Ancient Polynesians didn't always "jump-ship" when the population boomed.  Using Kanaka Maoli (Native Hawaiians) as an example, higher population estimates suggest the population may have reached one million (not far from the current Hawai'i resident pop.) prior to the arrival of Captain Cook in the latter part of the 18th century.  

Native Hawaiian socio-political-economic sustainability was the result of long-term planning.  These ancients balanced resource supply with resource consumption and maximized their economy.  Unfortunately, those values were largely suppressed by foreign settlers and settler colonialism.  

Today, we're over capacity because we simply aren't balancing our supply.  That, in large part, is a result of outsiders controlling us; outsiders that don't have to pay the incredibly high cost of living.  Hey, when a foreign/out-of-state developer drops thousands of homes over agricultural lands - we're basically being subjected to external exploitation.