The answer to this can be found in Chapter 17. There, beginning on p. 336 in the paperback edition of the book, Diamond tells us that language distributions show us that speakers of Austronesian languages left Southeast Asia only recently and spread out across the Pacific.
The evidence for this is the fact that the vast majority of Austronesian languages are in the Malayo-Polynesian subfamily. These languages are spoken over the bulk of the geographical range of Austronesian languages. Diamond says that this shows that Malayo-Polynesian speakers broke away from other Austronesians very recently. As they spread across Oceania, they developed many languages for the many isolated islands on which they live. These languages are still closely related, showing that the split was quite recent.
In this way, the distribution of Austronesian languages tells us where the peoples of Oceania came from and how recently they left.