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.

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Multiplicative versus additive fitness and the limit of weak selection

Previously, I have discussed the importance of understanding how fitness is defined in a given model. So far, I’ve focused on how mathematically equivalent formulations can have different ontological commitments. In this post, I want to touch briefly on another concern: two different types of mathematical definitions of fitness. In particular, I will discuss additive fitness versus multiplicative fitness.[1] You often see the former in continuous time replicator dynamics and the latter in discrete time models.

In some ways, these versions are equivalent: there is a natural bijection between them through the exponential map or by taking the limit of infinitesimally small time-steps. A special case of more general Lie theory. But in practice, they are used differently in models. Implicitly changing which definition one uses throughout a model — without running back and forth through the isomorphism — can lead to silly mistakes. Thankfully, there is usually a quick fix for this in the limit of weak selection.

I suspect that this post is common knowledge. However, I didn’t have a quick reference to give to Pranav Warman, so I am writing this.
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Eukaryotes without Mitochondria and Aristotle’s Ladder of Life

In 348/7 BC, fearing anti-Macedonian sentiment or disappointed with the control of Plato’s Academy passing to Speusippus, Aristotle left Athens for Asian Minor across the Aegean sea. Based on his five years[1] studying of the natural history of Lesbos, he wrote the pioneering work of zoology: The History of Animals. In it, he set out to catalog the what of biology before searching for the answers of why. He initiated a tradition of naturalists that continues to this day.

Aristotle classified his observations of the natural world into a hierarchical ladder of life: humans on top, above the other blooded animals, bloodless animals, and plants. Although we’ve excised Aristotle’s insistence on static species, this ladder remains for many. They consider species as more complex than their ancestors, and between the species a presence of a hierarchy of complexity with humans — as always — on top. A common example of this is the rationality fetish that views Bayesian learning as a fixed point of evolution, or ranks species based on intelligence or levels-of-consciousness. This is then coupled with an insistence on progress, and gives them the what to be explained: the arc of evolution is long, but it bends towards complexity.

In the early months of TheEGG, Julian Xue turned to explaining the why behind the evolution of complexity with ideas like irreversible evolution as the steps up the ladder of life.[2] One of Julian’s strongest examples of such an irreversible step up has been the transition from prokaryotes to eukaryotes through the acquisition of membrane-bound organelles like mitochondria. But as an honest and dedicated scholar, Julian is always on the lookout for falsifications of his theories. This morning — with an optimistic “there goes my theory” — he shared the new Kamkowska et al. (2016) paper showing a surprising what to add to our natural history: a eukaryote without mitochondria. An apparent example of a eukaryote stepping down a rung in complexity by losing its membrane-bound ATP powerhouse.
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Mutation-bias driving the evolution of mutation rates

In classic game theory, we are often faced with multiple potential equilibria between which to select with no unequivocal way to choose between these alternatives. If you’ve ever heard Artem justify dynamic approaches, such as evolutionary game theory, then you’ve seen this equilibrium selection problem take center stage. Natural selection has an analogous ‘problem’ of many local fitness peaks. Is the selection between them simply an accidental historical process? Or is there a method to the madness that is independent of the the environment that defines the fitness landscape and that can produce long term evolutionary trends?

Two weeks ago, in my first post of this series, I talked about an idea Wallace Arthur (2004) calls “developmental bias”, where the variation of traits in a population can determine which fitness peak the population evolves to. The idea is that if variation is generated more frequently in a particular direction, then fitness peaks in that direction are more easily discovered. Arthur hypothesized that this mechanism can be responsible for long-term evolutionary trends.

A very similar idea was discovered and called “mutation bias” by Yampolsky & Stoltzfus (2001). The difference between mutation bias and developmental bias is that Yampolsky & Stoltzfus (2001) described the idea in the language of discrete genetics rather than trait-based phenotypic evolution. They also did not invoke developmental biology. The basic mechanism, however, was the same: if a population is confronted with multiple fitness peaks nearby, mutation bias will make particular peaks much more likely.

In this post, I will discuss the Yampolsky & Stoltzfus (2001) “mutation bias”, consider applications of it to the evolution of mutation rates by Gerrish et al. (2007), and discuss how mutation is like and unlike other biological traits.

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Variation for supply driven evolution

I’ve taken a very long hiatus (nearly 5 years!) from this blog. I suppose getting married and getting an MD are good excuses, but Artem has very kindly let me return. And I greatly appreciate this chance, because I’d like to summarize an idea I had been working on for a while. So far, only two publication has come out of it (Xue et al., 2015a,b), but it’s an idea that has me excited. So excited that I defended a thesis on it this Tuesday. For now, I call it supply-driven evolution, where I try to show how the generation of variation can determine long-term evolution.

Evolutionary theoreticians have long known that how variation is generated has a decisive role in evolutionary outcome. The reason is that natural selection can only choose among what has been generated, so focusing on natural selection will not produce a full understanding of evolution. But how does variation affect evolution, and can variation be the decisive factor in how evolution proceeds? I believe that the answer is “frequently, yes,” because it does not actually compete with natural selection. I’ll do a brief overview of the literature in the first few posts. By the end, I hope how this mechanism can explain some forms of irreversible evolution, stuff I had blogged about five years ago.

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Evolutionary non-commutativity suggests novel treatment strategies

In the Autumn of 2011 I received an email from Jacob Scott, now a good friend and better mentor, who was looking for an undergraduate to code an evolutionary simulation. Jake had just arrived in Oxford to start his DPhil in applied mathematics and by chance had dined at St Anne’s College with Peter Jeavons, then a tutor of mine, the evening before. Jake had outlined his ideas, Peter had supplied a number of email addresses, Jake sent an email and I uncharacteristically replied saying I’d give it a shot. These unlikely events would led me to where I am today — a DPhil candidate in the Oxford University Department of Computer Science. My project with Jake was a success and I was invited to speak at the 2012 meeting of the Society of Mathematical Biology in Knoxville, TN. Here I met one of Jake’s supervisors, Alexander Anderson, who invited me to visit the Department of Integrated Mathematical Oncology at the Moffitt Cancer Center and Research Institute for a workshop in December of that year. Here Dr. Anderson and I discussed one of the key issues with the work I will present in this post, issues that now form the basis of my DPhil with Dr. Anderson as one of two supervisors. Fittingly, the other is Peter Jeavons.

Jake was considering the problem of treating and avoiding drug resistance and in his short email provided his hypothesis as a single question: “Can we administer a sequence of drugs to steer the evolution of a disease population to a configuration from which resistance cannot emerge?”

In Nichol et al. (2015), we provide evidence for an affirmative answer to this question. I would like to use this post to introduce you to our result, and discuss some of the criticisms.

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Cataloging a year of blogging: cancer and biology

Welcome to 111101111.

Another year has come to an end, and it is time to embrace tradition and reflect on the past twelve months. In fact, I will try to do one better and start a new tradition: cataloging a year of blogging.

Last year, I split up the 83 content heavy posts of 2013 into nine categories in three themes: established applications of evolutionary game theory (ethnocentrism and the public good; and mathematical oncology), expanding from behavior to society and mind (representations and rationality for replicators; feedback between finance & economics and ecology & evolution; and, learning, intelligence, and the social brain), and envisioning the algorithmic world (proof, automata, and physics; natural algorithms and biology; fitness landscapes and evolutionary equilibria; and, metamodeling and the (algorithmic) philosophy of science). In 2014 there was a sharp decrease in number of posts with only 44 articles of new content (and the 3 posts cataloging 2013, so 47 total) — this was due to a nearly 4 month blogging silence in the middle of the year — but a quarter increase in readership with 151,493 views compared to 2013’s 119,935 views. This time, I will need only two posts to survey the past year; this post for the practical and the next for the philosophical.

MathOncoFor me, the year was distributed between three cities, the usual suspects of Montreal and New York, and in October I moved down to Tampa, Florida to work with David Basanta and Jacob Scott in the Intergrated Mathematical Oncology department of the H. Lee Moffitt Cancer Center and Research Institute. A winter without snow is strange but wearing shorts in December makes up for it; plus the sunsets over the Gulf of Mexico are absolutely beautiful. Unsurprisingly, this move has meant that the practical aspects of my focus have shifted almost completely to biology; cancer, in particular.

This post is about the biology and oncology articles that made up about half of last year’s content. Given the autobiographical turn of this post, it will be (loosely) structured around three workshops that I attended in 2014, and the online conversations and collaborations that TheEGG was a host to.
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Algorithmic Darwinism

The workshop on computational theories of evolution started off on Monday, March 17th with Leslie Valiant — one of the organizers — introducing his model of evolvability (Valiant, 2009). This original name was meant to capture what type of complexity can be achieved through evolution. Unfortunately — especially at this workshop — evolvability already had a different, more popular meaning in biology: mechanisms that make an organism or species ‘better’ at evolving, in the sense of higher mutations rates, de novo genes, recombination through sex, etc. As such, we need a better name and I am happy to take on the renaming task.
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Computational theories of evolution

If you look at your typical computer science department’s faculty list, you will notice the theorists are a minority. Sometimes they are further subdivided by being culled off into mathematics departments. As such, any institute that unites and strengthens theorists is a good development. That was my first reason for excitement two years ago when I learned that a $60 million grant would establish the Simons Institute for the Theory of Computing at UC, Berkeley. The institute’s mission is close to my heart: bringing the study of theoretical computer science to bear on the natural sciences; an institute for the algorithmic lens. My second reason for excitement was that one of the inaugural programs is evolutionary biology and the theory of computing. Throughout this term, a series workshops are being held to gather and share the relevant experience.

Right now, I have my conference straw hat on, as I wait for a flight transfer in Dallas on my way to one of the events in this program, the workshop on computational theories of evolution. For the next week I will be in Berkeley absorbing all there is to know on the topic. Given how much I enjoyed Princeton’s workshop on natural algorithms in the sciences, I can barely contain my excitement.
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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.

StromatolitesThrow 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.
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