Well, the islands were usually settled in waves over long periods of time, so gradually you would have more people arriving on the island as it became more productive and sustained a larger population-- which of course provided more labour to effect an even greater ecological transformation of the island. So genetic bottlenecks were often avoid simply because the islands were not isolated from one another; especially during the generations following initial settlement contact and exchange networks would be maintained. Distant islands; such as Tahiti and Hawaii might eventually lose contact as genealogical links became weaker, but that seems to usually happen over the course of hundreds of years; plenty of time for more people to be moving and expanding the gene pool. And of course islands within island groups; like the Hawaiian archipelago, the Society islands, or the whole network of islands between Tonga-Samoa-Fiji stayed in pretty regular contact through more regional voyaging.

Now, what we might consider incestuous marriages (kissing cousins) did take place in some instances when the spiritual power or sacredness of an individual was so great due to their genealogy and bloodline, that the only suitable match for marriage was a close family member who could match their level. This was less a problem for powerful individuals who could travel to other islands to find a suitable a match and more of a power for powerful individuals in highly centralized or stratified societies. Otherwise incest was generally not acceptable (thus helping to prevent inbreeding).

If you want to read a bit more on the topic and have access to a good library--

• Irwin, Geoffrey. The Prehistorical Exploration and Colonisation of the Pacific. Cambridge: Cambridge University Press, 1994.

Irwin's focus is on voyaging and focuses on different types of voyaging and how/why networks are maintained or formed. The book is a good starting point for establishing the regularity of voyaging regionally by also between distant islands or points using various computer models.

• Kirch, Patrick Vinton. A Shark Going Inland is My Chief: The Island Civilization of Ancient Hawaiʻi. Berkeley: University of California Press, 2012.

Good overview of some of the oral traditions about voyaging-- or settlement patterns/waves and about hierarchy in Polynesia in general (focused mostly on Hawaii though).

• Kirch, Patrick Vinton. On the Road of the Winds. Berkeley: University of California Press, 2002.

Basically a textbook, but an excellent overview of the field of Pacific archeology that helps answer this query.

• Matsuda, Matt. Pacific Worlds: A History of Seas, Peoples, and Cultures. Cambridge: Cambridge University Press, 2012.

More recent introductory text; but the first couple chapters have good information about voyaging and settlement; though not as in-depth as the Kirch.