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Linear Processes in Stochastic Population Dynamics: Theory and Application to Insect Development

Solari, Hernán and Natiello, Mario LU (2014) In Scientific World Journal 2014.
Abstract
We consider stochastic population processes (Markov jump processes)

that develop as consequence of the occurrence of randon events at

random time-inervals. The population is divided into sub-populations or compartments. The events occur at rates that depend linearly with the number of individuals in the different described compartments. The dynamics is presented in terms of a Kolmogorov Forward Equation in the space of events and projected onto the space of populations when needed. The general properties of the problem are discussed. Solutions are obtained using a revised version of the Method of Characteristics. After a few examples of exact solutions we systematically develop short-time-approximations to the problem.... (More)
We consider stochastic population processes (Markov jump processes)

that develop as consequence of the occurrence of randon events at

random time-inervals. The population is divided into sub-populations or compartments. The events occur at rates that depend linearly with the number of individuals in the different described compartments. The dynamics is presented in terms of a Kolmogorov Forward Equation in the space of events and projected onto the space of populations when needed. The general properties of the problem are discussed. Solutions are obtained using a revised version of the Method of Characteristics. After a few examples of exact solutions we systematically develop short-time-approximations to the problem. While the lowest order approximation matches the Poisson and multinomial heuristics previously

proposed, higher-order approximations are completely new. Further, we

analyse a model for insect development as a sequence of E developmental

stages regulated by rates that are linear in the implied subpopulations. Transitions to the next stage compete with death at all times. The process ends at a predetermined stage, for example pupation or adult emergence. In its simpler version all the stages are distributed with the same characteristic time. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Population dynamics stochastic Events Linear rates Insect development
in
Scientific World Journal
volume
2014
publisher
Hindawi Publishing Corporation
external identifiers
  • wos:000332314800001
  • pmid:24696664
  • scopus:84896367829
ISSN
2356-6140
DOI
10.1155/2014/873624
language
English
LU publication?
yes
id
ca4e6efb-269b-4884-8b8b-27e70a11e849 (old id 4144970)
date added to LUP
2013-11-14 14:21:46
date last changed
2017-03-14 13:42:25
@article{ca4e6efb-269b-4884-8b8b-27e70a11e849,
  abstract     = {We consider stochastic population processes (Markov jump processes)<br/><br>
that develop as consequence of the occurrence of randon events at<br/><br>
random time-inervals. The population is divided into sub-populations or compartments. The events occur at rates that depend linearly with the number of individuals in the different described compartments. The dynamics is presented in terms of a Kolmogorov Forward Equation in the space of events and projected onto the space of populations when needed. The general properties of the problem are discussed. Solutions are obtained using a revised version of the Method of Characteristics. After a few examples of exact solutions we systematically develop short-time-approximations to the problem. While the lowest order approximation matches the Poisson and multinomial heuristics previously<br/><br>
proposed, higher-order approximations are completely new. Further, we<br/><br>
analyse a model for insect development as a sequence of E developmental<br/><br>
stages regulated by rates that are linear in the implied subpopulations. Transitions to the next stage compete with death at all times. The process ends at a predetermined stage, for example pupation or adult emergence. In its simpler version all the stages are distributed with the same characteristic time.},
  articleno    = {873624},
  author       = {Solari, Hernán and Natiello, Mario},
  issn         = {2356-6140},
  keyword      = {Population dynamics stochastic Events Linear rates Insect development},
  language     = {eng},
  publisher    = {Hindawi Publishing Corporation},
  series       = {Scientific World Journal},
  title        = {Linear Processes in Stochastic Population Dynamics: Theory and Application to Insect Development},
  url          = {http://dx.doi.org/10.1155/2014/873624},
  volume       = {2014},
  year         = {2014},
}