caa a22 4500 477140599 CHVBK 20180405111731.0 cr unu---uuuuu 170330e19971101xx s 000 0 eng 10.1007/s002850050096 doi (NATIONALLICENCE)springer-10.1007/s002850050096 Population growth with randomly distributed jumps [Elektronische Daten] [Floyd B. Hanson, Henry C. Tuckwell] Abstract.:  The growth of populations with continuous deterministic and random jump components is treated. Three special models in which random jumps occur at the time of events of a Poisson process and admit formal explicit solutions are considered: A) Logistic growth with random disasters having exponentially distributed amplitudes; B) Logistic growth with random disasters causing the removal of a uniformly distributed fraction of the population size; and C) Exponential decay with sudden increases (bonanzas) in the population and with each increase being an exponentially distributed fraction of the current population. Asymptotic and numerical methods are employed to determine the mean extinction time for the population, qualitatively and quantitatively. For Model A, this time becomes exponentially large as the carrying capacity becomes much larger than the mean disaster size. Implications for colonizing species for Model A are discussed. For Models B and C, the practical notion of a small, but positive, effective extinction level is chosen, and in these cases the expected extinction time rises rapidly with population size, yet at less than an e xponentially large order. Springer-Verlag Berlin Heidelberg, 1997 Key words: Population extinction nationallicence Randomly distributed jumps nationallicence Bonanzas nationallicence Disasters nationallicence Hanson Floyd B. Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinois at Chicago, 851 S. Morgan, Chicago, IL 60607-7045, USA e-mail: hanson@uic.edu, US aut Tuckwell Henry C. Epidemiologie et Sciences de l'Information, Universite Paris 6 (INSERM U444), Faculte de Medecine St Antoine, 27 rue Chaligny, 75571 Paris Cedex 12, France e-mail: tuckwell@b3e.jussieu.fr, FR aut https://doi.org/10.1007/s002850050096 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s002850050096 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hanson Floyd B. Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinois at Chicago, 851 S. Morgan, Chicago, IL 60607-7045, USA e-mail: hanson@uic.edu, US aut NATIONALLICENCE 700 1- Tuckwell Henry C. Epidemiologie et Sciences de l'Information, Universite Paris 6 (INSERM U444), Faculte de Medecine St Antoine, 27 rue Chaligny, 75571 Paris Cedex 12, France e-mail: tuckwell@b3e.jussieu.fr, FR aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer