Extinction times and moment closure in the stochastic logistic process

T J Newman; Jean-Baptiste Ferdy; C Quince

doi:10.1016/j.tpb.2003.10.003

Extinction times and moment closure in the stochastic logistic process

Theor Popul Biol. 2004 Mar;65(2):115-26. doi: 10.1016/j.tpb.2003.10.003.

Authors

T J Newman¹, Jean-Baptiste Ferdy, C Quince

Affiliation

¹ Department of Physics and Astronomy, Arizona State University, P.O. Box 871504, Tempe, AZ 85287, USA. timothy.newman@asu.edu

PMID: 14766186
DOI: 10.1016/j.tpb.2003.10.003

Abstract

We investigate the statistics of extinction times for an isolated population, with an initially modest number M of individuals, whose dynamics are controlled by a stochastic logistic process (SLP). The coefficient of variation in the extinction time V is found to have a maximum value when the death and birth rates are close in value. For large habitat size K we find that Vmax is of order K1/4 / M1/2, which is much larger than unity so long as M is small compared to K1/2. We also present a study of the SLP using the moment closure approximation (MCA), and discuss the successes and failures of this method. Regarding the former, the MCA yields a steady-state distribution for the population when the death rate is low. Although not correct for the SLP model, the first three moments of this distribution coincide with those calculated exactly for an adjusted SLP in which extinction is forbidden. These exact calculations also pinpoint the breakdown of the MCA as the death rate is increased.

Publication types

Comparative Study
Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

Animals
Biological Evolution*
Environment
Logistic Models*
Models, Biological*
Mortality
Population Density*
Population Dynamics*
Stochastic Processes
Time Factors