# Nature abhors an immutable replicator... usually

*Epistemic status:* Popped into my head yesterday and I am trying to clarify my reasoning about it out loud. I expect that I am overestimating the universality of this principle to at least some degree, and there is some chance that it's altogether wrong, but I think it may be a potentially useful framing.

### The claim in a nutshell

Replicating information patterns tend to maintain a significant rate of mutation, even when near-perfect replication is possible in principle, as a result of coopetition between sub-patterns with their own interests, which are not always perfectly aligned with the interests of the whole pattern.

### The argument

1.  To the extent that an information pattern is a replicator, its sub-patterns (which form a Boolean lattice if composed ultimately of discrete minimal units, such as nucleotides) must also be replicators in the sense that they are copied whenever the whole is.
2.  Whenever a replicator mutates - that is, when a copy of it is made with one or more minimal units modified compared to the parent - any sub-patterns not containing the mutated units will be unaffected, while those that do contain the mutation (including the whole original pattern) will essentially be "dead" and unable to replicate further in that lineage.
3.  Thus to the extent that sub-replicators are separately acted upon by selection, they should tend, to first approximation, to evolve towards greater stability - less probability of mutation. They "want" to remain unchanged. (A good example of sub-replicators is genes within a genome. The entire genome is a replicator, but the individual genes are too, with their own independent interests.)
4.  But, sometimes mutations make the resulting child replicator more fit than its parent for the current environment, which after all is the driver of evolution. So in the longer term, sub-patterns benefit from *other sub-patterns besides themselves* being mutable as long as there are peaks in the fitness landscape which can be climbed via that mutation.
5.  So if sub-replicators are comparable in "influence" - if mutating them has roughly equal effects on the fitness of the whole replicator - they should tend to all "agree" to retain a small chance of mutating in return for the "expectation" that other sub-patterns will be the ones to do it instead, so that they can benefit from the increased fitness of the whole pattern.
6.  If, however, one sub-pattern has a significantly greater effect on the fitness of the whole than the others it is competing with do, then it will have no "incentive" to allow itself to mutate, and this equilibrium will break down with others mutating at higher rates than it does. In the limit this can even look like a single gene in a genome, for instance, copying itself many times and thus using up metabolic energy others could be using, because it can afford to.

### Parallels with alignment

As you might expect, I think there are some parallels here with alignment and coordination. Every utility function (considered as a subagent with partial control over the behavior of at least one agent) in a society of interdependent agents benefits from all the agents it does not control being "malleable" - willing and able to modify or replace their own utility functions (change their goals, value systems, or sense of self).

So as long as they have approximately equal power, everyone is slightly malleable, and the society has "slack" enabling it to evolve with changing conditions. (Societies are not typically thought of as replicators, but they can divide in a crude form of mitosis, and they have differential persistence, and thus are acted upon by selection pressures.) But if one utility function has more power (due to, for instance, controlling an AI or a human dictator or cult leader), it can forcibly modify others in order to replicate itself more intensively - thus leading to misalignment, and, ironically, to a lesser ability to adapt.

### Vague implications for further thought

This also has something to do with continuity of identity and the Ship of Theseus. Replicators with more levels of sub-replicators will tend to change more due to the effects of all these dynamics in lower levels, yet in some sense are still "the same entity" as long as the rate of mutation is optimal for most of the sub-replicators. Perhaps a preliminary mathematical definition of continuity of identity could come out of examining this situation somehow? I'm unsure.

Also, as you probably noticed in my argument there, I feel like it's possible to think of potential impact on the fitness of the whole as a kind of currency, with the sub-replicators trading in a market, cooperating and competing, but is this a reasonable way to think about entities without cognition or the ability to make choices? I'm unsure of that also.

This framing does make testable predictions though, I think: namely that as long as there's even a very tiny rate of natural mutation, it will tend over time to rise towards some relatively stable optimum, though one that is contextual and relative to the local fitness landscape. There are some ideas nowadays that lineages gradually evolve to be better at evolving - to adapt more quickly to changing environments - leading to things like sexual reproduction, segmentation, etc - so perhaps that's related?