A new type of Rorschach test?
The graph provided could mean a lot of things, but the further left you go, it's based more and more on conjecture.
Near the origin it is difficult to tell what the population is supposed to be on a log scale of millions: Nearly 1 million or below one million? How much below? And based on what? The End of Ice Age census respondents?
Who drew up the graph? Were they making estimates from historical extrapolations, archeological inferences?
A couple of leveling off points might be due to events such as the Bronze Age collapse around 1200 BC, the collapse of the Roman West and the Plague of Justinian around 500 - AD. World wide plague in the 14th century and "anti-urban programs" originating in Central Asia directed by the Chengis Khan & sons - you would figure they would reflect as well, if 14th century plague reduced populations by a third to a half.
...But that doesn't explain the abrupt stop that Slimboyfat noticed.
Oddly enough, during that period, in the MidEast there was some long term consolidation of Empires under Persian control - which shifted to a Hellenic "commonwealth. Amid all that, one of the observations of the Thucydides about the Peloponnesian (~430 to 410 BC) War was the outbreak of plague. It could be that the communications made available by land empires and sea-going vessels for contagions, levying of large armies taking farm workers from out of the fields, bad harvests and intense plagues spread from one end of Eurasia to another - were worse on population numbers than the continuous fighting preceding it in the Levantine and Mesopotamia.
Or that the leveling off is simply questionable.
It could have been done by a geography department student with a pencil and a guess.