Speaker:

Ingemar Nasell

Title:

Persistence in Population Biology Models

Abstract:

Abstract. It is common in population biology modelling to use
discrete state Markov Chains in continuous time with absorbing
states. An important quantity for such a model is the persistence,
measured by the expected time to extinction from quasistationarity.
Results for the univariate logistic model are described.
The persistence measure behaves in qualitatively different ways in
three different parameter regions. Briefly, it grows exponentially
with the population size N in one of the regions, while it is much
smaller and approximately independent of N in another region,
and moderately large in a transition region between the two. This
is a large deviation result only in the first of these regions. A
uniform approximation that is valid throughout the three regions
is derived. It can be used to define a stochastic model threshold.
Extensions to bivariate and multi-variate models remain to
be treated.

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