On the size distribution of live genera

Abstract

This article deals with the theoretical size (number of species) distribution of live genera, arising from a simple model of macroevolution in which speciations and extinctions are assumed to occur independently and at random, and in which new genera are formed by the random splitting of existing genera. Mathematically, the distribution is that of the state of a homogeneous birth-and-death process after an exponentially distributed time. An ordinary differential equation for the generating function of the distribution is derived and solved and a recurrence relation for computing the probabilities in the distribution presented. Some properties of the distribution, including asymptotic behavio..