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Multitype infinite-allele branching processes in continuous time

  • Thomas O. McDonald (a1) and Marek Kimmel (a2)


We introduce extensions to an infinite-allele branching process that allows for multiple types to exist alongside labels. We consider a Markov branching process and general branching process under different assumptions, and show asymptotic results about the growth of the labels as well as the frequency spectrum. These results are motivated by two separate models. The Markov binary splitting results are motivated by a model of clonal evolution in cancer that considers the effect of both driver and passenger mutations on tumor growth. The general process has applications in viral reproduction and dynamics.


Corresponding author

*Current address: Department of Biostatistics and Computational Biology, Mailstop CLS-11054, Dana-Farber Cancer Institute, 450 Brookline Avenue, Boston, MA 02115, USA. Email address:
** Postal address: Department of Statistics, Rice University, MS-138, PO Box 1892, Houston, TX 77251-1892, USA. Email address:


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Multitype infinite-allele branching processes in continuous time

  • Thomas O. McDonald (a1) and Marek Kimmel (a2)


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