%0 Journal Article %1 alexander2013conditional %A Alexander, H. K. %D 2013 %I Applied Probability Trust %J Adv. in Appl. Probab. %K branching_processes conditioned_branching_processes hitting_times multitype_branching waiting_times %N 3 %P 692--718 %R 10.1239/aap/1377868535 %T Conditional distributions and waiting times in multitype branching processes %U http://dx.doi.org/10.1239/aap/1377868535 %V 45 %X In this paper we present novel results for discrete-time 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.

@article{alexander2013conditional, abstract = {In this paper we present novel results for discrete-time 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.}, added-at = {2015-03-04T18:50:09.000+0100}, author = {Alexander, H. K.}, biburl = {https://www.bibsonomy.org/bibtex/2dcbac2746795e2be65bddd8e6d2973f4/peter.ralph}, doi = {10.1239/aap/1377868535}, fjournal = {Advances in Applied Probability}, interhash = {285018bb4479cd7167fafdebdb0e803b}, intrahash = {dcbac2746795e2be65bddd8e6d2973f4}, journal = {Adv. in Appl. Probab.}, keywords = {branching_processes conditioned_branching_processes hitting_times multitype_branching waiting_times}, month = {09}, number = 3, pages = {692--718}, publisher = {Applied Probability Trust}, timestamp = {2015-03-04T18:50:09.000+0100}, title = {Conditional distributions and waiting times in multitype branching processes}, url = {http://dx.doi.org/10.1239/aap/1377868535}, volume = 45, year = 2013 }