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.

Read more of this post

Advertisements

Hobbes on knowledge & computer simulations of evolution

Earlier this week, I was at the Second Joint Congress on Evolutionary Biology (Evol2018). It was overwhelming, but very educational.

Many of the talks were about very specific evolutionary mechanisms in very specific model organisms. This diversity of questions and approaches to answers reminded me of the importance of bouquets of heuristic models in biology. But what made this particularly overwhelming for me as a non-biologist was the lack of unifying formal framework to make sense of what was happening. Without the encyclopedic knowledge of a good naturalist, I had a very difficult time linking topics to each other. I was experiencing the pluralistic nature of biology. This was stressed by Laura Nuño De La Rosa‘s slide that contrasts the pluralism of biology with the theory reduction of physics:

That’s right, to highlight the pluralism, there were great talks from philosophers of biology along side all the experimental and theoretical biology at Evol2018.

As I’ve discussed before, I think that theoretical computer science can provide the unifying formal framework that biology needs. In particular, the cstheory approach to reductions is the more robust (compared to physics) notion of ‘theory reduction’ that a pluralistic discipline like evolutionary biology could benefit from. However, I still don’t have any idea of how such a formal framework would look in practice. Hence, throughout Evol2018 I needed refuge from the overwhelming overstimulation of organisms and mechanisms that were foreign to me.

One of the places I sought refuge was in talks on computational studies. There, I heard speakers emphasize several times that they weren’t “just simulating evolution” but that their programs were evolution (or evolving) in a computer. Not only were they looking at evolution in a computer, but this model organism gave them an advantage over other systems because of its transparency: they could track every lineage, every offspring, every mutation, and every random event. Plus, computation is cheaper and easier than culturing E.coli, brewing yeast, or raising fruit flies. And just like those model organisms, computational models could test evolutionary hypotheses and generate new ones.

This defensive emphasis surprised me. It suggested that these researchers have often been questioned on the usefulness of their simulations for the study of evolution.

In this post, I want to reflect on some reasons for such questioning.

Read more of this post

Looking for species in cancer but finding strategies and players

Sometime before 6 August 2014, David Basanta and Tamir Epstein were discussing the increasing focus of mathematical oncology on tumour heterogeneity. An obstacle for this focus is a good definitions of heterogeneity. One path around this obstacle is to take definitions from other fields like ecology — maybe species diversity. But this path is not straightforward: we usually — with some notable and interesting examples — view cancer cells as primarily asexual and the species concept is for sexual organisms. Hence, the specific question that concerned David and Tamir: is there a concept of species that applies to cancer?

I want to consider a couple of candidate answers to this question. None of these answers will be a satisfactory definition for species in cancer. But I think the exercise is useful for understanding evolutionary game theory. With the first attempt to define species, we’ll end up using the game assay to operationalize strategies. With the second attempt, we’ll use the struggle for existence to define players. Both will be sketches that I will need to completely more carefully if there is interest.

Read more of this post

Darwin as an early algorithmic biologist

In his autobiography, Darwin remarked on mathematics as an extra sense that helped mathematicians see truths that were inaccessible to him. He wrote:

Darwin Turing HeadbandDuring the three years which I spent at Cambridge… I attempted mathematics… but got on very slowly. The work was repugnant to me, chiefly from my not being able to see any meaning in the early steps in algebra. This impatience was very foolish, and in after years I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for [people] thus endowed seem to have an extra sense. But I do not believe that I should ever have succeeded beyond a very low grade. … in my last year I worked with some earnestness for my final degree of B.A., and brushed up … a little Algebra and Euclid, which later gave me much pleasure, as it did at school.

Today, this remark has become a banner to rally mathematicians interested in biology. We use it to convince ourselves that by knowing mathematics, we have something to contribute to biology. In fact, the early mathematical biologist were able to personify the practical power of this extra sense in Gregor Mendel. From R.A. Fisher onward — including today — mathematicians have presented Mendel as one of their own. It is standard to attributed Mendel’s salvation of natural selection to his combinatorial insight into the laws of inheritance — to his alternative to Darwin’s non-mathematical blending inheritance.

But I don’t think we need wait for the rediscovery of Mendel to see fundamental mathematical insights shaping evolution. I think that Darwin did have mathematical vision, but just lacked the algorithmic lenses to focus it. In this post I want to give examples of how some of Darwin’s classic ideas can be read as anticipating important aspects of algorithmic biology. In particular, seeing the importance of asymptotic analysis and the role of algorithms in nature.
Read more of this post

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).
Read more of this post

A month in papers: mostly philosophy of biology

I’ve seen a number of people that have aimed for reading one paper a day for every day of the year. Unfortunately, I am not great at new years resolutions, and would never be able to keep pace for all 365 days. Instead, in April I tried a one paper a day challenge for the month. I still came up short, only finishing 24 of 30 papers. But I guess that is enough for one paper per weekday.

As I went along, I posted tweet-length summaries in a long thread. In this post, I want to expand on and share what I read in April. And in the future, I think I’ll transform the month-goals into week goals of five papers per week. Just to avoid colossal twitter threads. I tried that last week, for example. But I don’t think I’ll end up making those into posts. Although, as happened in April, they might inspire thematic posts.

Read more of this post

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.

Read more of this post

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.
Read more of this post

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.
Read more of this post

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.

Read more of this post