Extinction times and moment closure in the stochastic logistic process

TY - JOUR

T1 - Extinction times and moment closure in the stochastic logistic process

AU - Newman, T. J.

AU - Ferdy, Jean-Baptiste

AU - Quince, C.

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 V is of order K/M, which is much larger than unity so long as M is small compared to K. 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 V is of order K/M, which is much larger than unity so long as M is small compared to K. 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.

UR - https://www.scopus.com/pages/publications/1242277202

U2 - 10.1016/j.tpb.2003.10.003

DO - 10.1016/j.tpb.2003.10.003

M3 - Article

C2 - 14766186

AN - SCOPUS:1242277202

SN - 0040-5809

VL - 65

SP - 115

EP - 126

JO - Theoretical Population Biology

JF - Theoretical Population Biology

IS - 2

ER -