Branching Processes: The Long March from Simplistic Individualism to Collective Interaction
by Peter Jagers
Abstract: Branching processes arose in the 1800's as a theory describing reproduction of independently acting individuals of the simplest possible kind, characterized only by their reproduction numbers. Their XX:th
Century history can be viewed as a slow journey towards more and more refined modelling of individual behaviour, encompassing ultimately all other known population theories: individuals can be of various types, their life span distributions can take any forms and reproduction occur in multifarious ways.
Two great challenges remain (for the XXI:st Century!). One is that reproduction is still clonal; there is no mating. Another is that matters like resources and thus population size are not taken into account.
We have addressed this in two papers, presented at earlier Melbourne seminars, and now continue the work on (quasi-)stabilisation of the
age-distribution, during the long time such populations linger around the carrying capacity of their habitat.
This work is part of the Monash ARC DP Stochastic Populations: Theory and Applications (Coinvestigators: FC Klebaner and K Hamza).