Abstract
Phylogenies may be modelled using “birth-death” models for speciation and extinction, but even when a homogeneous rate of diversification is used, survivorship biases can generate remarkable rate heterogeneities through time. One such bias has been termed the “push of the past”, by which the length of time a clade has survived is conditioned on the rate of diversification that happened to pertain at its origin. This creates the illusion of a secular rate slow-down through time that is, rather, a reversion to the mean. Here we model the controls on the push of the past, and the effect it has on clade origination times, and show that it largely depends on underlying extinction rates. An extra effect increasing early rates of lineage generation is also seen in large clades. These biases are important but relatively neglected influences on many aspects of diversification patterns, such as diversification spikes after mass extinctions and at the origins of clades; they also influence rates of fossilisation, changes in rates of phenotypic evolution and even molecular clocks. These inevitable features of surviving and/or large clades should thus not be generalised to the diversification process as a whole without additional study of small and extinct clades.
