Computational methods for a specific class of size-independent branching processes called Markovian binary trees (MBTs) have been developed recently. The corresponding computational methods, which are called matrix analytic methods, focus on algorithms that have a clear probabilistic interpretation. The aim of this project is to adapt these computational methods to address fundamental questions on population-size-dependent branching processes (PSDBPs). In particular, the project will focus on general birth-and-death processes with a carrying capacity whose birth and death rates depend on current population sizes and on MBTs with population-size-dependent transition rates.
The University of Melbourne
Minyuan Li is a third-year Bachelor of Science student at the University of Melbourne, majoring in mathematics and statistics. She enjoys solving mathematical problems, particularly in the area of statistics and stochastic processes. Last year, Minyuan completed a supervised summer project in applied probability, which involved investigating the properties of probabilistic models using mathematical software. The experience gave her the opportunity to develop an interest in mathematical research and motivated her to pursue further studies in the areas related to mathematics.