Of course, I'm just getting into it, so take that with a grain of salt...
It's a beautiful idea that has an answer to the whole sweep of human history from Malthusian times to today.
I'm just not sure the answer makes sense.
First the demographic transition and take off is all driven by birth rates, which at a certain point start to fall while human capital and technological progress take off ("quality for quantity"). But what actually happens is a fall in death rates, not a fall in birth rates (which comes later - perhaps with a similar virtuous cycle to what UGT describes). But it seems to me the fall in death rates happens because of the technological growth, which is supposed to be caused by the initial population increase.
The other odd thing is that it seems to get the great divergence backwards, right? If population is driving technological change, why did the UK and the US take the lead? Why not India and China?
It's a very nice model. I think endogenizing population growth and introducing subsistence issues is the right way to go. I just think all the focus on the population as the instrument of change is probably wrong. I'm guesing technological shocks due to the scientific revolution instigated the change, and the population followed as UGT predicts it would. It seems odd to think that population took the lead. This would explain the fall in death rates before the fall in birth rates, and this would explain why the UK and the US and not India and China.