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Since your other questions have been about Guns, Germs, and Steel, I assume this one is as well. Please do specify that you are asking about that book so that you can be sure to get answers that are pertinent to your question.
In this book, Diamond talks about subsistence mainly in Chapter 2. He uses this term to refer to the ways in which people support themselves. Subsistence, then, is the sorts of foods that people eat and the ways in which they get those foods. For example, on p. 59 in the paperback edition of the book, Diamond says that
Polynesian subsistence depended on varying mixes of fishing, gathering wild plants and marine shellfish and crustacean, hunting terrestrial birds and breeding seabirds, and food production.
From this, we can see that subsistence refers to the ways in which the people fed themselves.
The connection between this and population size is that islands with more diverse types of subsistence could have larger populations (or, to be precise, higher population density). Diamond notes on p. 61 that the people of the Chathams had a population density of only 5 per square mile because they were hunter-gatherers. By contrast, there were 1,100 people per square mile on Anuta because that island was farmed intensively.
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