American Society of Naturalists

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“The equivocal mean age of parents in a cohort”

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François Bienvenu (Aug 2019)

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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

A western green lizard (<i>Lacerta bilineata</i>) spotted in the <br/><br/>Fontainebleau Forest near Paris (France). Out of the more than 3882 <br/><br/>matrix models for which the average age of the parents of the offspring <br/><br/>produced by a cohort and the mean age at reproduction were compared, <br/><br/>three were from the genus <i>Lacerta</i>. They all had a fairly typical <br/><br/>relative difference between the two measures (about 20%).<br />(Credit: Marc Manceau)
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A western green lizard (Lacerta bilineata) spotted in the Fontainebleau Forest near Paris (France). Out of the more than 3882 matrix models for which the average age of the parents of the offspring produced by a cohort and the mean age at reproduction were compared, three were from the genus Lacerta. They all had a fairly typical relative difference between the two measures (about 20%).
(Credit: Marc Manceau)

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.