VMSTA Modern Stochastics: Theory and Applications 2351-6054 2351-6046 2351-6046 VTeX Mokslininkų g. 2A, 08412 Vilnius, Lithuania VMSTA0907 10.15559/vmsta0907 Research Article Studies on generalized Yule models https://orcid.org/0000-0003-1971-214X Polito Federico federico.polito@unito.it Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Torino, Italy 2018 3 12 2018 0 0 1 15 16 7 2018 10 11 2018 16 11 2018 © 2018 The Author(s). Published by VTeX 2018 Open access article under the CC BY license.

We present a generalization of the Yule model for macroevolution in which, for the appearance of genera, we consider point processes with the order statistics property, while for the growth of species we use nonlinear time-fractional pure birth processes or a critical birth-death process. Further, in specific cases we derive the explicit form of the distribution of the number of species of a genus chosen uniformly at random for each time. Besides, we introduce a time-changed mixed Poisson process with the same marginal distribution as that of the time-fractional Poisson process.

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