The model then predicts a sudden shift in 2025 without any inherent explanation. There's a vaguely-defined downward-sloping "resources" line on the graph that seems to drive the sudden shift, but there's no actual data given for the 1975-2000 period to know if actual "resources" are tracking the model. I'd guess not --- as much as the Bakken shale oil formation may have some serious environmental impacts, it (and many other discoveries) have dramatically increased energy resources. Food production doesn't show any signs of immediate collapse. Renewable energy is still expensive, but it's getting better faster than many expected. Etc.
So, 25 years of steadily increasing population does not validate this model in any meaningful way. The model depends on a sudden shift in ~2025 that no empirical evidence supports. It might still happen -- I can't rule it out -- but the data given hardly confirms this model.