Books  Data Analysis & Modelling  Modelling 

Probabilistic Models of Population Evolution: Scaling Limits, Genealogies and Interactions

New

Series: Stochastics in Biological Systems Volume: 1.6

By: Étienne Pardoux (Author)

133 pages, 2 colour & 4 b/w illustrations, 4 colour tables

Springer-Verlag

Paperback | Jun 2016 | #232585 | ISBN-13: 9783319303260
Availability: Usually dispatched within 1-2 weeks Details
NHBS Price: £24.99 $32/€30 approx

About this book

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.


Contents

- Introduction
- Branching Processes
- Convergence to a Continuous State Branching Process
- Continuous State Branching Process (CSBP)
- Genealogies
- Models of Finite Population with Interaction
- Convergence to a Continuous State Model
- Continuous Model with Interaction
- Appendix


Write a review

There are currently no reviews for this product. Be the first to review this product!


Biography

Étienne Pardoux is Professor at Aix-Marseille University, working in the field of Stochastic Analysis, in particular Stochastic partial differential equations. He obtained his PhD in 1975 at University of Paris-Sud.

Bestsellers in this subject