TY - JOUR
T1 - Extinction times and moment closure in the stochastic logistic process
AU - Newman, T. J.
AU - Ferdy, Jean Baptiste
AU - Quince, C.
N1 - Funding Information:
T.J.N. is grateful to the Jeffress Foundation and the NSF (Division of Environmental Biology and Division of Applied Mathematics) under Grant DEB-0328267 for financial support. J.-B.F. has been supported by NSF Grant DEB-9527986 to Jane Molofsky.
PY - 2004/3
Y1 - 2004/3
N2 - 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.
AB - 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.
KW - Conservation
KW - Demographic stochasticity
KW - Fluctuations
KW - Moment closure approximation
KW - Quasi-stationary distribution
KW - Time to extinction
UR - http://www.scopus.com/inward/record.url?scp=1242277202&partnerID=8YFLogxK
U2 - 10.1016/j.tpb.2003.10.003
DO - 10.1016/j.tpb.2003.10.003
M3 - Article
C2 - 14766186
AN - SCOPUS:1242277202
VL - 65
SP - 115
EP - 126
JO - Theoretical Population Biology
JF - Theoretical Population Biology
SN - 0040-5809
IS - 2
ER -