According to Guns, Germs, and Steel, what are the main causes of low human population density in many Polynesian islands?
The answer to this question can be found in Chapter 2 of the book. It is found largely on pages 59 through 61 in the paperback edition of the book. The brief answer is that a lack of resources made farming impossible or very difficult on some Polynesian islands, thus leading to low population densities.
Diamond says throughout this book that farming (or food production, as it is also called) is the main factor that allows dense populations to arise. These dense populations can give rise to more complex societies with more advanced technologies. When farming is impossible or is very difficult, high population densities are impossible.
On some Polynesian islands, farming was difficult or impossible. On subantarctic islands like the Chathams, Polynesia crops could not grow because they were tropical plants. On other islands, there was not enough rain and/or the soil was poor. Really high population densities were only possible on islands with enough water and good soil to support intensive cultivation of taro.
Thus, when Polynesian islands had low population densities, it was because their environments were not conducive to farming.