Studies on generalized Yule models
Volume 6, Issue 1 (2019), pp. 41–55
Pub. online: 3 December 2018
Type: Research Article
Open Access
Open Access
Received
16 July 2018
16 July 2018
Revised
10 November 2018
10 November 2018
Accepted
16 November 2018
16 November 2018
Published
3 December 2018
3 December 2018
Abstract
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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