Extinction times for a birth-death process with two phases.

by: JV Ross, PK Pollett

Math Biosci, Vol. 202, No. 2. (August 2006), pp. 310-322.

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摘要

Many populations have a negative impact on their habitat or upon other species in the environment if their numbers become too large. For this reason they are often subjected to some form of control. One common control regime is the reduction regime: when the population reaches a certain threshold it is controlled (for example culled) until it falls below a lower predefined level. The natural model for such a controlled population is a birth-death process with two phases, the phase determining which of two distinct sets of birth and death rates governs the process. We present formulae for the probability of extinction and the expected time to extinction, and discuss several applications.

@article{citeulike:996839, abstract = {Many populations have a negative impact on their habitat or upon other species in the environment if their numbers become too large. For this reason they are often subjected to some form of control. One common control regime is the reduction regime: when the population reaches a certain threshold it is controlled (for example culled) until it falls below a lower predefined level. The natural model for such a controlled population is a birth-death process with two phases, the phase determining which of two distinct sets of birth and death rates governs the process. We present formulae for the probability of extinction and the expected time to extinction, and discuss several applications.}, address = {Department of Mathematics, University of Queensland, QLD 4072, Australia. jvr@maths.uq.edu.au <jvr@maths.uq.edu.au>}, author = {Ross, J. V. and Pollett, P. K. }, citeulike-article-id = {996839}, doi = {10.1016/j.mbs.2006.02.004}, issn = {0025-5564}, journal = {Math Biosci}, keywords = {birth, death, mathematics, stochastic, sub-bioinformatics}, month = {August}, number = {2}, pages = {310--322}, posted-at = {2006-12-15 10:24:58}, priority = {5}, title = {Extinction times for a birth-death process with two phases.}, url = {http://dx.doi.org/10.1016/j.mbs.2006.02.004}, volume = {202}, year = {2006} }

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TY - JOUR ID - citeulike:996839 L3 - citeulike-article-id:996839 TI - Extinction times for a birth-death process with two phases. JF - Math Biosci VL - 202 IS - 2 SP - 310 EP - 322 AD - Department of Mathematics, University of Queensland, QLD 4072, Australia. jvr@maths.uq.edu.au <jvr@maths.uq.edu.au> SN - 0025-5564 N2 - Many populations have a negative impact on their habitat or upon other species in the environment if their numbers become too large. For this reason they are often subjected to some form of control. One common control regime is the reduction regime: when the population reaches a certain threshold it is controlled (for example culled) until it falls below a lower predefined level. The natural model for such a controlled population is a birth-death process with two phases, the phase determining which of two distinct sets of birth and death rates governs the process. We present formulae for the probability of extinction and the expected time to extinction, and discuss several applications. KW - birth KW - death KW - mathematics KW - stochastic KW - sub-bioinformatics AU - Ross, JV AU - Pollett, PK PY - 2006/08// UR - http://dx.doi.org/10.1016/j.mbs.2006.02.004 ER -

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