Language is a spontaneous order.
Punctuated equilibrium is a feature of spontaneous orders. They are characterized by s-curve growth, in which there is a period of equilibrium, then exponential growth, then another period of equilibrium. Different systems of different complexity will have different time periods of equilibrium. At very high complexity, it is possible to witness what appears to be pure exponential growth, when in fact, if we were to look more closely at the data, we would see something more like a stairstep progression. A market economy in a high population density country with the right kinds of institutions is a good example of the latter.
The way our brains learn is a similar process. There are those who learn slowly, with long periods of equilibrium and short periods of exponential growth; there are those who learn quickly, with short periods of equilibrium and long periods of exponential growth; and there are many variations in between. The causes are many, and of course include genetic factors affecting neural development, connection, plasticity, etc. and environmental factors, including social complexity, stress and anxiety, and hope.
We should thus expect to see the same dynamics at work in language. And, indeed, this is exactly what we see. Miagawa hypothesizes that human language emerged rapidly. He developed the Integration Hypothesis after noting that there are words which have syntax. Of course, this dynamic remained once language itself emerged, finding itself repeated in the evolution of and within different languages themselves. In particular, "punctuational bursts of change at the time of language splitting are an important and general process in language evolution and account for 10 to 33% of the total divergence among these languages in their fundamental vocabularies" (Atkinson, et al. 588).
I think it would benefit us a great deal to pay more attention to these kinds of transitions. Not just in biology, the brain, and language, but in our social systems as well.
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