  Simple stochastic models for phylogenetic trees on species have been well
studied. But much paleontology data concerns time series or trees on
higher-order taxa, and any broad picture of relationships between extant groups
requires use of higher-order taxa. A coherent model for trees on (say) genera
should involve both a species-level model and a model for the classification
scheme by which species are assigned to genera. We present a general framework
for such models, and describe three alternate classification schemes. Combining
with the species-level model of Aldous-Popovic (2005), one gets models for
higher-order trees, and we initiate analytic study of such models. In
particular we derive formulas for the lifetime of genera, for the distribution
of number of species per genus, and for the offspring structure of the tree on
genera.
