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...
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1537744X_v2014_n_p_Solari http://hdl.handle.net/20.500.12110/paper_1537744X_v2014_n_p_Solari |
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paper:paper_1537744X_v2014_n_p_Solari2023-06-08T16:20:16Z Linear processes in stochastic population dynamics: Theory and application to insect development Solari, Hernán Gustavo Natiello, Mario Alberto 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. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1537744X_v2014_n_p_Solari 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, Hernán Gustavo Natiello, Mario Alberto 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. |
| author |
Solari, Hernán Gustavo Natiello, Mario Alberto |
| author_facet |
Solari, Hernán Gustavo Natiello, Mario Alberto |
| author_sort |
Solari, Hernán Gustavo |
| 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 |
| publishDate |
2014 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1537744X_v2014_n_p_Solari http://hdl.handle.net/20.500.12110/paper_1537744X_v2014_n_p_Solari |
| work_keys_str_mv |
AT solarihernangustavo linearprocessesinstochasticpopulationdynamicstheoryandapplicationtoinsectdevelopment AT natiellomarioalberto linearprocessesinstochasticpopulationdynamicstheoryandapplicationtoinsectdevelopment |
| _version_ |
1768546225886330880 |