Is There Slack in Evolution?

In a recent blog post, Studies on Slack, Scott Alexander discusses how slack (particularly the rationalist conception of it) interacts with competition in various situations, and models it in terms of two-layered competitive systems. Many of his example use evolution as the competitive system, and his very first example claims that in certain circumstances a useful adaption is more likely to occur if there is less evolutionary pressure:

Imagine a distant planet full of eyeless animals. Evolving eyes is hard: they need to evolve Eye Part 1, then Eye Part 2, then Eye Part 3, in that order. Each of these requires a separate series of rare mutations. Here on Earth, scientists believe each of these mutations must have had its own benefits – in the land of the blind, the man with only Eye Part 1 is king. But on this hypothetical alien planet, there is no such luck. You need all three Eye Parts or they’re useless. Worse, each Eye Part is metabolically costly; the animal needs to eat 1% more food per Eye Part it has. An animal with a full eye would be much more fit than anything else around, but an animal with only one or two Eye Parts will be at a small disadvantage. So these animals will only evolve eyes in conditions of relatively weak evolutionary pressure. In a world of intense and perfect competition, where the fittest animal always survives to reproduce and the least fit always dies, the animal with Eye Part 1 will always die – it’s less fit than its fully-eyeless peers. The weaker the competition, and the more randomness dominates over survival-of-the-fittest, the more likely an animal with Eye Part 1 can survive and reproduce long enough to eventually produce a descendant with Eye Part 2, and so on. There are lots of ways to decrease evolutionary pressure. Maybe natural disasters often decimate the population, dozens of generations are spend recolonizing empty land, and during this period there’s more than enough for everyone and nobody has to compete. Maybe there are frequent whalefalls, and any animal nearby has hit the evolutionary jackpot and will have thousands of descendants. Maybe the population is isolated in little islands and mountain valleys, and one gene or another can reach fixation in a population totally by chance. It doesn’t matter exactly how it happens, it matters that evolutionary pressure is low.

Is this situation realistic?

The first part that struck me is that Scott presupposed that each of these mutations occurs separately. This would make sense in ordinary evolution, where each mutation provides a benefit and reaches fixation. If each mutation is harmful, why bother going through normal competition that the organism is going to lose, and why not just have all three Eye Parts arising by chance at once? It may seem absurd that an organism would spontaneously form a fully-fledged eye, but actually all that indicates is that the entire pathway envisioned here is absurd: As creationists are so eager to point out, something as complex as a compound eye cannot just arise by chance. It requires evolution, which requires intermediate stages that are beneficial to the organism, exactly what has been positted not to occur. You can imagine we’re not actually talking about evolving eyes, but rather a much simpler adaption still goes against the flow of the fitness landscape. If you do it becomes easier to imagine that the entire adaption occurs as a single mutation at once.

But actually, Scott is right: An adaption like this would develop in stages rather than all at once. Let’s calculate this with some made-up numbers. I’ll suppose that each one of these Eye Parts has a 10-5 probability of occurring by chance. Multiply that for all three parts and you get a probably of 10-15 of all three mutations occurring at once. A mutation like that is only likely to occur in a species once 1015 organisms of that species have been born.

Let me emphasize the last sentence: The chance a mutation will occur in a population depends on the number of individuals born in that population, or in other words the total number of individual that have ever existed in the population. That is the product of the population size and the number of generations the population existed. In particular, larger populations acquire beneficial mutations faster. This will be important later.

Now, let’s compare this to developing eyes in stages. Suppose Eye Part 1 only reduces fitness by 1%. Then on average, an individual with Eye Part 1 has 1% fewer descendants, so on average 0.99 of its descendant will also have Eye Part 1. Adding up the geometric series, if an individual acquired Eye Part 1 through a spontaneous mutation it is likely to have around 100 descendants with Eye Part 1. The chance that one of them will acquire Eye Part 2 is 10^2 \cdot 10^{-5} = 10^{-3}. If an individual with both Eye Parts 1 and 2 loses another 1% in fitness than it will have 50 descendants with both Eye Parts 1 and 2, assuming perfect genetic linkage. Then there’s a 50 \cdot 10^{-5} = 5 \times 10^{-4} chance that one of these descendants will acquire Eye Part 3. Multiplying these together, including the probability for the initial Eye Part 1 mutation, there is a 10^{-5} \cdot 10^{-3} \cdot (5 \times 10^{-4}) = 5 \times 10^{-12} chance of eyes evolving per individual of eyes evolving. This is still very small, but significantly larger than the 10-15 odds of all mutations happening at once.

In contrast, imagine if each mutation is beneficial and immediately reaches fixation. It takes 105 individuals until one acquires Eye Part 1, and immediately everyone has it. Afterwards it takes 105 individuals each to evolve Eye Parts 2 and 3, a total of 3×105. Since it takes time for traits to reach fixation and even for beneficial traits this doesn’t always occur, it is expected to take a larger number of individuals until eyes evolve, but this is still much less than the numbers required in the above two scenarios where eye parts are maladaptive.

Okay, this is the model for evolving eyes in ordinary circumstances. But what if you add slack? Let’s look at Scott’s first scenario: A disaster wipes out most of the population and leaves behind a resource-rich environment for the survivors, so even individuals with below-average fitness can reproduce above replacement and not have their lineage die out. First of all, I want to question the notion that there is less “evolutionary pressure” here, whatever that means. Less fit individuals can propagate their genes when they wouldn’t have otherwise, but fitter individuals still propagate their genes even more. If by chance a high proportion of the population right after the disaster had some fitness-lowering gene, then by the time the population rebounded the gene would be much less frequent, because the fitter individuals without the gene will repopulate faster than the less fit individuals with the gene. So it’s a matter of perspective: Are we looking at the absolute number of offspring and descendants an individual will have, or are we interested in the proportion of a trait relative to the whole population? If the former then the population boon meaningfully reduces the evolutionary pressure, if the latter than it doesn’t affect it at all.

But we’re not asking a broad qualitative question that could depend on the perspective we take, we’re asking a concrete question: Will this disaster-and-repopulation make evolving eyes more likely? Let’s think. Normally an individual with Eye Part 1 has around 100 descendants like it each which can develop Eye Part 2. During the time of plenty it can have many more than that. Sounds good?

Not so much, once you compare this with what every other individual is doing. If this individual has 100 relatedness-weighted offspring, so does every other individual during time of plenty. If there is sexual reproduction this can be tricky to think about: The first individual with Eye Part 1 has more than 100 descendant, but only some retain Eye Part 1. Other individuals also typically have more than 100 descendants. However, each descendant has many ancestors, so it’s hard to count how many descendants there should be. It’s easier to count genes: Each descendant gene comes from exactly one ancestral gene. If the spontaneously formed Eye Part 1 gene spreads to 100 descendants, then in that time every other gene should also spread to 100 descendants, or a bit more since Eye Part 1 gene reduces fitness. Since we need individuals to store all of these genes — what else are individuals good for? — the population size increases by roughly one hundred.

Now remember what I said earlier about the effect of population size on evolution? If the population increased by a factor of one hundred, that means that at the start — right after the disaster occurred — the population was one hundred times less than the ordinary stable population. That means that the mutation for Eye Part 1 was one hundred times less likely to occur in the first place! This nullifies any advantage that seems to have been gained by the plentiful conditions increasing the chance Eye Part 2 develops. Overall, a disaster that decreases population does not increase the speed the eye evolves.

1 thought on “Is There Slack in Evolution?

  1. When Scott talks about evolutionary pressure, he means the degree to which moderately disadvantageous genetic mutations are competitively extinguished from the genetic pool.

    If a relatively neutral feature that provides no advantage, and costs very few resources can survive for a long period of time, then the opportunity for two such mutations to interact in a way that produces a competitive advantage is greatly increased.

    If even a slight expenditure of resources significantly disadvantages creatures in this environment, then such mutations are far more likely to become extinct without ever being combined in a single creature.

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