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Are there empirical examples of self-regulated punctuated evolution (with time)?

This is when a quantity grows over time in a stepwise fashion, with each growth step having less amplitude than the previous one, eventually reaching an asymptote:

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A simple question yet I can't find any examples that can illustrate such a process. I found many experiments that show such a punctuated evolution but they have an exogeneous (human) control.

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The growth of a tree, each year grow a little, in winter rest, reached top of the canopy stops growing.

A measure of the efficiency of metabolic systems during natural evolution (Jumps: new chemical pathways; limit:100%).

Elevation of a mountain chain (steps: landslides/earthquakes; limit: flatlands)

Liquid saturation of a sponge (steps: new pores invaded; limit: full saturation)

(similar to previous) Magnetization of a piece of steel (steps: new magnetic domain aligned; limit: equilibrium/saturation)

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