  We introduce a model for the evolution of species triggered by generation of
novel features and exhaustive combination with other available traits. Under
the assumption that innovations are rare, we obtain a bursty branching process
of speciations. Analysis of the trees representing the branching history
reveals structures qualitatively different from those of random processes. For
a tree with n leaves, the average distance of leaves from root scales as (log
n)^2 to be compared to log n for random branching. The mean values and standard
deviations for the tree shape indices depth (Sackin index) and imbalance
(Colless index) of the model are compatible with those of real phylogenetic
trees from databases. Earlier models, such as the Aldous' branching (AB) model,
show a larger deviation from data with respect to the shape indices.
