We extend the infinite-allele simple branching process of Griffiths and Pakes (1988) allowing the offspring to change types and labels. The model is developed and limit theorems are given for the growth of the number of labels of a specific type. We also discuss the asymptotics of the frequency spectrum. Finally, we present an application of the model's use in tumorigenesis.
"A multitype infinite-allele branching process with applications to cancer evolution." J. Appl. Probab. 52 (3) 864 - 876, September 2015. https://doi.org/10.1239/jap/1445543852