That source was published in 1978; as of now, it is 39 years old (!). In that time, there have been many archaeological discoveries and demographic studies which have increased our knowledge on historical demography. One blatant mistake I found was the map of populations in 200 AD, where it was claimed that Germania and Asia Minor both had about six million inhabitants; not only was Asia Minor quite urbanized whereas Germania was not, Asia Minor could rely on grain imports (from Egypt), heightening the carrying capacity, whereas Germania was autarkic and had to rely on what they could grow themselves, severely lowering the carrying capacity.@NakedBeast
For consistency's sake I used McEvedy and Jones' Atlas of World Population History for every population figure. You can download a full PDF of it here https://www.fichier-pdf.fr/2014/12/21/pour-happliquer/ (the website is French but the PDF is entirely English).
My population figures are based on 867, though that applies almost perfectly to 769 for most areas, and in the worst areas is only off by ~20%. When I have the time I will update the map for exact 769 figures. I got those figures by taking the nearest dated population estimates in the Atlas, and extrapolating from there. Usually there are figures for 700, 800, and 900 CE, so it isn't that hard to do.
I can guarantee that the figures you see in game are accurate for the Atlas' estimates, with minor exceptions in some areas that fall well within the margin of error on historical estimates like this. The only areas that are not properly represented are Egypt, Yemen, and India, where some provinces need to have more than 300k rural pops to reach historical figures. Ideally, the Nile Delta, one or two Yemeni highland provinces, and the entire Indo-Gangetic plain would have 100k population per holding.
The figures only become significantly divorced from the Atlas when it comes to carrying capacity. With the current number of provinces, virtually all of France and Germany and a few other European regions would have full holding slots, making it impossible to represent subregional differences. For that reason, holding slots were reduced in some areas to make the holding slot distribution line up more with a map of early modern population density. I'd estimate that the carrying cap is reduced in some areas by up to 20% of what it should be, but I felt it was acceptable given that we're dealing with generally rough estimates, and that it isn't an exact science to translate historical population figures into carrying capacity.
India is the only place where there are huge problems. I based carrying capacity on max population achieved before 1700 (or in some cases 1650), reasoning that agricultural technology and crop usage didn't change dramatically in Europe until after that point. Presumably, in an ideal situation (e.g. a major centralized pan-European empire with no frequent wars, and with no Black Death), these figures should be reachable even by 1453. But in India, the population in 1500 (my old carrying cap cutoff date) was ~100 million. In 1700, it was ~160 million. That's an average of 8.7 versus 14 holdings per province. Even in the former case, and with the Indo-Gangetic plain provinces buffed immensely, India is still mostly a blob of provinces with 7 holding slots. In the latter case, it would be much worse.
India can look somewhat sane with 100 million max pop, so I went with that. I think a detailed, realistic map of India can be made with TwiddleFactor's variable carrying capacity, but to work with variable carrying cap per holding, the holding slot map will have to be redone for the entire world.
Also, for the maximum carrying capacities in general, don't forget that in most parts of Europe, the population only got back to pre-black death levels around 1700. Seeing how the plague itself followed after a dip in population levels, I suggest you don't use 1700 as a reference to determine the maximum carrying capacity of the provinces in this otherwise quite interesting and promising mod.