The British officials at the time, and later demographers, insist there is no evidence of large Arab immigration. Some people, like Joan Peters and Fred Gottheil, bring evidence for such immigration from neighboring Arab countries to Palestine. Gottheil in particular showed that even within Palestine, the Arabs would move near where the Jews were concentrated, because the economic opportunities were coming from Jewish areas - and there is no reason to think that Arabs outside Palestine weren't similarly attracted to the booming economy that came from the Jews.
I thought that a comparison of Arab population growth in Palestine to that of its neighbors in Egypt and Syria would help shed light on this question. After all, if Palestine's Arab population growth was way faster than its neighbors in the north and the south, it sure sounds like something unique was happening with the Arabs in Palestine - and immigration is the most likely explanation, since there wouldn't be much of a cultural reason for a baby boom (and no contemporaneous descriptions of one that I am aware of.)
In fact, Palestine's population remained steady from the 16th century to the 19th. Only in the 19th century did it start to increase significantly.
Here is my chart of population grown of Palestine, Egypt and Syria for the years that Palestine had censuses:
We can see that the Palestinian Arab population exploded at double the rate (480%) of those of its neighboring countries Egypt (250%) and Syria (201%)..
If the actual natural growth in Palestine would have mirrored that of Egypt and Syria, then that implies that nearly half of the Arabs living in Palestine in 1948 - over 600,000 - had immigrated since 1882.
If true, that means that half of today's "Palestinians'" ancestors lived in Palestine for fewer years than Israel has existed.
