EVOLUTIONARY DYNAMICS OF GENUS SIZE-FREQUENCY DISTRIBUTIONS

The frequency distribution of the number of species within a genus has received sporadic attention for decades, but models of this distribution have often been statistical rather than process-based. Here I present an evolutionary approach in the spirit of Patzkowsky's (1995, Paleobiology 21:440) hierarchical birth-death model. Only two parameters are needed to generate a size-frequency distribution: the ratio of species extinction rate to speciation rate, and the ratio of genus origination rate to speciation rate. For a given set of parameter values, the distribution stabilizes to the same form irrespective of the initial conditions; therefore, perturbations such as mass extinctions have only transient effects. Given a size-frequency distribution at an arbitrary moment of time, such as the present day, the evolutionary rates can be estimated via maximum likelihood. This can provide a cross-check against approaches that attempt to estimate speciation and extinction rates from evolutionary trees of living species. If incomplete sampling of species is incorporated into the model, the sampling probability and the true size-frequency distribution (i.e. the true evolutionary rates) can be jointly estimated from the observed, incomplete size-frequency distribution. Given the resulting applicability to paleontological data, it is possible to estimate species-level extinction rates from genus-level data at discrete events such as mass extinctions, and to assess selectivity of species extinction with respect to genus membership.