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A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations
We develop mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we formulate a complete kinetic framework for age-structured interacting populations undergoing birth, death and fission processes in spatially dependent environment...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer US
2016
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4894939/ https://www.ncbi.nlm.nih.gov/pubmed/27335505 http://dx.doi.org/10.1007/s10955-016-1524-x |
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author | Chou, Tom Greenman, Chris D. |
author_facet | Chou, Tom Greenman, Chris D. |
author_sort | Chou, Tom |
collection | PubMed |
description | We develop mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we formulate a complete kinetic framework for age-structured interacting populations undergoing birth, death and fission processes in spatially dependent environments. We define the full probability density for the population-size age chart and find results under specific conditions. Connections with more classical models are also explicitly derived. In particular, we show that factorial moments for non-interacting processes are described by a natural generalization of the McKendrick-von Foerster equation, which describes mean-field deterministic behavior. Our approach utilizes mixed-type, multidimensional probability distributions similar to those employed in the study of gas kinetics and with terms that satisfy BBGKY-like equation hierarchies. |
format | Online Article Text |
id | pubmed-4894939 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2016 |
publisher | Springer US |
record_format | MEDLINE/PubMed |
spelling | pubmed-48949392016-06-20 A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations Chou, Tom Greenman, Chris D. J Stat Phys Article We develop mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we formulate a complete kinetic framework for age-structured interacting populations undergoing birth, death and fission processes in spatially dependent environments. We define the full probability density for the population-size age chart and find results under specific conditions. Connections with more classical models are also explicitly derived. In particular, we show that factorial moments for non-interacting processes are described by a natural generalization of the McKendrick-von Foerster equation, which describes mean-field deterministic behavior. Our approach utilizes mixed-type, multidimensional probability distributions similar to those employed in the study of gas kinetics and with terms that satisfy BBGKY-like equation hierarchies. Springer US 2016-05-14 2016 /pmc/articles/PMC4894939/ /pubmed/27335505 http://dx.doi.org/10.1007/s10955-016-1524-x Text en © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
spellingShingle | Article Chou, Tom Greenman, Chris D. A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations |
title | A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations |
title_full | A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations |
title_fullStr | A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations |
title_full_unstemmed | A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations |
title_short | A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations |
title_sort | hierarchical kinetic theory of birth, death and fission in age-structured interacting populations |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4894939/ https://www.ncbi.nlm.nih.gov/pubmed/27335505 http://dx.doi.org/10.1007/s10955-016-1524-x |
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