What was the world population around 970 BC? Does it fit the biblical narrative?

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According to the graph on the World Population wiki page, global population at 1000 BC was about 50 million. The vast majority of that would have been in the areas of intensive farming, which at that time means Mesopotamia, Egypt, China, and perhaps the Indus valley.

So that number doesn't seem completely out of line. However, Israel is much more marginal agricultural territory than Mesopotamia. Reconstructing the Society of Ancient Israel, by Paula M. McNutt postulates a far lower population for the area. In particular, based on archeological evidence, perhaps 40,000 people in the 12th century (which gives them a lot of ground to cover to make a over a million warriors in the next 2 centuries). She admits this doesn't jibe well with biblical accounts.

Here's what McEvedy and Jones' Atlas of World Population History has to say on this very subject:

The collapse of the Egyptian Empire in 1200BC left Palestine
and Jordan defenceless: the Philistines seized the coast, the children of Israel moved in from the desert. According to scripture the Israelites were numbered at something over 2m. Ten thousand would be a better figure, but if they were few they were tenacious: they multiplied and proselytized with such remarkable success that by 800BC they constituted rather more than half the total population of the area - say 0.3m out of 0.5m

For a modern comparison, the state of Israel today has about only 1.5 million men considered "fit for military service". So this Biblical passage would have you believe they almost had as many available in the same area 3000 ago as they could muster today.

Note that current thinking is that Samuel was written sometime around 630-540 BCE, which would have been 300 to 500 years after the events being described. As such, this portion of The Bible should not be taken as a literal history.

The edit I made to the question (adding back in the bit about Judah) should be your first clue. There was no such thing as "Judah" until the civil war after the death of Solomon in 930 (50 years later). That's when the state split, with the 10 northern tribes continuing to call themselves "Israel" and the two southern ones calling themselves "Judah" (which was one of the two tribes' names).

So the sentence is an anachronism. There was no such split then, and "Judah" was just one of the 12 tribes in the country. Most likely if such a report were given, it either wouldn't have been split up at all, or it would have been split up by tribe (which would have required 12 numbers, not two).

Samuel was trying to relate a story, and tell some deeper truths about the authors' conception of God. It was not trying to be a modern-style historical documentary. If you are poking around in it looking for history in every detail, you are completely missing the point.

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According to this site the population was around 100 million and the Jewish population was 2 million people, fitting the biblical narrative.

But it could be that this data was extracted solely from the Bible, and not from other sources.

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How about this explanation: Yes, scripture is literal history, but the translation of the Hebrew word 'eleph' as meaning 1000 is incorrect. Eleph became 1000 about the time of the minor prophets, about 400 BC. This change from the original meaning was a consequence of Hellenistic influence which came into northern Israel from ~450 BC onwards.

Greek thinking involved mathematical precision. Prior to that, eleph was an early Hebrew word with no clear literal numerical number. It was originally imprecise, something like a clan, extended family, troop, company, or something similar - very much less than 1000!

Correct this in its every occurrence of early Hebrew meaning, and all the 'number problems' of scripture (of which there are legion) disappear like the sun on the morning mist.

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