If we're talking about a diet that enables survival, sustainability is part of that conversation. Claiming that we don't need to eat meat to stay alive because we can rely on plains of quinoa and rice to sustain us instead, is problematic if your bottom line is survival...climate change and peak oil are both going to affect a diet dependent on protein rich crops.
There are no studies that I'm aware of - Polynesians are a small group of humans, population-wise. That, and their long period of isolation from other human cultures means that interest in their traditions and diet is limited.
The main source for Samoans that I know is An Account of Samoan History up to 1918 by Teo Tuvale.
In it he writes:
For one meal: 1 pound of baked taro, one or two breadfruit averaging three quarters of a pound in weight, half a pound of fish, 3 papasami [sic], half a pound of pork and in addition anything else that can be procured or is prepared. This is usually followed by the juice of a cocoanut [sic]. If available the above foods and amounts will be consumed twice a day as the Samoan's digestive capacity seems to be limited only by his ability to procure the food or have it procured for him. The above foods and quantities have been checked several times from personal observation and should the amount consumed at a feast be mentioned one would be liable to be put down as a liar.
There are theories that to sail from one island to another, the convoy was often out at sea for long periods of time - so natural selection favoured those who were able to eat everything that was available, when it was made available, and store it preceding a long stretch of low calorie and fluid intake.