This just in: that appalling colonial thing we white folks did is what made the people of the South Pacific so dreadfully fat today:
Anthropologists Dr Amy McLennan and Professor Stanley Ulijaszek found that islanders lost many of their traditional food cultivation, preparation and preserving skills after settlers insisted that they learn western ways of eating.
They taught the locals to fry fish rather than eat it raw, and forced them to import unhealthy produce after co-opting farmland for mining.
“Under colonial rule, much changed in how food was sourced, grown and prepared and the social change was swift,” said lead author Dr McLennan
“What happened to the land also changed as colonial agriculture and mining industries expanded. There was an increase in family size meaning food was increasingly imported.”
It's that last sentence that should have been a clue to our intrepid scientists. A change in diet, a change in the amount of food available (for that's what imports manage) leads to a removal of the Malthusian limits on family size. They couldn't have large families before because there wasn't enough food to feed them. After that dreadful, hateful, arrival of the colonialists food supplies increased and it was possible to raise larger families.
Or to make the same statement another way: the colonialists improved the diets of those who lived on such islands. It might not be an improvement by the standards of the modern prodnoses but population does respond quite well to food availability in a subsistence economy. That population and family size did increase is proof perfect that the diet was "better".