Population-size-dependent, age-structured branching processes linger around their carrying capacity

Peter Jagers, Fima Klebaner

Research output: Chapter in Book/Report/Conference proceedingChapter (Book)Researchpeer-review

14 Citations (Scopus)

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
Original languageEnglish
Title of host publicationNew frontiers in applied probability
EditorsP Glynn, T Mikosch, T Rolski
Place of PublicationSheffield UK
PublisherApplied Probability Trust
Pages249 - 260
Number of pages12
EditionSpecial Volume 48A
ISBN (Print)0902016083
DOIs
Publication statusPublished - 2011

Cite this

Jagers, P., & Klebaner, F. (2011). Population-size-dependent, age-structured branching processes linger around their carrying capacity. In P. Glynn, T. Mikosch, & T. Rolski (Eds.), New frontiers in applied probability (Special Volume 48A ed., pp. 249 - 260). Applied Probability Trust. https://doi.org/10.1239/jap/1318940469