  For taxonomic levels higher than species, the abundance distributions of
number of subtaxa per taxon tend to approximate power laws, but often show
strong deviationns from such a law. Previously, these deviations were
attributed to finite-time effects in a continuous time branching process at the
generic level. Instead, we describe here a simple discrete branching process
which generates the observed distributions and find that the distribution's
deviation from power-law form is not caused by disequilibration, but rather
that it is time-independent and determined by the evolutionary properties of
the taxa of interest. Our model predicts-with no free parameters-the
rank-frequency distribution of number of families in fossil marine animal
orders obtained from the fossil record. We find that near power-law
distributions are statistically almost inevitable for taxa higher than species.
The branching model also sheds light on species abundance patterns, as well as
on links between evolutionary processes, self-organized criticality and
fractals.
