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The mean age of parents of offspring produced by a cohort is not a good measure of the mean age at reproduction

Open any demography textbook and you will find information on how to
quantify reproductive timing. In particular, you should find an
expression for the mean age at reproduction of a typical individual.
This classic formula has been used for decades and is one of the most
popular measures of generation time.

Unfortunately, its well-accepted interpretation is incorrect; and the
difference between what some reseachers have in mind and what they
actually compute can be quite large in practice. By detailing the
rigorous interpretation of the formula and providing an alternative
expression for the mean age at reproduction, this article points out the
need to think more deeply about what we mean by “average age at giving
birth”.

Abstract

The mean age at which parents give birth is an important notion in demography,
ecology and evolution, where it is used as a measure of generation time.
A standard way to quantify it is to compute the mean age of the parents of
all offspring produced by a cohort, and the resulting measure is thought to
represent the mean age at which a typical parent produces offspring. In this
note, I explain why this interpretation is problematic. I also introduce a
new measure of the mean age at reproduction and show that it can be very
different from the mean age of parents of offspring of a cohort. In
particular, the mean age of parents of offspring of a cohort systematically
overestimates the mean age at reproduction, and can even be greater than the
expected lifespan of parents.