Linear processes in stochastic population dynamics: theory and application to insect development
type: Item
instance of: scholarly article
title: Linear processes in stochastic population dynamics: theory and application to insect development
zbMATH Open document ID: 1328.92068
DOI: 10.1155/2014/873624
published in: The Scientific World Journal. Probability and Statistics
publication date: 2016-01-13T00:00:00Z
review text: Summary: We consider stochastic population processes (Markov jump processes) that develop as a consequence of the occurrence of random events at random time intervals. The population is divided into subpopulations or compartments. The events occur at rates that depend linearly on the number of individuals in the different described compartments. The dynamics is presented in terms of 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. Transition to the next stage competes 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.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 60J75
zbMATH DE Number: 6529691
zbMATH Keywords: insect development
zbMATH Keywords: Markov jump processes
zbMATH Keywords: Kolmogorov forward equation
Wikidata QID: Q51097593
author: Hernán G. Solari
author: Mario Natiello
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/873624
OpenAlex ID: W2009122917
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description: scientific article; zbMATH DE number 6529691