Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Branching Processes

  • Mikko J. Alava
  • Kent Bækgaard Lauritsen
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_43-3

Definition of the Subject

Consider the fate of a human population on a small, isolated island. It consists of a certain number of individuals, and the most obvious question, of importance in particular for the inhabitants of the island, is whether this number will go to zero. Humans die and reproduce in steps of one, and therefore one can try to analyze this fate mathematically by writing down what is called master equations, to describe the dynamics as a “branching process” (BP). The branching here means that if at time t = 0 there are N humans, at the next step t = 1 there can be N − 1 (or N + 1 or N + 2 if the only change from t = 0 was that a pair of twins was born). The outcome will depend in the simplest case on a “branching number” or the number of offsprings λ that a human being will have (Harris 1989; Kimmel and Axelrod 2002; Athreya and Ney 2004; Haccou et al. 2005).

If the offsprings created are too few, then the population will decay or reach an “absorbing state” out of...


Acoustic Emission Event Tauberian Theorem Sandpile Model Branch Process Avalanche Size Distribution 
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Applied PhysicsAalto UniversityEspooFinland
  2. 2.Research DepartmentDanish Meteorological InstituteCopenhagenDenmark