A Multitype Branching Processes Approach to the Evolutionary Dynamics of Escape
Doktorsavhandling, 2007

Evolutionary dynamics of escape is a recent development in theoretical biology. It is an attempt to predict possible patterns of population dynamics for a certain strain of viruses placed in a hostile environment. The only way to escape extinction for the virus is to find a new form better adapted to the new environment. This is usually achieved by mutations in certain positions of the genome. In this thesis we use multitype Galton-Watson branching processes to model the evolution of such virus populations and provide answers to some of the most relevant questions arising in them. We determine the asymptotic probability of escape for a population stemming from a single progenitor. The calculations are obtained assuming mutations are rare events and generalize results previously known for particular reproduction laws. We also give a description of the random path to escape, that is the chain of mutations leading to the escape form of the virus. Using this description, we also study the waiting time to escape, i.e., the time it takes to produce the escape form of the virus. We start by deriving results for simple populations allowing for two-types of individuals and simple mutation schemes. Later we perform asymptotic analysis, again assuming mutations are rare, for populations with quite general reproduction and mutation schemes.

Galton-Watson branching processes

decomposable processes

extinction

multitype

waiting time to escape

population dynamics

path to escape

mutation

Pascal, Matematiska Vetenskaper, Chalmers Tvärgata 3, Chalmers tekniska högskola
Opponent: Professor Nikolay Yanev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria

Författare

Maria Conceicao Serra

Chalmers, Matematiska vetenskaper

Göteborgs universitet

Ämneskategorier

Beräkningsmatematik

ISBN

978-91-7291-997-6

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 2678

Pascal, Matematiska Vetenskaper, Chalmers Tvärgata 3, Chalmers tekniska högskola

Opponent: Professor Nikolay Yanev, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Bulgaria