Small population effects in stochastic population dynamics
The discreteness of units of small populations can produce large fluctuations from a classical continuous representation, especially when null populations play a crucial role. These belong to what are here referred to as emergent and evanescent species. A few model biological systems are introduced...
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| Published in | Bulletin of mathematical biology Vol. 67; no. 6; pp. 1173 - 1194 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
United States
Elsevier Ltd
01.11.2005
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
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| Abstract | The discreteness of units of small populations can produce large fluctuations from a classical continuous representation, especially when null populations play a crucial role. These belong to what are here referred to as emergent and evanescent species. A few model biological systems are introduced in which this is the case, as well as a toy model that suggests a path to avoid the associated mathematical complexities. The corresponding division into null and non-null population sectors is carried out to leading order for the model systems, with promising results. |
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| AbstractList | The discreteness of units of small populations can produce large fluctuations from a classical continuous representation, especially when null populations play a crucial role. These belong to what are here referred to as emergent and evanescent species. A few model biological systems are introduced in which this is the case, as well as a toy model that suggests a path to avoid the associated mathematical complexities. The corresponding division into null and non-null population sectors is carried out to leading order for the model systems, with promising results. The discreteness of units of small populations can produce large fluctuations from a classical continuous representation, especially when null populations play a crucial role. These belong to what are here referred to as emergent and evanescent species. A few model biological systems are introduced in which this is the case, as well as a toy model that suggests a path to avoid the associated mathematical complexities. The corresponding division into null and non-null population sectors is carried out to leading order for the model systems, with promising results.[PUBLICATION ABSTRACT] |
| Author | Percus, Jerome K. |
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| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/16005504$$D View this record in MEDLINE/PubMed |
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| DOI | 10.1016/j.bulm.2005.01.005 |
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| References | Erdi, Toth (b1) 1988 Nowak, Krakauer, Klug, May (b6) 1998; 1 Jilbert, Miller, Scougall, Turnbull, Burrell (b4) 1996; 226 Gardiner (b2) 1983 Harrison, Chan, Prussiner, Cohen (b3) 2001; 10 McQuarrie (b5) 1967; 4 Van Kampen (b9) 1981 Srivastava, You, Summers, Yin (b7) 2002; 218 Stone, Shulgin, Agur (b8) 2000; 31 |
| References_xml | – volume: 4 start-page: 413 year: 1967 end-page: 478 ident: b5 article-title: Stochastic approach to chemical kinetics publication-title: J. Appl. Probab. contributor: fullname: McQuarrie – volume: 1 start-page: 3 year: 1998 end-page: 15 ident: b6 article-title: Prion infection dynamics publication-title: Integr. Biol. contributor: fullname: May – volume: 226 start-page: 338 year: 1996 end-page: 345 ident: b4 article-title: Kinetics of duck hepatitis B infection publication-title: Virology contributor: fullname: Burrell – volume: 31 start-page: 207 year: 2000 end-page: 215 ident: b8 article-title: Theoretical examination of the pulse vaccination policy in the SIR epidemic model publication-title: Math. Comput. Modelling contributor: fullname: Agur – volume: 218 start-page: 309 year: 2002 end-page: 321 ident: b7 article-title: Stochastic vs deterministic modelling of intracellular viral kinetics publication-title: J. Theor. Biol. contributor: fullname: Yin – year: 1988 ident: b1 article-title: Mathematical Models of Chemical Reaction contributor: fullname: Toth – volume: 10 start-page: 819 year: 2001 end-page: 835 ident: b3 article-title: Conformational propagation and prion-like characteristic publication-title: Protein Sci. contributor: fullname: Cohen – year: 1983 ident: b2 article-title: Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences contributor: fullname: Gardiner – year: 1981 ident: b9 article-title: Stochastic Processes in Physics and Chemistry contributor: fullname: Van Kampen |
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| SubjectTerms | Ecosystem Models, Biological Population Dynamics Stochastic Processes |
| Title | Small population effects in stochastic population dynamics |
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