Statistical Science

The Growth and Stabilization of Populations

Peter Jagers

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Abstract

Population models in the birth-and-death style tradition have the unpleasant (and usually not advertised) implication that individuals do not age: It follows from the Markov properties of the whole population that life spans must be exponentially distributed and reproduction occur as splitting or in a Poisson process. This can be remedied only in parts (and at a high esthetical cost) by assuming more complicated Markovian properties in real time, like the age and parity dependent models of demography. Instead, if there is a sensible Markov structure in population growth, it resides in the pedigree, daughters inheriting genotypes from their mothers and being independent of their ancestors, given these types. This idea is used to define general branching processes and to analyze their properties: extinction, growth and asymptotic composition. The results are used to interpret the hypothesis of a molecular clock of mutations in biological evolution.

Article information

Source
Statist. Sci., Volume 6, Number 3 (1991), 269-274.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.ss/1177011694

Digital Object Identifier
doi:10.1214/ss/1177011694

Mathematical Reviews number (MathSciNet)
MR1144241

Zentralblatt MATH identifier
0955.60535

JSTOR
links.jstor.org

Keywords
Branching processes population dynamics Markov fields stable population theory evolution neutral mutations molecular clock

Citation

Jagers, Peter. The Growth and Stabilization of Populations. Statist. Sci. 6 (1991), no. 3, 269--274. doi:10.1214/ss/1177011694. https://projecteuclid.org/euclid.ss/1177011694


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See also

  • See Comment: Joel E. Cohen. [The Growth and Stabilization of Populations]: Comment: Partially Observed Markov Chains and Genetic Demography. Statist. Sci., Volume 6, Number 3 (1991), 275--277.
  • See Comment: Peter Donnelly. [The Growth and Stabilization of Populations]: Comment. Statist. Sci., Volume 6, Number 3 (1991), 277--279.
  • See Comment: Stanley Sawyer. [The Growth and Stabilization of Populations]: Comment: The Geographical Structure of Populations. Statist. Sci., Volume 6, Number 3 (1991), 280--281.
  • See Comment: Peter Jagers. [The Growth and Stabilization of Populations]: Rejoinder. Statist. Sci., Volume 6, Number 3 (1991), 282--283.