At the ASI.
If family size went up when the colonialists changed the South Seas diet then it cannot have been a worse diet, can it?
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”.