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Abstract:

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. © 2014 Hernán G. Solari and Mario A. Natiello.

Registro:

Documento: Artículo
Título:Linear processes in stochastic population dynamics: Theory and application to insect development
Autor:Solari, H.G.; Natiello, M.A.
Filiación:Departamento de Física, FCEN-UBA, IFIBA-CONICET, C1428EGA Buenos Aires, Argentina
Centre for Mathematical Sciences, Lund University, P.O. Box 118, 221 00 Lund, Sweden
Palabras clave:article; conformational transition; death; developmental stage; evolutionary rate; insect development; life cycle stage; linear system; nonhuman; Poisson distribution; population dynamics; pupation; stochastic model; algorithm; animal; insect; population dynamics; statistics; theoretical model; Algorithms; Animals; Insects; Models, Theoretical; Population Dynamics; Stochastic Processes
Año:2014
Volumen:2014
DOI: http://dx.doi.org/10.1155/2014/873624
Título revista:The Scientific World Journal
Título revista abreviado:Sci. World J.
ISSN:1537744X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1537744X_v2014_n_p_Solari

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Citas:

---------- APA ----------
Solari, H.G. & Natiello, M.A. (2014) . Linear processes in stochastic population dynamics: Theory and application to insect development. The Scientific World Journal, 2014.
http://dx.doi.org/10.1155/2014/873624
---------- CHICAGO ----------
Solari, H.G., Natiello, M.A. "Linear processes in stochastic population dynamics: Theory and application to insect development" . The Scientific World Journal 2014 (2014).
http://dx.doi.org/10.1155/2014/873624
---------- MLA ----------
Solari, H.G., Natiello, M.A. "Linear processes in stochastic population dynamics: Theory and application to insect development" . The Scientific World Journal, vol. 2014, 2014.
http://dx.doi.org/10.1155/2014/873624
---------- VANCOUVER ----------
Solari, H.G., Natiello, M.A. Linear processes in stochastic population dynamics: Theory and application to insect development. Sci. World J. 2014;2014.
http://dx.doi.org/10.1155/2014/873624