Journal of Applied Probability

Population-size-dependent, age-structured branching processes linger around

Peter Jagers and Fima C. Klebaner

Abstract

Dependence of individual reproduction upon the size of the whole population is studied in a general branching process context. The particular feature under scrutiny is that of reproduction changing from supercritical in small populations to subcritical in large populations. The transition occurs when the population size passes a critical threshold, known in ecology as the carrying capacity. We show that populations either die out directly, never coming close to the carrying capacity, or grow quickly towards the carrying capacity, subsequently lingering around it for a time that is expected to be exponentially long in terms of a carrying capacity tending to infinity.

Article information

Source
J. Appl. Probab., Volume 48A (2011), 249-260.

Dates
First available in Project Euclid: 18 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1318940469

Digital Object Identifier
doi:10.1239/jap/1318940469

Mathematical Reviews number (MathSciNet)
MR2865630

Zentralblatt MATH identifier
1229.60098

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 92D25: Population dynamics (general)

Keywords
Age structure branching process carrying capacity

Citation

Jagers, Peter; Klebaner, Fima C. Population-size-dependent, age-structured branching processes linger around. J. Appl. Probab. 48A (2011), 249--260. doi:10.1239/jap/1318940469. https://projecteuclid.org/euclid.jap/1318940469


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