caa a22 4500 445329807 CHVBK 20180317142733.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s00285-010-0362-8 doi (NATIONALLICENCE)springer-10.1007/s00285-010-0362-8 Jones Graham 21e Balnakeil, Durness, Lairg, IV27 4PT, Sutherland, UK aut Calculations for multi-type age-dependent binary branching processes [Elektronische Daten] [Graham Jones] This article provides a method for calculating the joint probability density for the topology and the node times of a tree which has been produced by an multi-type age-dependent binary branching process and then sampled at a given time. These processes are a generalization, in two ways, of the constant rate birth-death process. There are a finite number of types of particle instead of a single type: each particle behaves in the same way as all others of the same type, but different types can behave differently. Secondly, the lifetime of a particle (before it either dies, changes to another type, or splits into 2) follows an arbitrary distribution, instead of the exponential lifetime in the constant rate case. Two applications concern models for macroevolution: the particles represent species, and the extant species are randomly sampled. In one application, 1-type and 2-type models for macroevolution are compared. The other is aimed at Bayesian phylogenetic analysis where the models considered here can provide a more realistic and more robust prior distribution over trees than is usually used. A third application is in the study of cell proliferation, where various types of cell can divide and differentiate. Springer-Verlag, 2010 Tree nationallicence Tree shape nationallicence Branching process nationallicence Bellman-Harris nationallicence Bayesian phylogenetic analysis nationallicence Macroevolution nationallicence Cell proliferation nationallicence Journal of Mathematical Biology Springer-Verlag 63/1(2011-07-01), 33-56 0303-6812 63:1<33 2011 63 285 https://doi.org/10.1007/s00285-010-0362-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00285-010-0362-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Jones Graham 21e Balnakeil, Durness, Lairg, IV27 4PT, Sutherland, UK aut NATIONALLICENCE 773 0- Journal of Mathematical Biology Springer-Verlag 63/1(2011-07-01), 33-56 0303-6812 63:1<33 2011 63 285 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer