Probabilistic models of population evolution : scaling limits, genealogies and interactions / Etienne Pardoux.
Material type:
TextSeries: Mathematical Biosciences Institute lecture series ; 1.6 | Stochastics in biological systemsPublication details: Switzerland : Springer, 2016.Description: viii, 125 pages : illustrations ; 24 cmISBN: - 9783319303260
- 519.234 23 P226
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 519.234 P226 (Browse shelf(Opens below)) | Available | 137781 |
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| 519.234 K27est Estimation theory for branching processes | 519.234 L693 Measure-valued branching Markov processes | 519.234 M689 Multitype branching processes | 519.234 P226 Probabilistic models of population evolution : | 519.234 R147 Random sums and branching stochastic processes | 519.234 R147 Random sums and branching stochastic processes | 519.234 W926 Trees |
Includes bibliographical references and index.
1. Introduction.-
2. Branching Processes.-
3. Convergence to a Continuous State Branching Process.-
4. Continuous State Branching Process (CSBP).-
5. Genealogies.-
6. Models of Finite Population with Interaction.-
7. Convergence to a Continuous State Model.-
8. Continuous Model with Interaction.-
Appendix.
This expository book presents the mathematical description of evolutionary models of populations subject to interactions (e.g. competition) within the population. The author includes both models of finite populations, and limiting models as the size of the population tends to infinity. The size of the population is described as a random function of time and of the initial population (the ancestors at time 0). The genealogical tree of such a population is given. Most models imply that the population is bound to go extinct in finite time. It is explained when the interaction is strong enough so that the extinction time remains finite, when the ancestral population at time 0 goes to infinity. The material could be used for teaching stochastic processes, together with their applications.
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