Abstract
In this paper we present novel results for di screte-ti me and Markovian continuous-time multitype branching processes. As a population develops, we are interested in the waiting time until a particular type of interest (such as an escape mutant) appears, and in how the distribution of individuals depends on whether this type has yet appeared. Specifically, both forward and backward equations for the distribution of type-specific population sizes over time, conditioned on the nonappearance of one or more particular types, are derived. In tandem, equations for the probability that one or more particular types have not yet appeared are also derived. Brief examples illustrate numerical methods and potential applications of these results in evolutionary biology and epidemiology.
| Original language | English |
|---|---|
| Pages (from-to) | 692-718 |
| Journal | Advances in Applied Probability |
| Volume | 45 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Sept 2013 |
Keywords / Materials (for Non-textual outputs)
- multitype brancing process
- probability generating function
- waiting time
- escape mutant
- evolutionary biology
- epidemiology