  Demographic indicators are an essential element in considering various
problems in the social economy, such as predicting economic fluctuations and
establishing policies. The literature widely discusses the growth of the world
population or issues pertaining to its aging, but has given little to no
attention to population structures and transition patterns. In this article, we
take advantage of the characteristics of compositional data to examine the
transition of the world population structure. Using the Aitchison distance, we
examine the similarity of the world population structure from the 1990s to 2080
and that of countries and regions in 2015 and create maps to illustrate the
results. Accordingly, we identify the following countries and regions as
epitomes of the world population structure through different periods: India,
Northern Africa and South Africa, in the 1990s, South America in 2015 to 2030,
Oceania and Northern America in 2040, Uruguay and Puerto Rico in 2050 to 2060,
and Italy and Japan in the distant future. We then cluster countries based on
the similarity of their population structures in 2015 and correspond each
cluster to a certain period. We found that Russia and Western Europe gather in
a cluster that does not correspond to any period, indicating a recessive
population structure.
