What are the main causes of low human population density in many polynesian islands? What constructions alowed for high human population in...

What Diamond is saying in this book is that civilization
is sort of an accident -- places that have good climates and good luck can have lots of
people and civilizations.  In Chapter 2, he is saying that high population densities
come about by luck in these islands too -- places where farming is possible can have
large populations, places where people have to be hunter-gatherers cannot have dense
populations.

The only real "construction" that allows for
high population densities is agriculture.  Agriculture allowed people to grow excess
amounts of food and, thereby, to feed more people.