Followup to: The First World Takeover

As last we looked at the planet, Life's long search in organism-space had only just gotten started.

When I try to structure my understanding of the unfolding process of Life, it seems to me that, to understand the optimization velocity at any given point, I want to break down that velocity using the following abstractions:

The searchability of the neighborhood of the current location, and the availability of good/better alternatives in that rough region. Maybe call this the optimization slope. Are the fruit low-hanging or high-hanging, and how large are the fruit?
The optimization resources, like the amount of computing power available to a fixed program, or the number of individuals in a population pool.
The optimization efficiency, a curve that gives the amount of searchpower generated by a given investiture of resources, which is presumably a function of the optimizer's structure at that point in time.

Example: If an object-level adaptation enables more efficient extraction of resources, and thereby increases the total population that can be supported by fixed available resources, then this increases the optimization resources and perhaps the optimization velocity.

How much does optimization velocity increase - how hard does this object-level innovation hit back to the meta-level?

If a population is small enough that not all mutations are occurring in each generation, then a larger population decreases the time for a given mutation to show up. If the fitness improvements offered by beneficial mutations follow an exponential distribution, then - I'm not actually doing the math here, just sort of eyeballing - I would expect the optimization velocity to go as log population size, up to a maximum where the search neighborhood is explored thoroughly. (You could test this in the lab, though not just by eyeballing the fossil record.)

This doesn't mean all optimization processes would have a momentary velocity that goes as the log of momentary resource investment up to a maximum. Just one mode of evolution would have this character. And even under these assumptions, evolution's cumulative optimization wouldn't go as log of cumulative resources - the log-pop curve is just the instantaneous velocity. If we assume that the variance of the neighborhood remains the same over the course of e...

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