Stochastic models of closed populations predict eventual extinction with certainty. Consequently, their behavior is often characterized by the quasi-stationary state, i.e. the long-term distribution of population sizes conditional on non-extinction. In contrast, models which allow for immigration exhibit a regular stationary state. At the limit of a low immigration rate, a population is expected to alternate between three states: the quasi-stationary state of a closed population, the extinction state, and the transient phase during which a newly arrived immigrant either establishes a new population or fails to do so. We develop this argument into a simple and intuitive framework that can be used to assess the effect of immigration in a general class of population models. We exemplify the framework for models in which immigrants arrive either singly or in groups, for models with an Allee effect, for models with environmental stochasticity, and for models leading to metapopulation dynamics.
You have requested a machine translation of selected content from our databases. This functionality is provided solely for your convenience and is in no way intended to replace human translation. Neither BioOne nor the owners and publishers of the content make, and they explicitly disclaim, any express or implied representations or warranties of any kind, including, without limitation, representations and warranties as to the functionality of the translation feature or the accuracy or completeness of the translations.
Translations are not retained in our system. Your use of this feature and the translations is subject to all use restrictions contained in the Terms and Conditions of Use of the BioOne website.
Vol. 54 • No. 1–4