An approximation of populations on a habitat with large carrying capacity

Naor Bauman, Pavel Chigansky*, Fima Klebaner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider stochastic dynamics of a population which starts from a small colony on a habitat with large but limited carrying capacity. A common heuristics suggests that such population grows initially as a Galton–Watson branching process and then its size follows an almost deterministic path until reaching its maximum, sustainable by the habitat. In this paper we put forward an alternative and, in fact, more accurate approximation which suggests that the population size behaves as a special nonlinear transformation of the Galton–Watson process from the very beginning.

Original languageAmerican English
Article number44
JournalJournal of Mathematical Biology
Issue number4
StatePublished - Apr 2024

Bibliographical note

Publisher Copyright:
© The Author(s) 2024.


  • 60J80
  • 92D25
  • Approximation
  • Branching processes
  • Limit theorems
  • Population dynamics


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