On the lifetime of a size-dependent branching process

A1 Journal article (refereed)

Internal Authors/Editors

Publication Details

List of Authors: Göran Högnäs
Publisher: Taylor and Francis
Publication year: 2019
Journal: Stochastic Models
Journal acronym: Stoch. Models
Volume number: 35
Issue number: 2
Start page: 119
End page: 131
eISSN: 1532-4214


We discuss lifetimes for a family of population-dependent branching
processes. The attenuation factor (due to environment or competition,
for example) is of Ricker type, i.e., the probability of an individual
having offspring at all is of the form e−γn" role="presentation">e−γn if the total population is n. Equivalently we can write the probability as e−nK" role="presentation">e−nK where the carrying capacity K is γ−1," role="presentation">γ−1, the inverse of the attenuating factor. It is well known that the expected lifetime of such a process is exponential in K. If the carrying capacities {Kt}" role="presentation">{Kt}
vary much over time, for instance, if they are i.i.d. with a
heavy-tailed distribution, the extinction scenario may change to a
growth-catastrophe one with expected lifetimes much shorter. In addition
to Ricker’s model, production functions of the Beverton–Holt and
Hassell types are also discussed.


Last updated on 2020-02-07 at 05:02