## Fusion and sex in protocells & the start of evolution

In 1864, five years after reading Darwin’s On the Origin of Species, Pyotr Kropotkin — the anarchist prince of mutual aid — was leading a geographic survey expedition aboard a dog-sleigh — a distinctly Siberian variant of the HMS Beagle. In the harsh Manchurian climate, Kropotkin did not see competition ‘red in tooth and claw’, but a flourishing of cooperation as animals banded together to survive their environment. From this, he built a theory of mutual aid as a driving factor of evolution. Among his countless observations, he noted that no matter how selfish an animal was, it still had to come together with others of its species, at least to reproduce. In this, he saw both sex and cooperation as primary evolutionary forces.

Now, Martin A. Nowak has taken up the challenge of putting cooperation as a central driver of evolution. With his colleagues, he has tracked the problem from myriad angles, and it is not surprising that recently he has turned to sex. In a paper released at the start of this month, Sam Sinai, Jason Olejarz, Iulia A. Neagu, & Nowak (2016) argue that sex is primary. We need sex just to kick start the evolution of a primordial cell.

In this post, I want to sketch Sinai et al.’s (2016) main argument, discuss prior work on the primacy of sex, a similar model by Wilf & Ewens, the puzzle over emergence of higher levels of organization, and the difference between the protocell fusion studied by Sinai et al. (2016) and sex as it is normally understood. My goal is to introduce this fascinating new field that Sinai et al. (2016) are opening to you, dear reader; to provide them with some feedback on their preprint; and, to sketch some preliminary ideas for future extensions of their work.

## Chemical games and the origin of life from prebiotic RNA

From bacteria to vertebrates, life — as we know it today — relies on complex molecular interactions, the intricacies of which science has not fully untangled. But for all its complexity, life always requires two essential abilities. Organisms need to preserve their genetic information and reproduce.

In our own cells, these tasks are assigned to specialized molecules. DNA, of course, is the memory store. The information it encodes is expressed into proteins via messenger RNAs.Transcription (the synthesis of mRNAs from DNA) and translation (the synthesis of proteins from mRNAs) are catalyzed by polymerases necessary to speed up the chemical reactions.

It is unlikely that life started that way, with such a refined division of labor. A popular theory for the origin of life, known as the RNA world, posits that life emerged from just one type of molecule: RNAs. Because RNA is made up of base-complementary nucleotides, it can be used as a template for its own reproduction, just like DNA. Since the 1980s, we also know that RNA can act as a self-catalyst. These two superpowers – information storage and self-catalysis – make it a good candidate for the title of the first spark of life on earth.

The RNA-world theory has yet to meet with empirical evidence, but laboratory experiments have shown that self-preserving and self-reproducing RNA systems can be created in vitro. Little is known, however, about the dynamics that governed pre- and early life. In a recent paper, Yeates et al. (2016) attempt to shed light on this problem by (1) examining how small sets of different RNA sequences can compete for survival and reproduction in the lab and (2) offering a game-theoretical interpretation of the results.

## 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.

## Misleading models in mathematical oncology

I have an awkward relationship with mathematical oncology, mostly because oncology has an awkward relationship with math. Although I was vaguely familiar that evolutionary game theory (EGT) could be used in cancer research, mostly through Axelrod et al. (2006), I never planned to work on cancer. I wasn’t eager to enter the field because I couldn’t see how heuristic models could be of use in medicine; I thought only insilications could be useful, but EGT was not at a level of sophistication where it could build predictive models. I worried that selling non-predictive models as advice for treatment would only cause harm. However, the internet being the place it is, I ended up running into David Basanta — one of the major advocates of EGT in oncology — and Jacob Scott on twitter. After looking through some of the literature, I realized that most of experimental cancer research was more piecemeal than I expected and theory was based mostly on ad-hoc mental models. This convinced me that there is room for clear mathematical (and maybe computational) reasoning to help formalize and explore these mental models. Now we have a paper applying the Ohtsuki-Nowak transform to studying edge effects in the go-grow game prepped (Kaznatcheev, Scott, & Basanta, 2013), and David and I have a project on chronic myeloid leukemia in the works. The first is a heuristic model building on top of previously developed tools (from my experience, it is rather uncommon to build directly on others’ work in evolutionary game theory and mathematical oncology) and the other an abductive model using a combination of analytic and machine learning techniques to produce a predictive tool useful in the clinic.

## Cooperation, enzymes, and the origin of life

Enzymes play an essential role in life. Without them, the translation of genetic material into proteins — the building blocks of all phenotypic traits — would be impossible. That fact, however, poses a problem for anyone trying to understand how life appeared in the hot, chaotic, bustling molecular “soup” from which it sparked into existence some 4 billion years ago.

Throw a handful of self-replicating organic molecules into a glass of warm water, then shake it well. In this thoroughly mixed medium, molecules that help other molecules replicate faster –- i.e. enzymes or analogues thereof — do so at their own expense and, by virtue of natural selection, must sooner or later go extinct. But now suppose that little pockets or “vesicles” form inside the glass by some abiotic process, encapsulating the molecules into isolated groups. Suppose further that, once these vesicles reach a certain size, they can split and give birth to “children” vesicles — again, by some purely physical, abiotic process. What you now have is a recipe for group selection potentially favorable to the persistence of catalytic molecules. While less fit individually, catalysts favor the group to which they belong.

This gives rise to a conflict opposing (1) within-group selection against “altruistic” traits and (2) between-group selection for such traits. In other words, enzymes and abiotic vesicles make an evolutionary game theory favourite — a social dilemma.

## Approximating spatial structure with the Ohtsuki-Nowak transform

Can we describe reality? As a general philosophical question, I could spend all day discussing it and never arrive at a reasonable answer. However, if we restrict to the sort of models used in theoretical biology, especially to the heuristic models that dominate the field, then I think it is relatively reasonable to conclude that no, we cannot describe reality. We have to admit our current limits and rely on thinking of our errors in the dual notions of assumptions or approximations. I usually prefer the former and try to describe models in terms of the assumptions that if met would make them perfect (or at least good) descriptions. This view has seemed clearer and more elegant than vague talk of approximations. It is the language I used to describe the Ohtsuki-Nowak (2006) transform over a year ago. In the months since, however, I’ve started to realize that the assumptions-view is actually incompatible with much of my philosophy of modeling. To contrast my previous exposition (and to help me write up some reviewer responses), I want to go through a justification of the ON-transform as a first-order approximation of spatial structure.

## Enriching evolutionary games with trust and trustworthiness

Fairly early in my course on Computational Psychology, I like to discuss Box’s (1979) famous aphorism about models: “All models are wrong, but some are useful.” Although Box was referring to statistical models, his comment on truth and utility applies equally well to computational models attempting to simulate complex empirical phenomena. I want my students to appreciate this disclaimer from the start because it avoids endless debate about whether a model is true. Once we agree to focus on utility, we can take a more relaxed and objective view of modeling, with appropriate humility in discussing our own models. Historical consideration of models, and theories as well, should provide a strong clue that replacement by better and more useful models (or theories) is inevitable, and indeed is a standard way for science to progress. In the rapid turnover of computational modeling, this means that the best one could hope for is to have the best (most useful) model for a while, before it is pushed aside or incorporated by a more comprehensive and often more abstract model. In his recent post on three types of mathematical models, Artem characterized such models as heuristic. It is worth adding that the most useful models are often those that best cover (simulate) the empirical phenomena of interest, bringing a model closer to what Artem called insilications.

## Cooperation through useful delusions: quasi-magical thinking and subjective utility

Economists 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.

## Micro-vs-macro evolution is a purely methodological distinction

On the internet, the terms macroevolution and microevolution (especially together) are usually used primarily in creationist rhetoric. As such, it is usually best to avoid them, especially when talking to non-scientists. The main mistake creationist perpetuate when thinking about micro-vs-macro evolution, is that the two are somehow different and distinct physical processes. This is simply not the case, they are both just evolution. The scientific distinction between the terms, comes not from the physical world around us, but from how we choose to talk about it. When a biologist says “microevolution” or “macroevolution” they are actually signaling what kind of questions they are interested in asking, or what sort of tools they plan on using.

## Evolutionary games in set structured populations

We have previously discussed the importance of population structure in evolutionary game theory, and looked at the Ohtsuki-Nowak transform for analytic studies of games on one of the simplest structures — random regular graphs. However, there is another extremely simple structure to consider: a family of inviscid sets. We can think of each agent as belonging to one or more sets and interacting with everybody that shares a set with them. If there is only one set then we are back to the case on a completely inviscid population. If we associate a set with each edge in a graph and restrict them to have constant size then we have standard evolutionary graph theory. However, it is more natural to allow sets to grow larger if their members have high fitness.

Tarnita et al. (2009) consider a population of $N$ individuals and $M$ sets, where each individual can belong to $K$ of the sets. Strategy and set membership are heritable (with mutation probabilities $u$ and $v$, respectively), and interactions are only with agents that share a set (if two agents share more than one set then they interact more than once). However, reproduction is inviscid: a random individual is selected to die and everybody competes to replace them with a child. This set-dependent interaction, makes the model equivalent to the earliest models of ethnocentrism, but the model is not equivalent to more modern approaches to ethnocentrism. Since sets cannot reproduce and migration (through mutation) between sets is purely random, the model also cannot capture group selection. However, cooperation for the Prisoners’ dilemma still emerges in this model, if we have:

$\frac{b}{c} \geq \frac{K}{M - K}(\nu + 2) + \frac{M}{M - K}\frac{\nu^2 + 3\nu + 3}{\nu(\nu + 2)}$

Where $\nu = 2Nv$ is the population-scaled set mutation rate, even when this is zero we get cooperation when $\frac{b}{c} \geq \frac{3}{2} + \frac{7K}{2(M - K)}$. Alternatively, to simplify we can take the limit of $M >> K = 1$ to get:

$\frac{b}{c} \geq 1 + \frac{1}{\nu}(1 + \frac{1}{\nu + 2}) + \frac{\nu + 2}{M}$

If we allow the maximum number of sets ($M = N$) and take the further limit of large populations $N >> 2$ then this becomes a very simple:

$\frac{b}{c} \geq 1 + 2v$

Finally, in the supplementary materials, the authors derive a very nice relationship for evolution of cooperation on arbitrary cooperate-defect games given by a payoff matrix $\begin{pmatrix}1 & U \\ V & 0\end{pmatrix}$ of:

$\sigma \geq V - U$

where $\sigma$ is a structural constant given by:

$\sigma = \frac{1 + \nu + \mu}{3 + \nu + \mu)}\frac{K(\nu^2 + 2\nu + \nu\mu) + M(3 + 2\nu + \mu}{K(\nu^2 + 2\nu + \nu\mu) + M(1 + \mu)}$

Which in the limit of small population-scaled strategy mutation ($\mu = 0$), and $M >> K$ becomes:

$\sigma = 1 + \nu + \frac{\nu(\nu + 1)}{\nu + 3}$

Since the structural constant is always greater than 1, and since we typically care about large $\nu$, it is more enlightening to look at the reciprocal that in the limit of large $\nu >> 3$ becomes:

$\frac{1}{\sigma - 1} = \frac{1}{2\nu}$

And simplifies the general equation for cooperation to emerge to:

$1 + 2\nu \geq V - U$

Which can be seen as a relaxation of the classic game theory concept of risk-dominance.

Tarnita, C., Antal, T., Ohtsuki, H., & Nowak, M. (2009). Evolutionary dynamics in set structured populations Proceedings of the National Academy of Sciences, 106 (21), 8601-8604 DOI: 10.1073/pnas.0903019106