Cataloging a year of blogging: cancer and fitness landscapes

Happy 2019!

As we leave 2018, the Theory, Evolution, and Games Group Blog enters its 9th calendar year. This past year started out slowly with only 4 posts in the first 5 months. However, after May 31st, I managed to maintain a regular posting schedule. This is the 32nd calendar week in a row with at least one new blog post released.

I am very happy about this regularity. Let’s see if I can maintain it throughout 2019.

A total of 38 posts appeared on TheEGG last year. This is the 3rd most prolific year after the 47 in 2014 and 88 in 2013. One of those being a review of the 12 posts of 2017 (the least prolific year for TheEGG).

But the other 37 posts are too much to cover in one review. Thus, in this catalogue, I’ll focus on cancer and fitness landscapes. Next week, I’ll deal with the more philosophical content from the last year.
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Open-ended evolution on hard fitness landscapes from VCSPs

There is often interest among the public and in the media about evolution and its effects for contemporary humans. In this context, some argue that humans have stopped evolving, including persons who have a good degree of influence over the public opinion. Famous BBC Natural History Unit broadcaster David Attenborough, for example, argued a few years ago in an interview that humans are the only species who “put halt to natural selection of its own free will”. The first time I read this, I thought that it seemed plausible. The advances in medicine that we made in the last two centuries mean that almost all babies can reach adulthood and have children of their own, which appears to cancel natural selection. However, after more careful thought, I realized that these sort of arguments for the ‘end of evolution’ could not be true.

Upon more reflection, there just seem to be better arguments for open-ended evolution.

One way of seeing that we’re still evolving is by observing that we actually created a new environment, with very different struggles than the ones that we encountered in the past. This is what Adam Benton (2013) suggests in his discussion of Attenborough. Living in cities with millions of people is very different from having to survive in a prehistoric jungle, so evolutionary pressures have shifted in this new environment. Success and fitness are measured differently. The continuing pace of changes and evolution in various fields such as technology, medicine, sciences is a clear example that humans continue to evolve. Even from a physical point of view, research shows that we are now becoming taller, after the effects of the last ice age faded out (Yang et al., 2010), while our brain seems to get smaller, for various reasons with the most amusing being that we don’t need that much “central heating”. Take that Aristotle! Furthermore, the shape of our teeth and jaws changed as we changed our diet, with different populations having a different structure based on the local diet (von Cramon-Taubadel, 2011).

But we don’t even need to resort to dynamically changing selection pressures. We can argue that evolution is ongoing even in a static environment. More importantly, we can make this argument in the laboratory. Although we do have to switch from humans to a more prolific species. A good example of this would be Richard Lenski’s long-term E-coli evolution experiment (Lenski et al., 1991) which shows that evolution is still ongoing after 50000 generations in the E-coli bacteria (Wiser et al., 2013). The fitness of the E. coli keeps increasing! This certainly seems like open-ended evolution.

But how do we make theoretical sense of these experimental observations? Artem Kaznatcheev (2018) has one suggestion: ‘hard’ landscapes due to the constraints of computational complexity. He suggests that evolution can be seen as a computational problem, in which the organisms try to maximize their fitness over successive generations. This problem would still be constrained by the theory of computational complexity, which tells us that some problems are too hard to be solved in a reasonable amount of time. Unfortunately, Artem’s work is far too theoretical. This is where my third-year project at the University of Oxford comes in. I will be working together with Artem on actually simulating open-ended evolution on specific examples of hard fitness landscapes that arise from valued constraint satisfaction problems (VCSPs).

Why VCSPs? They are an elegant generalization of the weighted 2SAT problem that Artem used in his work on hard landscapes. I’ll use this blog post to introduce CSPs, VCSPs, explain how they generalize weighted 2 SAT (and thus the NK fitness landscape model), and provide a way to translate between the language of computer science and that of biology.

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Local peaks and clinical resistance at negative cost

Last week, I expanded on Rob Noble’s warning about the different meanings of de novo resistance with a general discussion on the meaning of resistance in a biological vs clinical setting. In that post, I suggested that clinicians are much more comfortable than biologists with resistance without cost, or more radically: with negative cost. But I made no argument — especially no reductive argument that could potentially sway a biologist — about why we should entertain the clinician’s perspective. I want to provide a sketch for such an argument in this post.

In particular, I want to present a theoretical and extremely simple fitness landscape on which a hypothetical tumour might be evolving. The key feature of this landscape is a low local peak blocking the path to a higher local peak — a (partial) ultimate constraint on evolution. I will then consider two imaginary treatments on this landscape, one that I find to be more similar to a global chemotherapy and one that is meant to capture the essence of a targetted therapy. In the process, I will get to introduce the idea of therapy transformations to a landscape — something to address the tendency of people treating treatment fitness landscapes as completely unrelated to untreated fitness landscapes.

Of course, these hypothetical landscapes are chosen as toy models where we can have resistance emerge with a ‘negative’ cost. It is an empirical question to determine if any of this heuristic capture some important feature of real cancer landscapes.

But we won’t know until we start looking.

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Minimal models for explaining unbounded increase in fitness

On a prior version of my paper on computational complexity as an ultimate constraint, Hemachander Subramanian made a good comment and question:

Nice analysis Artem! If we think of the fitness as a function of genes, interactions between two genes, and interactions between three genes and so on, your analysis using epistasis takes into account only the interactions (second order and more). The presence or absence of the genes themselves (first order) can change the landscape itself, though. Evolution might be able to play the game of standing still as the landscape around it changes until a species is “stabilized” by finding itself in a peak. The question is would traversing these time-dependent landscapes for optima is still uncomputable?

And although I responded to his comment in the bioRxiv Disqus thread, it seems that comments are version locked and so you cannot see Hema’s comment anymore on the newest version. As such, I wanted to share my response on the blog and expand a bit on it.

Mostly this will be an incomplete argument for why biologists should care about worst-case analysis. I’ll have to expand on it more in the future.

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Labyrinth: Fitness landscapes as mazes, not mountains

Tonight, I am passing through Toulouse on my way to Montpellier for the 2nd Joint Congress on Evolutionary Biology. If you are also attending then find me on 21 August at poster P-0861 on level 2 to learn about computational complexity as an ultimate constraint on evolution.

During the flight over, I was thinking about fitness landscapes. Unsurprising — I know. A particular point that I try to make about fitness landscapes in my work is that we should imagine them as mazes, not as mountain ranges. Recently, Raoul Wadham reminded me that I haven’t written about the maze metaphor on the blog. So now is a good time to write on labyrinths.

On page 356 of The roles of mutation, inbreeding, crossbreeding, and selection in evolution, Sewall Wright tells us that evolution proceeds on a fitness landscape. We are to imagine these landscapes as mountain ranges, and natural selection as a walk uphill. What follows — signed by Dr. Jorge Lednem Beagle, former navigator of the fitness maze — throws unexpected light on this perspective. The first two pages of the record are missing.

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Proximal vs ultimate constraints on evolution

For a mathematician — like John D. Cook, for example — objectives and constraints are duals of each other. But sometimes the objectives are easier to see than the constraints. This is certainly the case for evolution. Here, most students would point you to fitness as the objective to be maximized. And at least at a heuristic level — under a sufficiently nuanced definition of fitness — biologists would agree. So let’s take the objective as known.

This leaves us with the harder to see constraints.

Ever since the microscope, biologists have been expert at studying the hard to see. So, of course — as an editor at Proceedings of the Royal Society: B reminded me — they have looked at constraints on evolution. In particular, departures from an expected evolutionary equilibrium is where biologists see constraints on evolution. An evolutionary constraint is anything that prevents a population from being at a fitness peak.

Winding path in a hard semi-smooth landscape

In this post, I want to follow a bit of a winding path. First, I’ll appeal to Mayr’s ultimate-proximate distinction as a motivation for why biologists care about evolutionary constraints. Second, I’ll introduce the constraints on evolution that have been already studied, and argue that these are mostly proximal constraints. Third, I’ll introduce the notion of ultimate constraints and interpret my work on the computational complexity of evolutionary equilibria as an ultimate constraint. Finally, I’ll point at a particularly important consequence of the computational constraint of evolution: the possibility of open-ended evolution.

In a way, this post can be read as an overview of the change in focus between Kaznatcheev (2013) and (2018).
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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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Misleading models: “How learning can guide evolution”

HintonI often see examples of mathematicians, physicists, or computer scientists transitioning into other scientific disciplines and going on to great success. However, the converse is rare, and the only two examples I know is Edward Witten’s transition from an undergad in history and linguistics to a ground-breaking career in theoretical physicist, and Geoffrey Hinton‘s transition from an undergrad in experimental psychology to a trend setting career in artificial intelligence. Although in my mind Hinton is associated with neural networks and deep learning, that isn’t his only contribution in fields close to my heart. As is becoming pleasantly common on TheEGG, this is a connection I would have missed if it wasn’t for Graham Jones‘ insightful comment and subsequent email discussion in early October.

The reason I raise the topic four months later, is because the connection continues our exploration of learning and evolution. In particular, Hinton & Nowlan (1987) were the first to show the Baldwin effect in action. They showed how learning can speed up evolution in model that combined a genetic algorithm with learning by trial and error. Although the model was influential, I fear that it is misleading and the strength of its results are often misinterpreted. As such, I wanted to explore these shortcomings and spell out what would be a convincing demonstration of a qualitative increase in adaptability due to learning.
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Software through the lens of evolutionary biology

My preferred job title is ‘theorist’, but that is often too ambiguous in casual and non-academic conversation, so I often settle for ‘computer scientist’. Unfortunately, it seems that the overwhelming majority of people equate computer scientists to programmers or some general ‘tech person’, forgetting M.R. Fellows rallying cry: “Computer science is not about machines, in the same way that astronomy is not about telescopes.” Although — like most theorists — I know how to program, the programming I do is nothing like what (I hear) is in industry. In particular, all of my code is relatively small and with concentration, or maybe a single sheet of paper, I can usually keep the whole thing in my head. In fact, the only time I’ve worked in a large code base was developing extensions for MediaWiki during my first summer of college to be used by some groups at the Canadian Light Source. Combined with the preceeding semester of drawing UML diagrams and writing up req&spec documents, I was convinced that I would never be a software engineer. However, I did learn a valuable lessons: real world projects are big and unwieldy, logistics have to be taken seriously, comments and documentation are your friends, and for a sufficiently large software project there is no single person that knows the whole code.

FirefoxBugsWith that much unknown, it is not surprising that bugs abound. Even back in 2002 software bugs cost the US $59.5 billion annually or 0.6% of the GDP, and I imagine the cost has only gone up. If you count ultrafast extreme events or flash crashes of automated hight-frequency traders as bugs, then some argue that you have part of our recent financial crises to blame on software errors (Johnson et al., 2013). To get a feel for the numerosity, a big project like Mozilla Firefox can easily get 2000 new bugs in a year (see figure at left), and Yet most of these bugs are not particularly difficult, and don’t require major overhauls to fix. Even the most serious failures can be fixed by a 12 year-old, why not let evolution have a go?
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Semi-smooth fitness landscapes and the simplex algorithm

Leonid_KantorovichAs you might have guessed from my strange and complicated name, I’m Russian. One of the weird features of this is that even though I have never had to experience war, I still feel a strong cultural war-weariness. This stems from an ancestoral memory of the Second World War, a conflict that had an extremely disruptive affect on Russian society. None of my great-grandfathers survived the war; one of them was a train engineer that died trying to drive a train of provisions over the Road of Life to resuply Leningrad during its 29 month seige. Since the Germans blocked all the land routes, part of road ran over the ice on Lake Ladoga — trucks had to be optimally spaced to not crack the ice that separated them from a watery grave while maximizing the amount of supplies transported into the city. Leonid Kantorovich — the Russian mathematician and economist that developed linear programming as the war was starting in western Europe — ensured safety by calculating the optimal distance between cars depending on the ice thickness and air temperature. In the first winter of the road, Kantorovich would personally walk between trucks on the ice to ensure his guidelines were followed and to reassure the men of the reliability of mathematical programming. Like his British counterpart, Kantorovich was aplying the algorithmic lens to help the Allied war effort and the safety of his people. Although I can never reciprocate the heroism of these great men, stories like this convince me that the algorithmic lens can provide a powerful perspective in economics, engineering, or science. This is one of the many inspirations behind my most recent project (Kaznatcheev, 2013) applying the tools of theoretical computer science and mathematical optimization — such as linear programming — to better understand the rate of evolutionary dynamics.
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