Linear processes in stochastic population dynamics: Theory and application to insect development

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...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Solari, H.G., Natiello, M.A.
Formato: JOUR
Materias:
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
statistics
theoretical model
Algorithms
Animals
Insects
Models, Theoretical
Population Dynamics
Stochastic Processes
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_1537744X_v2014_n_p_Solari
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_1537744X_v2014_n_p_Solari
record_format dspace
spelling todo:paper_1537744X_v2014_n_p_Solari2023-10-03T16:21:56Z Linear processes in stochastic population dynamics: Theory and application to insect development Solari, H.G. Natiello, M.A. 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 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. Fil:Solari, H.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Natiello, M.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_1537744X_v2014_n_p_Solari
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic 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
spellingShingle 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
Solari, H.G.
Natiello, M.A.
Linear processes in stochastic population dynamics: Theory and application to insect development
topic_facet 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
description 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.
format JOUR
author Solari, H.G.
Natiello, M.A.
author_facet Solari, H.G.
Natiello, M.A.
author_sort Solari, H.G.
title Linear processes in stochastic population dynamics: Theory and application to insect development
title_short Linear processes in stochastic population dynamics: Theory and application to insect development
title_full Linear processes in stochastic population dynamics: Theory and application to insect development
title_fullStr Linear processes in stochastic population dynamics: Theory and application to insect development
title_full_unstemmed Linear processes in stochastic population dynamics: Theory and application to insect development
title_sort linear processes in stochastic population dynamics: theory and application to insect development
url http://hdl.handle.net/20.500.12110/paper_1537744X_v2014_n_p_Solari
work_keys_str_mv AT solarihg linearprocessesinstochasticpopulationdynamicstheoryandapplicationtoinsectdevelopment
AT natielloma linearprocessesinstochasticpopulationdynamicstheoryandapplicationtoinsectdevelopment
_version_ 1782029854030430208

Ejemplares similares