Contra Paul Christiano on Sex

I have come to think that many people don’t understand evolution. Not in the “believe that a sentient deity created the universe after a template” sense. A lot of people seem to “get” the idea of evolution in broad strokes but then fail at explaining its various oddities or making inferences based on it.

I count myself and basically everyone I know among these people because evolution is actually surprisingly hard. The reasons why its hard to get are exactly why understanding it better helps in a multitude of other domains.

Evolution is a simple principle, but when faced with the oddities of reality, it gets exponentially complex. If you were to think of evolution with causality backwards, it’s like a programmer trying to write a highly optimized piece of software that, in theory, could fit into 100 lines of lisp. But, when faced with the realities of hardware and customers, it turns into a sprawling codebase with thousands of files, hundreds of dependencies and a mixture between multiple languages.

It starts “simple”, literally, in that it can start with just RNA, a model under which “survival of the fittest” works in its most simplistic form, sometimes in a very literal lock-and-key sense of “fit”. But then it quickly (d)evolves into things like apes and cetaceans, which make absolutely no sense when viewed in this framework.

This mirrors the real-world process of engineering, and it provides a very good foil for any sort of “positive feedback” theories ala intelligence explosion.

I am in no position to explain evolution, but maybe I can enlighten some people a bit by showcasing how people get it wrong. In this case, I want to harp on something Paul Christiano (coincidentally an advocate of intelligence explosion type theories) wrote about why sex is useful. Paul Christiano is really smart. So if he can make these kinds of errors, I will assume they are fairly common, and thus this correction might be rather useful, rather than just attacking a strawman.

He writes about the role of sex, to me, his explanation sounds similar to how most biologists in the 20th century would have (wrongly) thought about it:

From the perspective of an organism trying to propagate its genes, sex is like a trade: I’ll put half of your DNA in my offspring if you put half of my DNA in yours. I still pass one copy of my genes onto the next generation per unit of investment in children, so it’s a fair deal. And it doesn’t impact the average fitness of my kids very much, since on average my partner’s genes will be about as good as mine. (ETA: but see the discussion below, in which case the costs might be much bigger.)

But the trade has transaction costs, so I’m only going to do it if I get some benefit. In this post, I’ll tell a particularly simple story about the benefit of sex. I think this is basically equivalent to the standard story, but I find it much clearer. It also makes it more obvious that we don’t require group selection, and that the benefit is very large.

Why doesn’t sex change the average fitness of my kids? The possibility of a “lucky” kid who gets the better genes from both of us is offset by the possibility of an unlucky kid who gets the worse genes from both of us. If the effects of genes are linear, the average fitness will be exactly the same as the parents. In practice I expect it to be slightly lower because of convexity and linkage disequilibrium.

But sex increases the average fitness of my grandchildren, because my fittest children will be responsible for a disproportionate fraction of my grandkids. More precisely, if my if an organism with fitness dX has (1+dX) kids per generation, then the total fitness of my grandkids is E[(1 + dX)^2] = 1 + 2 E[dX] + E[dX^2]. So increasing variance by 1 unit is as good as increasing average fitness by 0.5 units.

Reproductive decisions are naturally a tradeoff between average fitness and variance. Sex slightly lowers the average but increases the variance. If you try to get the same amount of variance with random mutations, you’ll have to totally tank your kid’s expected fitness, because your current genome is well-optimized, and you’ll also pass on fewer genes to the next generation (since some of yours got destroyed). In fact, it’s hard to think of any way to get similar benefits without exchanging genes.

Variance becomes linearly more important over time. For the fitness of my grandkids, 1 unit of variance is worth 0.5 units of fitness; for great-grandkids, they are equally valuable; for great-great-great-grandkids variance is twice as valuable. I don’t think we have to look too many generations ahead before the variance bonus from sex outweighs the costs. For example, if genetic fitness differs by 5% between my offspring, and sex reduces fitness by 1%, then sex breaks even within 6 generations.

This view is “correct” in outlining variance as one of the benefits of sexed reproduction. But utterly fails in thinking that variance is THE benefit that makes sexed reproduction worth it.

It’s like saying “locomotion over flat ground” is the benefit of crab legs. But “locomotion over flat ground” is something boring that can come about 1000 different ways, and crab legs are a silly complex and expensive way to do it. That’s not to say crab legs haven’t evolved, in part, for that. But focusing on that misses the point; The reason crab legs are interesting and special and worth evolving is showcased when looking at how crabs move on steep terrain.

There are much easier ways to get variance in your genes than sex, with much lower costs. Sex is expensive, in some species, such as peacocks and apes, the vast majority of resources over an organism’s lifespan are spent on finding mates. Even in primitive organisms, sex introduces a whole lot of issues. (more on this later)

You can get variance by simple mutations of your DNA, or in more complex organisms, by a mutation in the DNA of germinal cells (e.g. ovums). This is something that does happen, with huge variation in frequency among species. You can also get variance via gene transfer, which is the main mechanism for bacteria and does happen in some simple eukaryotes. But the more “complex” an organism gets, more and more of the variance is sex-related (a few odd species of reptiles aside).

Mutation in germinal cells is awesome in many ways, for one you can control which genes or bases of a gene are more likely to get mutated. For example, assuming you have a really awesome set of genes around this or that enzyme, you can protect it from mutations, and assuming you have a gene that could benefit a lot from variation, you can make mutation more likely.

This is hard in simple organisms, but easy in complex ones. As an example, the adaptive immune system does just this. It engages in “selection events” when presented with enough of an antigen, where a specific set of genes become much more likely to mutate. It’s not impossible to assume such a mechanism could happen in germline cells. Think for example of mitochondrial mutations being selected based on the amount of available glucose. In practice, these environment-based changes seem to mainly happen in-utero and don’t affect DNA directly, but in theory, if we wanted more variance, we might imagine it as a mechanism that could be evolved.

Based on sheer numbers, environments, long-lasting configurations and length of existence, bacteria are much more “fit” than eukaryotes. And this is kinda what they do, they react to the environment and “drop” bits of DNA or uptake DNA dropped by neighbouring bacteria.

So why pick sex instead of one of these low-cost mechanisms?

The answer is… I don’t know, nobody really does, that’s why evolution is complex.

One theory is that sex is a hidden trait preserving mechanism.

The chromosomal setup that allows for sex means we can have hidden traits that only show up in a small % of offspring (e.g. simple story is you need 2x SNPs which are present only on one of the chromosomes for each parent => 25% occurrence). This allows for e.g. sickle cell anaemia to be a thing that can be selected for when malaria incidence is high in the population and selected against when incidence is low. So you have “fitter” hunters in no-malaria times and fitter malaria-resisters in loads-of-malaria times.

You don’t get rid of either genotype entirely, because it can be carried around and only manifested in a small % of kids (which are going to be selected out early on) until it’s needed, and then the small % with the adaptive mutation are heavily selected for.

This “hidden trait” explanation is what the chromosomal setup we have provides over bacteria, which have a “looser” structure for their DNA in order to facilitate more mutation and gene exchanges. It’s not “better” per se, but it might facilitate more “complex” organisms evolving.

The question that remains is something like:

• Why not carry around 4x different ones in your germinal cells all the time but only “activate” two while allowing all 4 to mutate?

The answers might be something like:

might be harder to evolve, since you want to keep the embryonal stage as simple as possible, that’s when most mistakes in growth happen

that requires carrying around extra DNA

asymmetric selection has benefits

actually < these weird species of fungi>

group selection

But again, the real answer is that we can’t really know.

Remember, this hidden trait theory is just that, a theory. There are other theories about why sex works, and none of them yields a definitive answer. You’d likely have to simulate evolution “from scratch” in a bunch of Earth-like environments to get an answer with any degree of certainty, given how complex sexually reproducing organisms are.

Maybe it was sheer chance that introduced sex, and it’s actually a really bad selection mechanism, but it stuck because sexed organisms and intermediaries happened to also carry around a bunch of useful mutations, which were really hard to evolve (i.e. low probability of), and the sex-related genes were too hard to get rid of. This is similar to the way many mammals carry around a bunch of deactivated or even outright harmful viral DNA… it’s not that it’s good, it’s just that “getting rid” of it is really hard, and those mammals have other advantages that allow them to carry this genetic burden.

But the takeaway here should be that sex doesn’t exist for the sake of variance, it’s one of the benefits of sex, but it’s a benefit you could also get in 1001 other ways that are seemingly cheaper, and most lifeforms do.

I wrote something like this as a reply to the original article, and Paul responded, though I don’t think his response addresses my main point. The reply:

Mutations of germline cells come with huge fitness penalties. Taking 0.01% of your genes introduces an extremely small amount of variance. And unilaterally replacing 50% of my genes with yours is equivalent to a 50% drop in fitness (!). The bacterial method itself also doesn’t seem to work in humans (because you need to have the genes during development, and less importantly you need to spread them throughout your body). So it seems to me like sex adds very significant benefits over these alternatives.

Is your view here coming from some quantitative estimate or further reasoning you didn’t include in the comment, or is it reflecting the consensus view in some field? In either case, it would be great to see a pointer. If this is just your guess based on the reasoning in the comment, that’s fine and I’m happy to leave the argument here (or with your rebuttal).

To address the last point, I honestly have no idea if my view here reflects a consensus among most (or among most good) biologists. I’d be hard to tell because my view boils down to:

• The problem is too complicated to get a definitive answer, and any explanation currently on the market can be rebutted with a <but then why not use this simpler mechanism that already exists?> style argument.

And saying “I don’t know” doesn’t really generate any paper. I’d further claim that consensus is a really bad measure because the vast majority of researchers will default to a “popular” opinion without giving it much thought. But I do believe that nobody has really tried to justify sex in terms of variance since the 70s, people are now focused on other aspects precisely because variance doesn’t explain its advantages over much simpler and less expensive mechanisms.

The more interesting part of this reply is:

Mutations of germline cells come with huge fitness penalties. Taking 0.01% of your genes introduces an extremely small amount of variance. And unilaterally replacing 50% of my genes with yours is equivalent to a 50% drop in fitness (!).

I’m honestly not sure what the argument being made here is. As in, it seems to me that you can control the amount of variance in both mutations and sex. In mutation, you can do so via mutation-promoting proteins and DNA repair proteins, as well as by the way DNA is structured, which can lead to more or fewer mutations from e.g. radiation in various regions. in sex, you can do so via mate selection.

The bacterial method itself also doesn’t seem to work in humans (because you need to have the genes during development, and less importantly you need to spread them throughout your body). So it seems to me like sex adds very significant benefits over these alternatives

I think this overlooks the point that sex exists in much simpler organisms. It even exists in colonial animals. These are simple enough to be comparable with bacterial colonies. Indeed, there are many simple multi-cellular eukaryotes in which horizontal gene transfer works just fine as a mechanism for introducing variance in a better-than-random way (for more details, see, for example, this paper)

How would asexual variance induction look in something as complex as humans? Besides random germline mutations, I don’t know, there aren’t things are complex as humans that rely on anything but sex to induce variance (again, some potential *s here, but mainly edge cases or organisms where “sex” looks different enough that it might be argued it doesn’t quite fit the common definition).

Similarly, the reason sexed reproduction is interesting and special and worth evolving only becomes obvious when thinking of things that you can only accomplish using it (or at least that are much more costly to accomplish otherwise, and that no other lifeforms do in other ways)

Additional questions to ponder might be:

• Why always 2 sexes (outside of weird fungi)
• Why is the sex stable (outside of a few weird animals, and probably fungi… damn fungi, always messing up nice models of multicellular life)

I’m not saying they can be answered, but trying to do so might shed some more light on the potential advantages of sex, or at least on the fact that the current configuration might just be a stroke of randomness and not something particularly good.

I’m paraphrasing my arguments here a little bit, so that might point Paul’s reply in a bad light. I’d have finished the conversation with him, but he seem to have gone silent on it, so I thought I’d publish it as an article, since, as state above, I think it’s a useful example.

I should say that I am by no means 100% convinced that I am correct here, and obviously welcome a reply from Paul or anyone else that believes that variance is the cause-du-jour for sex, or that there is any theory that compellingly explains sex which hasn’t been thoroughly falsified.

Somewhere in the background, I am thinking of a more complex model that explains this phenomenon, but I doubt my explanation will be better than the current theories. I am simply trying to disprove things that seem wrong, I don’t claim to have a right answer.