First the link to this week’s complete list as HTML and as PDF.
In Shennan et al. their diagram for all regions combined is highly suggestive. For their hypothesis to hold they would have to demonstrate it for individual regions and highly diverse timings for individual onset of agriculture though. To my eye their figure 3 is a failure. Central and Southern Germany especially deviate from their model and suggest a rise synchronous to the northern ones. No doubt there were population crashes as there must have been in the Palaeolithic, but they didn’t come at a predictable time after neolithisisation.
From parsimonious assumptions and a rather simple model Turchin et al. have managed to predict the rise of statehood with astonishing precision and detail. The lack of subsaharan Africa is explicable by their excluding its steppes from the model and I don’t know enough about America to estimate, whether it could work there as well.