The equivocal mean age of parents in a cohort

The mean age at childbirth 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.