    # SMILE

## A New Approach to the Generation Time in Matrix Population Models

### 2015 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.

# Bibtex

@Article{BienvenuLegendreAmNat2015,
Author = {Bienvenu, Fran\c{c}ois and Legendre, St\'ephane},
Title = {A New Approach to the Generation Time in Matrix
Population Models},
Journal = {The American Naturalist},
Volume = {185},
Number = {6},
Pages = {834--843},
year = {2015},
DOI = {10.1086/681104},
URL = {https://zenodo.org/record/49440},
Abstract = {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.},
Keywords = {generation time, matrix population models, markov chain,
return time, elasticity},
}