The Polynesians have been agricultural people far longer than the English. With a couple of tiny exceptions they were less dependent on wild fruit than the English. Just because someone lives outside Europe doesn’t mean that they don’t know how to be successful farmers.
The only Polynesian group that I know of that was entirely dependent on wild resources were the Mori Ori and some of the other New of New Zealanders of south. Of course the reasons why they were dependent on wild foods was because they were well outside the tropics so their crops wouldn’t grow. So naturally they never saw much tropical wild fruit, or any tropical fruit at all.
New Zealand itself was temporarily as you describe. When people first arrived the prey was so numerous and so naive that they could feed themselves without resource to agriculture. As a result all domestic animals except dogs and several domestic plants were allowed to become extinct. After a period of between 200 and 500 years the prey had been exterminated and at the time of European discovery the population had crashed, probably to less than 20% of its peak, and people in the North were struggling to cultivate tropical crops such as sweet potato, while people in the south were cultivating bracken to try to survive. Warfare was constant and territorial defence fierce, with frequent raids being carried out to obtain human flesh, since this and dogs were the only source of readily available protein remaining. SO in the case of the NZ Moari there had definitely been a period of exponential increase followed by a crash, but that was as a result of colonisation of new lands and quite unrelated to normal practice. The same seems to have occurred when people entered Northern Europe, Australia. Madagascar and the Americas as well.
There are some groups of people in various tropical locales who do derive a great deal of their food from wild resources. Most of them, like the inhabitants of the Amazon, are still agriculturalists and their population density is limited ultimately by agricultural yield. However in practical terms warfare and murder accounts for a massive number of deaths. Homicide is the most likely way for young men to die in these societies. This seems to be caused by year-round food production devaluing co-operative social systems and placing a premium on military and sexual aggression.
A few are hunter-gatherers, and their population is limited exactly as is the population if every hunter-gatherer group, chiefly infanticide with a small portion of starvation. Living in the tropics or the arctic doesn’t make much difference to those practices. Resources are limited and can’t be bolstered and are unpredictable. Population has to be kept below median carrying capacity.
Try to keep in mind that Polynesia is much larger than Europe, and much more diverse. Your question is akin to asking what kind of wars people had in neolithic Europe: it ranged from cavalry battles to bands of ten hunter gathers throwing stone axes at each other, right? Well Polyneisa was the same.
The North Isalnd of NZ was the most extreme in terms of warfare, with everybody on the living within or near walled towns with a central fort, raids being conducted against neighbouring tribes every few weeks, battles and sieges lasting for days and wars being fought for anything up to two months at a time, all casualties and captives being either enslaved or eaten, often both. Imagine something between Mad Max and the worst of Medieval Europe and you’ve probably got a pretty good view of North Island warfare.
In many of the smaller islands warfare was often ritualised. One of the islands groups, I can’t remember where, the men would attempt to burst into the enemy village by surprise. If they did so the enemy warriors were expected to stand back and yell defiance, but actual physical aggression at that point was
bad form. The raiders then took what they could before the enemy could regroup and sailed off. If the enemy could form up a large enough force to surround them then they had to give it back. If the enemy spotted them before they got to the village they had to go home. There were also the standard war games that most cultures had for young men to prove themselves. While real wars and real raids occurred they seem to have been rare.
The most extreme example of passive people were the Mori Ori who lived on an island group just off New Zealand. There were HGs who appeared to practice no warfare at all and had no concept of it. Europeans took a msall group of Maori to the islands, and they promptly killed and ate or enslaved then entire population, which outnumbered them at least 10 to one and had the same technology level. It was even more bizarre than the conquest of the Aztecs.
And of course you had anything in between those tow extremes. Generally speaking the Polynesians were a pretty warlike people, but most people are.