title: Time to a single hybridization event in a group of species with unknown ancestral history.
abstract: We consider a stochastic process for the generation of species which combines a Yule process with a simple model for hybridization between pairs of co-existent species. We assume that the origin of the process, when there was one species, occurred at an unknown time in the past, and we condition the process on producing n species via the Yule process and a single hybridization event. We prove results about the distribution of the time of the hybridization event. In particular we calculate a formula for all moments and show that under various conditions, the distribution tends to an exponential with rate twice that of the birth rate for the Yule process.
authors: Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Gothenburg, Sweden.
authors: Krzysztof
authors: K
authors: Bartoszek
authors: Graham
authors: G
authors: Jones
authors: Bengt
authors: B
authors: Oxelman
authors: Serik
authors: S
authors: Sagitov
mesh_terms: D000818:Animals; D049810:Genetic Speciation; D006824:Hybridization, Genetic; D008957:Models, Genetic; D010802:Phylogeny; D011123:Polyploidy; D013045:Species Specificity; D013269:Stochastic Processes; D013997:Time Factors