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A new approach to the generation time in matrix population models
François Bienvenu1, Stéphane Legendre
1Unité Mixte de Recherche 8197, Institut de Biologie de l'École Normale Supérieure (Centre National de la Recherche Scientifique, École Normale Supérieure), 46 Rue d'Ulm, 75230 Paris Cedex 05, France.
The American Naturalist
|May 22, 2015
Summary
We introduce a novel Markov chain method to calculate population generation time, simplifying complex formulas. This approach reveals generation time is the inverse of fertility elasticities, offering new insights into population dynamics.
Area of Science:
- Ecology
- Population Dynamics
- Mathematical Biology
Background:
- The generation time, often defined as mean maternal age at birth, is crucial for understanding population dynamics.
- Existing formulas for calculating generation time in matrix population models are complex and difficult to interpret.
Purpose of the Study:
- To develop a new, interpretable method for calculating generation time using Markov chains.
- To provide a simpler formula for generation time and offer new insights into elasticity interpretations.
Main Methods:
- Envisioning generation time as a return time in a Markov chain.
- Deriving a general formula for generation time based on this Markov chain approach.
- Analyzing the relationship between generation time, elasticities, and population growth rate.
Main Results:
- Generation time is the inverse of the sum of elasticities of the growth rate to changes in fertilities.
- Elasticities correspond to the frequency of events in the ancestral lineage.
- A generalized version of Lebreton's formula was derived.
- The generation time can be treated as a random variable with a general distribution.
Conclusions:
- The Markov chain approach simplifies the calculation and interpretation of generation time.
- This method provides a new perspective on the meaning of elasticities in population models.
- The findings offer a more accessible framework for analyzing population dynamics and evolutionary processes.
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