Metaphors for natural selection

Explainer for non-specialists (19-02-2025)

When I began my PhD I was very focused on computing things which hadn’t been computed yet. This resulted in complicated results on which I was unable to communicate. Amusingly, as the PhD progressed the problems we tackled became simpler, and every time I explained them they became a bit simpler. The goal here is to give an accessible metaphor for the system I am studying, to which I can possibly redirect any future laypeople curious about my work. In particular, I will not to write a single equation.

I will start by the end, giving my metaphor without context. I will then (briefly) retrace the rich history of metaphors for natural selection, and explain how my metaphor inserts itself within.

The balanced abacus

                                                   

Let us imagine an abacus, which has a single bead per row (left figure). Imagine you want it to be perfectly balanced. The simplest way to do this is just to take half the beads and put them on the right, and put the other half of the beads on the left (center figure). But now, imagine you’re not allowed to pick beads individually. Imagine the only way you can move the beads is by reclining the entire abacus thus moving all beads at once to the left or to the right (right figure). Finally, imagine that you’re trying to do this right next to a guy working the street with a jackhammer. Not so easy then is it ?

The creator

It is very common in evolutionary biology to speak of Natural Selection as a person. Darwin already did it, because he developped his ideas by making a parallel with artificial selection : if a breeder can pick any trait (such as yield, strength, mass…) and increase its value in their population by selecting the organisms with the desired trait, then in a state of nature we can imagine an invisible goddess picking organisms depending on wether their traits are suited for survival and reproduction.

Natural selection as a breeder picking out the best plants (painting from Maurice de Vlaminck).

This metaphor enables us to use phrases such as « we have eyes to see ». The « to » here refers to the fantasized intention of natural selection. The most frequent and careless use of this metaphor sees natural selection as an engineer, building organisms from scratch and optimizing them carefully. Of course, under such a metaphor natural selection just replaces God (the God from intelligent design), one of the few differences being more cynicism, in particular when discussing selfishness or conflicts. François Jacob famously elaborated on this metaphor, claiming that natural selection is better thought of as a tinkerer. This metaphor brings a new flavour : the idea of constraints. Natural selection cannot work from scratch, and cannot start over : she only uses what is available to her at present. She cannot optimize the living perfectly, but that doesn’t matter as long as organisms are good enough. She cannot foresee future changes in the environment, she also cannot plan ahead by reserving some material for future purposes (this last point is sometimes discussed under the keyword evolvability).

Natural selection as a tinkerer creating a new species. Art by Elizabeth Peiró.

This view of natural selection was focused on traits, organisms, populations, species. Just like a breeder would focus their view on a trait (such as yield), an organism (their favorite cow), a population (their cattle) or a variety (every population of cows across the world). At the end of the nineteenth century it was embodied by the works of the biometricians, starting with Galton and developped by his students Weldon and Pearson. Crucially, the mechanisms of heredity were not known to them : they knew (from breeders) that the offspring of tall people are usually taller than those of shorter people, but didn’t know why. Around the same time, another field of research emerged : genetics, following the rediscovery of Mendel’s laws. This field was led by other students of Galton (most notably Bateson), and I won’t go into the details here but there is a fascinating story of the sometimes bitter clash between these two schools, biometricians and mendelians (the historical references on the subject are The Origins of Population genetics by William Provine and Francis Galton: pioneer of heredity and biometry by Michael Bulmer ). For our purpose, what interests us is the concept of the gene (before the discovery of the structure of DNA). A gene (in the evolutionary sense) is a hidden biological cause for heritable differences. This means that in a population, part of the diversity in traits (tall people, small people…) is caused by an underlying diversity of genes (genes influencing height…), or to put it another way if all had the same genes there would be less diversity in trait values.

Definitions from genetics

It is crucial for the rest of this article that I give a bit more detail, and in particular that I introduce the barbarian vocabulary associated. Keep in mind that the words here defined are sometimes used in other fields with slightly different definitions (typically, molecular biology). In a given population, every organism has the same number of genes, each of which has a given position in the genome. A position in the genome is a locus. In diploids (such as mammals), each locus has two genes (one from the biological mother, one from the biological father). In our mathematical framework, we can consider that a gene at a given locus can only have two different flavors, which we will denote (+) and (-). These flavors are called alleles. We won't need any more complexity.

Here we have two organisms, with five loci. The organism on the left has (+/+) alleles at locus 1, (+/-) alleles at locus 2, and so on.

The gene’s eye-view

How does genetic affect the way we think of natural selection ? It led to the birth of population genetics, under the combined efforts of Fisher, Wright and Haldane.

To make sense of the change of perspective this field brought about, let's make a parallel. Boltzmann (one of Fisher's heroes) was trying to describe the behavior of enclosed air, seen as a bunch of particles moving really fast around, crashing into one another and into the walls of the box. His crucial idea was to change his point of view : instead of looking at the list of particles (particle 1 is at position (x,y,z) and moving in the direction u at speed v, particle 2 is at position...), he looks at the distribution of positions and velocities of particles (there are 6 particles at position (x,y,z) moving in the direction u at speed v, there are 3 particles at position…). Population geneticists wants to do the same thing for a biological population. Instead of saying « Organism n°1 has (+/+) alleles at locus 1, (-/+) alleles at locus 2…, organism n°2 has allele… », population geneticists says « the frequency of the (+) allele at locus 1 in the population is 30 %, the frequency of the (-) allele at locus 1 is 70 %, the frequency of the (+) allele at locus 2 is 90 %… ».

Under this new point of view, what is the effect of natural selection ? At a given time, if I only look at a certain locus, there exist a certain number of alleles in the population. Imagine one of these alleles is bad (for instance, the - allele causes a genetic disease). Then natural selection will decrease the frequency of that allele. Conversely, imagine another allele is good (for instance the + allele makes those who have it resistant to a certain parasite). Then natural selection will increase the frequency of that allele. I deliberately used the words good and bad, hoping that the reader sprung up reading them and yelled « what if it’s neither good or bad ? » This is precisely what we will be getting to later, but for now we will accept this vision.

Accepting this idea that there are « good » and « bad » alleles, we obtain what is called in the academic world the gene’s eye-view, but which was popularized by Richard Dawkins under the name selfish gene. Under this view, natural selection is only concerned with genes (and in particular, natural selection can be metaphorically seen as genes « selfishly » increasing their own survival and reproduction).

This view is then completed with the idea of mutation. Imagine I have a population of genetically identical organisms. Then, suppose a mutation creates a new allele. Then if that allele is « good », natural selection will try (but sometimes fail) to increase its frequency until a many generations later everyone has this allele. If instead the mutation is deleterious, natural selection will try (but occasionally fail) to drive it to extinction.

This allows me to introduce another metaphor I really like. It turns out that if I look at a population right now, most mutations are neutral (meaning they have no detectable effect). Of the remaining mutations, the vast majority are slightly deleterious (this is studied under the keyword distribution of fitness effects). To put it bluntly, getting exposed to mutagens such as radioactive waste is more likely to cause harm than to give you superpowers. Scientists have made fascinating experiments to quantify this where they force a population to accumulate mutations: these are called mutation accumulation experiments, and the populations tend to get very sick very quickly (see for instance, though it's a bit dated, this review for Drosophila).

People bailing water out of a boat

So if we look at the everyday action of natural population, her routine so to speak, it is not focused on improving species ; rather, it is to prevent population collapse. When thinking of this purifying selection (this is the historical term), one is led to imagining a mariner bailing out water in a sinking ship: natural selection would be hard at work to prevent the boat from sinking under the influx of «bad» mutations. One is easily led to fantasize about how to « save » the population from this threat. The reader probably felt a shiver reading this, because this is one of the typical panics associated to eugenics (but there are others : there’s the fear that natural selection may act against our interests as humans (Idiocracy), or s imply the desire for enhanced humanity).

Polyphemos and recessive alleles

Let’s make the picture a little bit more complex by introducing a special kind of mutations called recessive lethals. As mentioned above, each of us has two genes at a given locus, one inherited from the father and one from the mother (this is called diploidy). Now imagine a locus with two alleles (as before, denoted (+) and (-)) such that if an organism has the combination (+/+), (+/-) or (-/+) of alleles it’s doing fine, but if it has the (-/-) combination it is very sick and quickly dies. This is known as a recessive lethal. It is very common to encounter recessive lethals. For instance, this article estimates that around one in two humans carries a recessive lethal allele.

Imagine a new mutation creates the (-) allele in a population where there was only (+). Then the first person carrying (-) is healthy, because they necessarily have the combination (+/-) or (-/+). So will their children and, most likely, their grandchildren. So we see here something quite interesting : natural selection cannot find the « bad » mutation (-), as long as it’s hidden by the « good » mutation (+).

In metaphorical terms, this reminds me of the famous scene from the Odyssey, in which a cyclops, Polyphemos, has been blinded by Odysseus. Polyphemos tries to find the « bad » men by feeling his way around, but the men hide under the « good » sheep, and so manage to survive. This metaphor is admitedly a bit far-fetched, so let us rework it a bit. Imagine a cave with sheep and men. They need to get out, but the cyclops blocks the entrance and wants to kill the men. The space between the legs of the cyclops is very narrow, so the sheep and men only go through by pairs. If two men pair up, the cyclops finds and eats them. If two sheep pair up, the cyclops lets them through. If a man and a sheep pair up, then the man clings to the sheep, hiding under its fleece, and the cyclops lets both out.

Ulysses fleeing the cave of Polyphemus, by Christoffer Wilhelm

In our system, we have the «good» allele (+) and the «bad» allele (-). Natural selection tries to get rid of the (-) allele by killing all the organisms with the combination (-/-). But because she cannot kill the organisms with the combination (-/+) or (+/-), this is not enough and the (-) allele survives generation after generation.

I wanted to mention this example not just because recessive deleterious mutations are extremely common. Like in the previous example, here we see natural selection overwhelmed and unable to control the « bad » genes. But maybe Polyphemos actually doesn’t care about the « bad genes ». What I mean is : we observe that when two men pair up, they are killed, whereas when a man and a sheep pair up, they survive. We describe this by saying that Polyphemos wants to kill all men, but cannot find the ones hidden under the fleece. This corresponds to saying that natural selection wants to get rid of the « bad gene » (-), but cannot find it when it is hidden. Yet, instead of saying that Polyphemos cannot identify the man-sheep pairs, we could also imagine that he simply doesn’t care about them. We could imagine that the cyclops specifically targets man-man pairs for bigotry reasons, and that he doesn’t mind men pairing up with sheep. The result would be the same (the man-man pairs die, the rest live).

Only man-man pairs die. The sheep-man pair is spared, either because the cyclops cannot find the man hidden under the fleece of the sheep, or because he doesn't care. Both are equivalent.

This actually corresponds to a discussion on the so-called « units of selection » : people like Richard Dawkins, who love the gene’s eye-view described in the previous section, will claim that the cyclops hates men, and tries to get rid of them without managing to do so. Similarly, natural selection tries to get gid of «bad» genes, but cannot find them when they are hidden. On the other hand, people who insist on organisms and traits will tend to adopt the second viewpoint, which in a way is more materialist : the cyclops only kills man-man pairs, therefore he only hates man-man pairs, and we have no reason to assume that he also wants to kill man-sheep pairs. Similarly, natural selection doesn't care about (+/-) or (-/+) combinations, and only targets (-/-) combinations.

My system : stabilizing selection

When we took the gene’s eye-view above, you probably felt slightly uneasy. Our initial discussion of natural selection was about continuous traits : height, velocity, productivity, etc. In fact, when studying the action of natural selection on a population, the typical framework used in ecology is called life history, and it is always focused on continuous traits (one example I once studied was nesting date in birds). The historical examples of natural selection such as Darwin’s finches’ beaks are continuous. And even the examples we give to children to explain natural selection often involve continuous traits : I recall the tale of the giraffe born with a new gene that makes its neck slightly larger.

Let us consider for instance a theoretical giraffe population. We could imagine that it’s better to be taller, but then as time goes by the giraffes would just keep getting taller and taller. It has to stop eventually, and reach a stage where it’s neither better to be taller nor shorter. Intuitively, we then expect natural (and sexual) selection to punish extreme heights : it’s not good to be too tall or too short (for instance, if you’re too tall your heart fails, if you’re too short you can’t reach food).

In our theoretical situation, giraffes with necks too short cannot reach tree leaves and die, whereas those with necks too long die of heart failure: only the medium-necked thrive.

Now, let us imagine a new mutation which makes those who have it 1cm taller. First question : are there really such mutations ? Does it really make sense to consider a gene such that those who have it are on average slightly taller than those who don’t ? The answer is « yes », this is known as the additive model and it works incredibly well. It’s been used for over a century, and despite much effort to find alternatives to this model (random energy models, deep learning…) it remains the most accurate tool to model the evolution of a continuous trait such as height. Now, what happens to this mutation ? It is not intuitive whether this mutation is « good » or « bad ».

This is where we go back to the balanced abacus from the first section. Each line represents a certain locus, that is, a certain position in the genome. On this locus, there are two alleles : the (+) allele makes you taller, the (-) allele shorter. The bead of the abacus represents which allele is more present : if the bead is all the way to the left, it means everyone has the short allele at this locus. If the bead is all the way to the right, it means everyone has the tall allele at this locus.

                                                   

In this system, the only goal of natural selection is to keep the abacus balanced. For instance, the abacus on the left is unbalanced: the beads are too far on the left. A simple way to balance this abacus is to pick the beads one by one, putting half all the way to the left and half all the way to the right (center Figure). But just like with Polyphemos, natural selection cannot pick the beads individually. All it can do is recline the abacus, so that all the tall alleles increase or decrease in frequency (right figure).

It’s difficult to stabilize the abacus. But imagine doing it next to a jackhammer. Why is there a jackhammer you ask ? It represents all the other forces acting on the population, in particular the sheer uncontrollable randomness of who gets to live and die in the population. A meteor just killed an average-sized giraffe ! A super tall giraffe just won the lottery, and is now the most popular giraffe in the population even though its size is theoretically detrimental.

This metaphor is not truer than the previous ones in any way. But it is true that stabilizing selection seems to be very common. In fact, this preprint (not yet peer-reviewed) seems to find that many genes which we would assume to be «bad genes» (genes associated with arthrosis, breast cancer, schizophrenia) behave as if they were under stabilizing selection. That is to say, the evolution of «schizophrenia genes» (I won't discuss here what is meant by this) looks more like the abacus metaphor than the cyclops metaphor. Or to put it another way: they are not «bad genes». If you have too many «schizophrenia genes», you will have a problem, but also if you don't get enough. There is a balance to find.

Conclusion

None of these metaphors are true. Similarly, none of the equations we could write to describe the evolution of the population are true. In fact, for each of these metaphors we can write a corresponding equation. Each metaphor corresponds to a point of view and a certain number of assumptions which can be used to create a model. The reason I find the steady abacus metaphor so interesting is that it takes the gene's eye-view, which is traditionally associated with the idea of selfishness, and yet there is no «good» or «bad» gene. The people who love talking in terms of gene's eye-view often exaggerate the power of natural selection: at their worse, they make up «just so» stories to justify any observable phenomenon as the result of hidden genes manipulating the world. But look at a single bead of this enormous abacus. Look at it jiggling under the vibrations of the jackhammer. Look at it go up and down, caught in the global tide. Look at how unimportant it is, one atom among tens of thousands of other beads. And maybe just smile at it, one atom to another. You and I, we are the atoms of the great human population which has kept creeping forward for centuries, advancing through time with the birth of newborns and the death of elders. Genes are atoms of the genome. Most of them are harmless, most of them are good enough. Sure, some of them leave a footprint on the whole population, just like some rare humans left theirs on our humanity. But the average gene and the average human, we don't have to ask too much of them. We can just let them be.