Biomedical subjects

M Zhien

Publications and source records attributed to M Zhien.

3 recordsLinked to original sources

PubMed1987

On density and extinction in continuous population models.

Survival analyses, investigations of extinction and persistence, are executed for populations represented by a nonautonomous differential equation model. The population is assumed governed by density dependent and time varying density independent demographic parameters. While traditional approaches to extinction postulate extinction on an infinite time horizon and at zero abundance level, survival analysis is developed not only for this traditional setting but also on a finite time horizon and at a nonzero threshold level. A main conclusion is that extinction of a temporally stressed population is determined by a totality of density independent and density dependent factors.

Animals↗

PubMed1987

Demographic variation and survival in discrete population models.

Persistence and extinction attributes of a discrete population model are explored on both a finite and an infinite time horizon. For a first-order autonomous nonlinear difference equation, a classification is found of when, for each positive integer N, trajectories go to extinction at time N. The dynamic complexity that is known to permeate difference-equation models is also present in the survival analyses developed here. Also found is an interesting decomposition of the continuum of initial population sizes into intervals where populations are persistent at time N and intervals leading to extinction at time n less than or equal to N.

Animals↗

PubMed1986

Persistence in population models with demographic fluctuations.

A persistence and extinction theory is developed through analytical studies of deterministic population models. Under hypotheses that require demographic parameters to fluctuate temporally, the populations may or may not oscillate. Extinction, when it occurs, is asymptotic. An hierarchy of persistence criteria, based upon fluctuations measured by time average means, is derived. In some situations a threshold value is found to separate persistent population models from those that tend to extinction. Application of the persistence-extinction theory is to the problem of assessing effects of a toxic substance on a population when toxicant inputs to the environment and to resources are oscillatory.

Demography↗