walk to the Stabile Research Building to drink espresso and sit in my cozy — although oversaturated with screens — office. Oh, and to chat about research with great people like Arturo Araujo, David Basanta, Jill Gallaher, Jacob Scott, Robert Vander Velde and other Moffitters. This walk to the office takes about 30 minutes each way, so I spend it listening to podcasts. For the past few weeks, upon recommendation from a friend, I’ve started listing to the archive of the Very Bad Wizards. This is a casual — although oversaturated with rude jokes — conversation between David Pizarro and Tamler Sommers on various aspects of the psychology and philosophy of morality. They aim at an atmosphere of two researchers chatting at the bar; although their conversation is over Skype and drinks. It is similar to the atmosphere that I want to promote here at TheEGG. Except they are funny.

While walking this Wednesday, I listed to episode 39 of Very Bad Wizards. Here the duo opens with a Wilson & Haidt’s TIME quiz meant to quantify to what extent you are liberal or conservative.[1] They are 63% liberal.[2]

To do the quiz, you are asked to rate 12 statements (well, 11 and one question about browsers) on a six point Likert scale from strongly disagree to strongly agree. Here are the three that caught my attention:

  1. If I heard that a new restaurant in my neighborhood blended the cuisines of two very different cultures, that would make me want to try it.
  2. My government should treat lives of its citizens as being much more valuable than lives in other countries.[3]
  3. I wish the world did not have nations or borders and we were all part of one big group.[4]

Do you strongly agree? Strongly disagree? What was your overall place on the liberal-conservative scale?


Regardless of your answers, the statements probably remind you of an important aspect of your daily experience. The world is divided into a diversity of groups, and they coexist in a tension between their arbitrary, often artificial, nature and the important meaning that they hold to both their own members and others. Often this division is accompanied by ethnocentrism — a favoring of the in-group at the expensive of, or sometimes with direct hostility toward, the out-group — that seems difficult to circumvent through simply expanding our moral in-group. These statements also confront you with the image of what a world without group lines might look like; would it be more cooperative or would it succumb to the egalitarian dilemma?[5]

As you know, dear reader, here at TheEGG we’ve grappled with some of these questions. Mostly by playing with the Hammond & Axelrod model of ethnocentrism (2006; also see: Hartshorn, Kaznatcheev & Shultz, 2012). Recently, Jansson’s (2015) extension of my early work on the robustness of ethnocentrism (Kaznatcheev, 2010) has motivated me to continue this thread. A couple of weeks ago I sketched how to reduce the dimensionality of the replicator equations governing tag-based games. Today, I will use this representation to look at how properties of the game affect the persistence and diversity of tags.
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From linear to nonlinear payoffs in the double public goods game

If you recall, dear reader, around this time last year, Robert Vander Velde, David Basanta, Jacob Scott and I got excited about the Archetti (2013,2014) approach to modeling non-linear public goods in cancer. We’ve been working on this intermittently for the last year, but aim to focus now that I have settled in here at Moffitt. This means there will be a lot more cancer posts as I resume thinking careful about mathematical oncology. Although I didn’t update the blog in the summer, it doesn’t mean that nothing was written. The work below is mostly from when I visited Tampa in late July. As are these two blackboards:


In this project, we are combining growth factor production (Archetti, 2013) and acidity (2014) as a pair of anti-correlated public goods. The resulting dynamics cannot be understood by studying just one or the other good. The goal is to explore the richer behaviors that are possible with coupled social dilemmas. At the start of the year — in my first analysis of the double public goods game — as a sanity check I considered the linear public goods f(q) = b_f q and m(p) = b_m p. After a long meeting with Robert a few month ago, I think that these were misleading payoffs to consider. I jotted these notes after the meeting, but forgot to release them on the blog. Instead, you get to enjoy them now while I refresh my memory.

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Radicalization, expertise, and skepticism among doctors & engineers: the value of philosophy in education

This past Friday was a busy day for a lot of the folks in Integrated Mathematical Oncology here at the Moffitt Cancer Center. Everybody was rushing around to put the final touches on a multi-million dollar research center grant application to submit to the National Cancer Institute. Although the time was not busy for me, I still stopped by Jacob Scott’s office towards the end of the day to celebrate. Let me set the scene for you: it is a corner office down the hall from me; its many windows are scribbled over with graphs, equations, and biological interaction networks; two giant screens crowd a standing desk, and another screen is hidden in the corner; the only non-glass wall has scribbles in pencil for the carpenters: paint blackboard here. There are too many chairs — Jake is a connector, so his office is always open to guests.

A different celerbation in Jake's office. The view is from his desk towards the wall that needs to be replaced by a blackboard.

A different celerbation in Jake’s office. The view is from his desk towards the wall that needs to be replaced by a blackboard.

In addition to the scientific and administrative stress of grant-writing, Jake was also covering for his friend as the doc-of-the-day for radiation oncology. So as I rambled on: “If we consider nodes of degree three or higher in this model, we would break up contingent blocks of mutants and result in the domain of our probability distribution going from n^2 to 2^n“, scribbling more math on his wall, we would get interrupted by phone calls. His resident calling to tell him that the neurosurgeons have scheduled a consultation for an acute myeloid leukemia patient who is recovering from surgery earlier that day.

“Only on a Friday afternoon do you get this kind of consult!” Jake fires off, “He’s still in surgery! We can’t do anything for at least a few days – schedule him for Monday.”

The call was on speakerphone, but I could not keep up with the conversation. After years of training and experience, this was an effortless context-shift for Jake. He went from the heavy skepticism of a scientist staring at a blackboard to the certainty of a doctor that needed to get shit done, and back, in moments. I couldn’t imagine having this sort of confidence in my judgements, mostly because I have no training in medicine, but also because I am not expected to be certain. That is why I lean towards using abductive models versus insilications for clinial research; I have more confidence in machine learning than in my own physical and biological intuitions about cancer. Even if that approach might produce less understanding.

In recent weeks, I’ve noticed a theme in some of the (news and blog) articles I’ve been reading. In this post, I wanted to provide an annotated collection of some of these links, along with my reflections on what they say about the tension between expertise and skepticism and how that can radicalize us, both in mundane ways and in drastic ones. And what role philosophy can play in helping us cope. I will end up touching on recent events and politics as a source context, but hopefully we can keep the overall conversation more or less detached from current events.
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Cytokine storms during CAR T-cell therapy for lymphoblastic leukemia

For most of the last 70 years or so, treating cancer meant one of three things: surgery, radiation, or chemotherapy. In most cases, some combination of these remains the standard of care. But cancer research does not stand still. More recent developments have included a focus on immunotherapy: using, modifying, or augmenting the patient’s natural immune system to combat cancer. Last week, we pushed the boundaries of this approach forward at the 5th annual Integrated Mathematical Oncology Workshop. Divided into four teams of around 15 people each — mathematicians, biologists, and clinicians — we competed for a $50k start-up grant. This was my 3rd time participating,[1] and this year — under the leadership of Arturo Araujo, Marco Davila, and Sungjune Kim — we worked on chimeric antigen receptor T-cell therapy for acute lymphoblastic leukemia. CARs for ALL.

Team Red busy at work in the collaboratorium

Team Red busy at work in the collaboratorium. Photo by team leader Arturo Araujo.

In this post I will describe the basics of acute lymphoblastic leukemia, CAR T-cell therapy, and one of its main side-effects: cytokine release syndrome. I will also provide a brief sketch of a machine learning approach to and justification for modeling the immune response during therapy. However, the mathematical details will come in future posts. This will serve as a gentle introduction.

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Symmetry in tag-based games & invariants under replicator dynamics

Mathematicians and physicists love finding symmetries. The reason is simple: symmetries make life easier. The situation is no different when studying the evolutionary dynamics of life. If the fitness functions of your organisms have some symmetry or other nice structure then you can usually exploit it to make analyzing your replicator equations easier. In this post, I want to show an example of this in tag-based models. This analysis is an essential base case when building more complicated models of ethnocentrism — like our work in the Hammond and Axelrod model — and I have been meaning to write about it for a while. This will give me a chance to show a concrete example where my method for factoring the replicator equation is useful, and how observing a straighforward symmetry can reduce the dimensionality of a problem. Maybe this exercise will also teach us something about the evolution of ethnocentrism.
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