The age-standardized asthma prevalence in Tokelauan migrants to New Zealand age 15 and older, was 2 - 6 times higher than in non-migrants from 1976 to 1982, depending on gender and year. The highest prevalence was in New Zealand migrant women in 1976, at 6.8%. The lowest was in Tokelauan men in 1976 at 1.1%.
A skeptic might suggest it's because these adults grew up around certain types of pollen or other antigens, and were exposed to new ones later in life. However, even migrant children in the 0-4 age group, who were most likely born in NZ, had more asthma than on Tokelau.
What could contribute to the increased asthma prevalence upon modernization? I'm not particularly knowledgeable about the mechanisms of asthma, but it seems likely to involve a chronic over-activation of the immune system ("inflammation").
The Tokelau Island Migrant Study: Background and Overview
The Tokelau Island Migrant Study: Dental Health
The Tokelau Island Migrant Study: Cholesterol and Cardiovascular Health
The Tokelau Island Migrant Study: Weight Gain
The Tokelau Island Migrant Study: Diabetes
The Tokelau Island Migrant Study data in this post come from the book Migration and Health in a Small Society: The Case of Tokelau.
Thanks to the EPA and Wikipedia for the graph image (public domain).