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Having no formal education in evolution, I was struck by this quote of Dyson: "Species once established evolve very little, and the big steps in evolution mostly occur at speciation events when new species appear with new adaptations. The reason for this is that the rate of evolution of a population is roughly proportional to the inverse square root of the population size."

I had never heard of this "inverse square root" law before. However, it occurs to me that this is probably quite a general principle.

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There may be a sense in which it is a general pronciple, but it is one of many general principles, since different evolutionary effects operate at different rates depending on the population size, some varying directly with the population size, and some inversely, and some having no dependence on population size.

The occurence of radical mutations/deviations (e.g., hopeful monsters) varies directly with the population. When a niche can be filled through a quantum leap, it may take less time for a large population to produce individuals who make that leap than a small population.

When another local optimum can be reached through several steps, a smaller population may tend to get there faster, since it is easier for a small population to take a backwards step, e.g., for a mildly deleterious gene to get lucky and eliminate a more favorable one.

I suspect that Dyson looked at some models where some inverse squareroot law was dominant, but I doubt this model is as widely applicable as would be needed to justify his statement. Even when a population is large, reproduction may occur mainly in subpopulations whose numbers can crash, providing opportunities for small-population evolution.

A deep thinker may be able to teach a lot, even when he is wrong. Trivial thoughts are worth little even when right.