This is the sentence you are referring to: But the dramatic and near-universal decline in birth rate and family size that has been one of the most pervasive social changes of the past two centuries, and that continues apace around the world, means that my situation is far from unusual.
The word apace in this paragraph means quickly, swiftly. It means that the decline in birth rate and family size is one of the most relevant social changes of today, and that it is rapidly decreasing. This is the case for almost every part of the world, and it doesn't seem natural to the author.
