The generation time is commonly defined as the mean age of

mothers at birth. In matrix population models, a general formula is

available to compute this quantity. However, it is complex and hard to

interpret. Here, we present a new approach where the generation time is

envisioned as a return time in an appropriate Markov chain. This yields

surprisingly simple results, such as the fact that the generation time is

the inverse of the sum of the elasticities of the growth rate to changes in

the fertilities. This result sheds new light on the interpretation of

elasticities (which as we show correspond to the frequency of events in the

ancestral lineage of the population), and we use it to generalize a result

known as Lebreton's formula. Finally, we also show that the generation time

can be seen as a random variable, and we give a general expression for its

distribution.

mothers at birth. In matrix population models, a general formula is

available to compute this quantity. However, it is complex and hard to

interpret. Here, we present a new approach where the generation time is

envisioned as a return time in an appropriate Markov chain. This yields

surprisingly simple results, such as the fact that the generation time is

the inverse of the sum of the elasticities of the growth rate to changes in

the fertilities. This result sheds new light on the interpretation of

elasticities (which as we show correspond to the frequency of events in the

ancestral lineage of the population), and we use it to generalize a result

known as Lebreton's formula. Finally, we also show that the generation time

can be seen as a random variable, and we give a general expression for its

distribution.