Assembly Theory is Cool ...

... but it doesn't quite do what its inventors say it does.

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Disclaimer: I am currently funded by the John Templeton Foundation (JTF). If you'd like to know more about my research project, you can find lots of information (and my book draft) here. I'm perfectly open about being funded by them and have no problem with it. I am a lifelong (in fact, second-generation) atheist and the research I'm doing is 100% mine: JTF does not interfere in any way. I've written a blog post on all that here. Read it before you complain. It's short.

If you'd like to argue, attack my arguments not my person or my funding source. Everything that's written here is 100% me, not them. Thank you.

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There's been a bit of a meltdown on Twitter/X (see, for example, the replies to this post). There's a lot of trollery and shouting on display, but precious little argumentation. I know, this happens all the time. But in this case, it concerns my own research field: evolutionary biology.

Many of my colleagues are OUTRAGED! Evolutionary theory is being grossly MISREPRESENTED!! Worse, it's chemists and physicists (yuk!) who dare challenge our field's DOGMA!!!

This aggression will not stand.

Accusations of "nonsense," "mumbo jumbo," "word salad," sinister creationist intent and, perhaps worst of all, introducing wokeness to evolutionary theory are flying from all kinds of directions. Some bystanders are already getting out the pop corn in anticipation of the approaching argumentative armageddon:

But what is all the fuss about?

It's about something called assembly theory. You can download the original research paper that caused the whole kerfuffle here, and a very well written news & views article (with a terrible clickbaity title) on the topic here.

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To get straight to the point: I find assembly theory intriguing and worth considering. It is a neat and simple model for the combinatorial generation of innovation in rule-based abstract "worlds" of recombining objects. It is a model of how evolution (or other higher-level processes) can lead to complexification. In that sense, it is classic complexity theory. Applied to the natural world, it may allow us to measure whether levels of organization above the basic laws of physics have emerged in an observed system, and to quantify the causal influence of these higher levels on the underlying dynamics. As an added bonus, it manages all this without having to assume anything specific about what those higher levels of organization actually are.

Isn't that cool? I'm excited. I think it's cool. And, at first sight, it does seem to fill a gap where existing evolutionary theory isn't very strong (i.e. on the issue of complexification).

But others don't seem to see it that way. And, I must admit, the hype the authors try to generate around their model does not help the situation. It maybe wasn't the best decision to call the paper "Assembly theory explains and quantifies selection and evolution" because this grandiose title raises expectations the paper utterly fails to meet. The problem is: assembly theory isn't specifically about Darwinian evolution by natural selection and, besides, it uses the term "selection" in a way that is much broader than its meaning in evolutionary theory, covering higher-level constraints that are not selective at all. This leads to lots of unnecessary confusion, as is evident from the online comments, but that's not all that is problematic here. Let's have a look at the abstract:

This is a textbook example how not to write an abstract. Probably, its hyperbolic tone helped to get the paper reviewed and accepted in Nature. But it totally fails to describe what the paper is actually about. And it's not exactly accessible to a wide audience. Finally: while making some rather big (shall we say gigantic?) claims, it remains oddly vague and ambiguous, opening doors to all kinds of misunderstandings.

The first thing that seems to trigger people is the claim that evolution requires reconciliation with the "immutable laws of the Universe defined by physics." No wonder that some may be reading creationist intent into the paper! What does that mean exactly? It's not clear. And why spell "Universe" with a capital "U"?! Do the authors want to raise suspicion? I don't get it.

The point seems to be, as the authors explain in the following sentence, that life and its evolution may obviously not break any laws of physics, yet cannot be predicted by these laws alone either. I think that's essentially correct although some of my more reductionist colleagues would probably take issue with it. Read Stuart Kauffman's excellent "Investigations" or our follow-up paper on this exact topic, if you want some detailed arguments on the point.

Next: does selection really explain why some things exist while some do not? Well, we can quibble about that. There is certainly a lot more to adaptive evolution than just selection. Even Darwin knew that. Again, this is oversimplified and vague, just like the following sentence, which formulates the aim of the paper as comprehending "how diverse, open-ended forms can emerge from physics without an inherent design blueprint." Arguably, that's exactly what existing evolutionary theory already does, and while this paper may add an original perspective to the problems of innovation and complexification, it certainly is not the first approach to ever tackle these questions. A bit more sensitivity and charity towards preexisting efforts would definitely have been beneficial here.

Another issue I have with this same sentence is that it suggests the authors mean to explain evolution completely in terms of physics. Yet, this does not fit their approach. Their concept of "assembly" is explicitly meant to capture higher-level influences (by the laws of chemistry and Darwinian evolution, let's say) on lower level phenomena (e.g., the prevalence of specific molecules). That's the whole point! Unfortunately, this is not at all clear from the somewhat befuddling abstract. Assembly theory does not aim to eliminate any existing theories in chemistry and evolution. Quite the contrary: it vindicates them!

All this does little to justify the claim that comes next: that we need a new way to understand and quantify selection. As I already mentioned, I find this claim misleading. I don't think the paper deals with a particularly Darwinian notion of "selection" at all. We'll return to that in a bit.

What follows is a short technical overview of assembly theory that is extremely hard to parse and understand for anyone not already familiar with the matter. It's not the most user-friendly introduction to the topic. But then, it is also not the jargon-laden disaster some critics have claimed it to be. In these days of hyperspecialization, scientists in a given field are a bit too easily put off by concepts and terms they cannot immediately grasp, that do not neatly fit their own preadapted conceptual structures. Sometimes, you know, it simply takes some time and effort to understand a new and unusual idea or argument. That's not necessarily a bad thing, but we generally give ourselves far too little space for it in today's cut-throat academic environment, and that is a real shame. But that's just my opinion.

What comes next after the model overview is by far the worst part of the abstract: the authors make the very, nay, overly bold claim that the paper integrates novelty generation and selection into "the physics of complex objects." Sorry, but it does not do anything like that. Despite its high-flying aspirations of integrating physics and biology, the paper contains surprisingly little actual physics. There is no talk about far-from-equilibrium thermodynamics and how it connects to the organization of the organism, for example, which seems a strange omission in a paper claiming to ground evolution in physics. So: I'm not sold on this at all.

The abstract ends on two sentences that are absolutely impossible to understand if you have not already read and digested the paper. This kind of thing certainly won't help people get into the flow or point of the argument. As I said, classical "how-not-to-write-an-abstract."

Now let's make one thing clear: it is not fair to kill a paper based on its abstract alone. In fact, I was surprised (and, frankly, pissed off) by the fact that most of the criticisms on social media are coming from trolls who have obviously (and sometimes admittedly) not read the paper. That's shameless and appalling. What happened to intellectual integrity, people? You have to do better than that, even when on Twitter. Maybe especially when on Twitter ... Shame on you! You know who you are.

That's why I did read the whole paper carefully. Let's dive a bit deeper into the good, the bad, and the ugly aspects of its arguments. TL;DR: I think assembly theory has lots of merit and potential, but this particular paper frames its argument in a way which is unfortunate and, frankly, more than just a bit misleading. My personal suspicion is that this has two reasons: (1) the authors hyped up their claims to get the paper published in a glam journal, plus (2) they also overestimate the reach and power of their model in ways which may be detrimental to its proper application and interpretation.

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THE GOOD

First and foremost, let me say this: assembly theory is new and interesting! And there are lots of potential applications. Also, despite claims to the contrary, I don't find the model or the paper hard to understand at all.

The fundamental idea behind constructing an assembly-theory model is that you define an "assembly universe," which consists of a (finite) set of basic building blocks (see the colored hexagons below) and some rules that allow you to assemble them into more complex composite objects (arrows). This universe, in principle, can contain all possible combinations of building blocks that do not violate your basic rules. If you want to simulate real-world chemistry, for example, you can build all kinds of composite molecules by recombining atoms with their corresponding chemical bonds.

So far so good: now you introduce a dimension of time to the model, which is implemented by recursivity. In other words, at each step of the assembly process, you can use all objects that are already assembled (not just the basic building blocks you started with) for further assembly. Thus, at each step, you get a bigger choice of objects to build with. In fact, the number of possible rule-based combinations will increase hyper-exponentially (i.e. very very very fast) with each step. You can now see what kinds of composites can emerge over time. An example of such a process is depicted here:

Recursivity makes the dynamics of the model historically contingent. In the end, the kinds of objects that you actually can assemble are not only restricted by the rules of your universe, but also by the starting point and trajectory you actually chose to take. This makes the whole model computationally tractable, because it greatly reduces the combinations of possible composites you can get. You don't have to deal with all possible combinations of building blocks, just the ones that are actually present in whatever "world" (a mix or "ensemble" of different objects) that you are simulating or observing. For instance, you can start with a given set of substrates, and simulate what kind of products you can get from there, given all the thermodynamically possible chemical reactions plus the concentrations of the substrates.

You can consider such a system a kind of a null model: given your basic building blocks and the assembly rules you defined, you can calculate how many steps you need to take before a specific composite object can arise. That minimal path to construct a composite object is called its assembly index. If your rules have specific weights or probabilities of application, you can also predict the expected abundance (copy number) for any composite object in your mix. This may not be easy to do in practice, but the authors at least show that it is possible in principle for any well-defined world with finite sets of building blocks and rules.

Things become truly interesting, once your model produces very complex composites. The higher the complexity of a composite, the longer it will take to appear, and the more unlikely it is to appear by chance, especially after just a minimal number of steps. Based on this, you'd generally expect many different complex composites to be present at very low abundance at later steps. Yet, if you find certain complex composites enriched, especially early on, that's a sign that things are not just random in your system. This figure illustrates the point:

Put simply: finding composites with high complexity at high abundance means the basic rules of your "world" have been skewed in some way. That's what the authors mean by "selection." This concept is, of course, much broader than what an evolutionary biologists means by the term. The bias called "selection" in assembly theory could be caused by processes that are very different from Darwinian evolution (some not selective at all). We'll come back to that shortly. All that "selection" means here is that the basic rules of your world have been constrained in some way to lead to an unexpected outcome.

This means that you can use assembly theory to check whether something unexpected is going on in a very broad range of model "worlds" or "universes" defined by different building blocks and rules. If that "something" is present, then more than just your basic rules must be at work. As a practical example, you could monitor the atmospheres of exoplanets for complex molecules at high abundance, which would mean something more than just the laws of chemistry are at work there. Likewise, you could monitor the complexity and abundance of some technology, let's say Schnitzel hammers in Austria, to infer that this technology must have been selected for in that particular environment. It did not just pop up randomly. So far, so good.

It's important to note that assembly theory does not (and need not) make any assumptions as to what is being "selected," and in what way. On the one hand, this is bad, because this is one of the main factors that is confusing the evolutionary biologists complaining about the model: assembly theory is not specifically about Darwinian evolution. It does not care about populations, individuals, genes, and so on. How then can it be relevant to evolutionary biologists? it does not fit their conceptual framework, that is for sure. And it almost certainly won't help you to measure selective pressures in the wild. On the other hand, its generality is also a strength of assembly theory: it is very broadly applicable to all kinds of "worlds" (if you can figure out how to measure the assembly index, which is far from trivial in most cases).

To be more specific: assembly theory is a tool to detect the emergence of new levels of organization and their causal influence on lower-level phenomena in your world. If the outcome you are observing is biased, the underlying rules must have been constrained in some way to generate that bias. This is called downward causation, and some reductionists find it objectionable, but for reasons that really don't hold up to closer scrutiny (more on that in a future post).

All you need to know at this point about downward causation is that it does not change the underlying rules. Instead, it channels and restricts the underlying processes in unexpected ways. And, if you think about it, that's exactly what evolution does with the laws of physics: selection never alters the rules of physics and chemistry underlying the processes that compose your body, but channels and restricts the direction of biological processes in ways that you fundamentally cannot predict from the underlying physics or chemistry alone. This is why (evolutionary) biology is (and will always remain) an independent science.

It is in this very general and roundabout way that assembly theory is useful for evolutionary biology. It may allow us to establish, once and for all, that biology is more than just chemistry and physics. More specifically, it provides us with a new perspective on what may be driving innovation and complexification in evolution (and other higher-level processes) at a very fundamental level: it's the emergence of ever new combinations of (chemical and higher-level cell-, tissue-level, or organismic) components. It's the constant growth of a co-evolving possibility space. This should make us reconsider how we formally describe what is possible in evolution, and it adds a temporal directionality to the random effects of mutations: for a mutation to produce a complex outcome, more time will be required than for simple ones.

It's not exactly rocket science, I know, and, personally, I think the view presented by assembly theory is still quite limited and does not capture the true extent of evolutionary innovation at all (see below). But it is definitely a step forward compared to accounts that simply take the emergence of complexity for granted or assume a global preexisting space of possibilities for evolution. Such views are still surprisingly widespread among reductionist evolutionary biologists and traditional complexity scientists, and that is a problem, in my opinion.

Maybe some of the people disparaging assembly theory as a matter of principle would profit from engaging in a more good-faith and open-minded manner with a different perspective on their field? It would not hurt you. It does not mean that you have to abandon (or even fundamentally question) what you're doing. And also: not everything that is published on your topic needs to be immediately understandable or applicable within your particular research approach. Being different and hard to understand are not really valid criteria to dismiss someone's work.

A new perspective, even if controversial and not yet thoroughly worked out, can be inspiring and useful. Give it some slack. Where else is conceptual progress supposed to come from if not the fringes of your field? Just by doing more of the same? There is more than enough of that already in evolutionary biology.

Personally, I find it enriching to engage with a different point of view every once in a while, because it allows me to see the advantages and limitations of my own approach much more clearly. Judging from what's going on online or when I get my papers or grants reviewed, this is not a common attitude in our field. And that's a real shame. It clearly limits the ways we think about the incredible richness of evolutionary phenomena. And this, I firmly believe, is hampering conceptual progress in evolutionary biology. The prevalence of bad or shallow theory has made us too narrow-minded. So, please, drop the gatekeeping! At least try to engage with arguments. Can we do that? New perspectives are needed in our field. Let's not kill the discussion before it even started.

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THE BAD

Now, let's turn to what I did not like about the paper. Mainly, I think its authors are wrapping it in a misleading package, both to appear more attractive to the glitzy venue of publication, and because they are genuinely fooling themselves about the scope and meaning of the model. This seriously impacts the message they should be wanting to convey, and not in a good way.

Before I focus in on more specific points, let me emphasize again: assembly theory is not a new theory of Darwinian evolution, nor is it a new interpretation of the concept of "selection" used in Darwinian theory. Granted, it can be applied to detect the signature of Darwinian evolution, although how this would be done in practice at the level of genes, organisms, or populations is left wide open in the paper. In fact, the authors do not even touch on this particular topic at all, focusing on the molecular (chemistry) level instead.

But the main elephant in the room is the following: assembly theory cannot distinguish what kind of process is generating the bias the authors call "selection." It could be many things other than Darwinian natural selection.

For instance, higher-level constraints on basic dynamic rules can arise through some form of self-organization, such as that observed in far-from-equilibrium (dissipative) systems, e.g., hurricanes, eddies, and candle flames, which can form highly complex and improbable structures. It can also arise through the peculiar self-referential organization of living matter, which goes beyond mere self-organization in non-living systems (more on that here, here, and here).

However, deviations from rule-based expected outcomes can also occur for much more mundane reasons. They can be caused, for instance, by stochastic phenomena such as random drift or founder effects in evolution, as long as the population of objects is small enough. Or they can be caused by some hidden or neglected external factor, such as environmental forcing that was omitted in the rules when formulating the model.

Therefore, how we interpret the bias in our outcomes (whether it is really due to Darwinian natural selection or some other process) largely depends on the assumptions we put in the model of our rule-based world in the first place. This kind of circularity is not necessarily vicious, and is common in modeling practice, but it clearly begs the question the paper is claiming to address. To say it again: assembly theory cannot tell us whether some bias is due to natural selection or not, just whether the bias is there, and how much of it is there, given the basic assumptions underlying the rule-based world we're modeling with assembly theory.

Of course, this also means that all the talk about biological function in the paper remains completely vacuous. Just like physics, assembly theory is utterly blind to function. If you cannot tell whether some bias in your outcome is the product of actual natural selection, or whether it is due to self-organization, random drift, or some neglected external forcing factor, you cannot tell whether it is functional in any of the many senses "function" is used in biology. As a matter of fact, assembly theory does not deal with function at all. So why bring it up?

Is this particular blind spot of assembly theory known to the authors? I do hope so. If not, I must conclude that they fundamentally misinterpret the nature and reach of their own model. But let us give them the benefit of the doubt and assume that they realize they're using the term "selection" in a way that is much broader than an evolutionary biologist would ever use it. In fact, it covers many biases that are not generated by selective processes at all. If they realize this, how can they not see that their use of the term "selection" is hugely misleading? How can they be so naive about the confusion they are creating? Or are they? I don't know.

Everything we have discussed so far points towards a crass misrepresentation of what the paper actually achieves. What assembly theory really does (and does in an interesting and potentially broadly applicable manner) is to detect and quantify bias caused by higher-level constraints in some well-defined rule-based worlds. That's it. Even if Darwinian selection may contribute to such bias, assembly theory cannot tell you if it does, how much it does, and if other factors play a role as well. This shows you just how misleading the title of the paper really is: it clearly does not even try to explain evolution or selection in a Darwinian sense. I'm sorry to say, but this is plain bullshit.

Why this bullshit packaging? It seems to do so much more harm than good. Unless we consider the fact that it is probably exactly this package that got the paper into Nature in the first place. Yet another gross editorial and peer-review failure on the part of this abominable tabloid. All the outrage and the negative reactions won't matter, as long as the authors can add this paper to their CV. Selling assembly theory for what it really is was not sexy enough. That's a pity. It reflects badly on the authors, and the whole scientific publication system. And it is probably detrimental to the actual cause that is put on the table here, because the whole exercise at obfuscation and the mud-slinging battle that will no doubt ensue will put a lot of people off who should really be looking into the actual problems that assembly theory is trying to bring to the fore.

Unfortunately, by now, PR spectacles (or disasters) like this one abound in our field and greatly outshine any serious theoretical discussions we could be having instead. We're in pretty bad shape overall. It'd be great if more people would see this and do something about it, instead of contributing their own little turd to the whole feces-hurling exercise.

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THE UGLY

Unfortunately, it does get worse though. And again, I must remind the reader that I do find assembly theory an interesting model for combinatorial innovation and complexification in rule-based computational worlds. It undoubtedly has merit and interesting potential applications. If its inventors would only sell it for what it is.

Strap yourself in, because this is where the hyped claims really take off. We're going on a wild ride, during which the map gets mistaken for the territory. Bear with me, it will get a little weird along the way.

In a recent essay for the popular science site Aeon, the senior authors of the current paper (Sara Walker and Lee Cronin) turn assembly theory beyond evolution to the nature of time itself. Their central claim (and the title of the essay) is that "time is a physical object." Sounds puzzling, to say the least, so let's see if there is any substance behind it.

The authors point out that most physicists consider time to be some kind of illusion. Most fundamental theories in physics today imply a block universe, where all points in space and time are equally real and there is no particular temporal directionality or flow. As the only exception, the second law of thermodynamics introduces an arrow of time, but entropy-maximization is an emergent phenomenon rather than fundamental: it is the property of ensembles of objects (e.g., molecules), not intrinsic to the objects themselves. All of this is difficult to reconcile, the authors claim, with a biological understanding of time, where each evolved object (organism) incorporates its own evolutionary and developmental history.

In other words, objects in physical theories are generally defined as point-like particles whose intrinsic properties remain unchanging, while the objects of evolutionary theory are defined by their formation history, which means their intrinsic properties constantly change over time. Assembly theory is supposed to bridge these two seemingly incompatible notions of time by making molecules objects with a formation history. Sounds simple enough.

There are two crucial points to consider if you want to understand the argument.

First, composite objects in assembly theory can be arranged by their respective assembly index: the larger the index, the longer the minimal path for their formation, and hence the later their moment of appearance. Therefore, the assembly index itself can be interpreted as representing a fundamental physical notion of time for our universe, via its connection to the definition of an assembled object. Basically, an assembled object is its formation history according to that definition. From this, the authors conclude that physical time literally is the same as the definition of an object in assembly theory. See, I told you it would get weird.

Second, the space of possibilities of an assembly-theory model constantly (and rapidly) expands over time due to its recursive combinatoric dynamics (see above). This means the future is always larger than the present, both in terms of the assembly universe growing larger, and in the sense that the averaged assembly index of all composite objects present at any given step in time constantly increases. This adds a natural temporal directionality to the world being modeled which is representing nothing but material change. Again, the authors conclude, time is a material property of the expanding assembly universe.

Are you still with me?

Apart from presenting an utterly bizarre notion of time (I'm still trying to get my head around it) there are a few additional problems with this kind of argument and model.

The first is a simple practical problem: the assembly index of what exactly is supposed to represent the fundamental notion of physical time? As we have seen above, assembly theory can be applied to any well-defined world of basic building blocks and rules. This raises the question of what kind of assembly universe would properly represent our actual universe. Is it the world of fundamental particles, chemical molecules, biological individuals, ecological communities, human cultures? And what rules do you include in the model?

The authors settle on using examples at the molecular level, for purely pragmatic reasons, as far as I can tell. Assembly indices are particularly straightforward to calculate for molecules, while their quantification for different kinds of objects poses significant conceptual and practical challenges. In the end, it all does not really matter though, because there is a much more fundamental issue: how can the time represented by assembly indices be a fundamental physical property of the universe, if it is crucially tied to the way the model is constructed? This is what I mean by mistaking the map for the territory. This notion of time is a property of the model, not of the reality it is supposed to be modeling.

The second problem is that the computationally well-defined worlds of assembly theory do not even remotely resemble our real universe, no matter what kind of fundamental objects and rules we chose. These two kinds of worlds are completely different in nature. An assembly universe is a highly abstracted space, with discrete objects and rules that can be combined in precisely circumscribed ways. This is what statistician Leonard Savage called a "small world." The natural world, the kind of universe we actually live in, however, is not small (see here). Few problems and phenomena we encounter in it are well defined. As far as we can tell, it does not consist of a well-defined and finite set of building blocks that recombine according to a well-defined and finite set of rules. It's all not that simple!

To be frank: assembly theory can only provide a rough cartoon of the real world. It captures some interesting features, that's for sure, but it can only go so far. Wouldn't it be great if its inventors would recognize these limitations? Especially because they affect and invalidate pretty much every one of their core claims directly.

Let me summarize once again. Physical time cannot be equivalent to an abstract parameter in a computational model. I don't need to be a physicist to recognize that. Furthermore, assembly universes cannot incorporate the emergence of new levels of organization, even if that is what the model is supposed to measure. The basic rules of an assembly universe must remain fixed by definition. Therefore, the model fails to reproduce some really fundamental aspects of evolutionary innovation and evolving possibility spaces. It is restricted to capturing novelties that arise through the rule-based rearrangement of objects. This won't be enough to capture the true open-ended nature of biological evolution, I'm afraid.

Have I forgotten anything? I think it covers pretty much all the claims made by the authors in both the Nature paper and the Aeon piece. We can strike all these claims off our list.

Despite this pretty abysmal score, there is much food for thought beyond the smokescreen of impenetrable language and implausible claims. If you have the patience to cut through the bullshit, go forth and explore the conceptual territory that lays beyond! You'll come out on the other end with new thinking tools and new perspectives on our inexhaustibly rich and open universe, I promise.

Wouldn't it be nice if scientific and philosophical authors would see their role as guides on our journey through such unknown conceptual landscapes? Instead, academic publishing has become a shameless swamp of self-promotion. The system is to blame, at least in part, but we cannot shirk our own responsibility as authors. This paper is a prime example of what is happening all over the place.

Kudos to the authors for presenting us with an interesting new model.

Shame on them for covering the whole thing is a steaming pile of narcissistic horse manure.