TY  - BOOK
AU  - Pardoux,Etienne
TI  - Probabilistic models of population evolution : : scaling limits, genealogies and interactions 
T2  - Mathematical Biosciences Institute lecture series
SN  - 9783319303260
U1  - 519.234 23
PY  - 2016///
CY  - Switzerland : 
PB  - Springer
KW  - Branching processes
N1  - 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
N2  - 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
ER  -