Evolution is coupled with branching across many granularities of life.

Across many scales of life, the rate of evolutionary change is often accelerated at the time when one lineage splits into two. The emergence of novel protein function can be facilitated by gene duplication (neofunctionalization); rapid morphological change is often accompanied by speciation (punctuated equilibrium); and the establishment of cultural identity is frequently driven by sociopolitical division (schismogenesis). In each case, the changes resist re-homogenization; promoting assortment into distinct lineages that are susceptible to different selective pressures, leading to rapid divergence. The traditional gradualistic view of evolution struggles to detect this phenomenon. We propose a probabilistic framework that constructs phylogenies, tests for saltative branching and improves divergence time estimation by estimating the independent contributions of gradual and abrupt change on each lineage. We provide evidence of saltative branching for proteins (aminoacyl transfer RNA (tRNA) synthetases), animal morphologies (cephalopods) and human languages (Indo-European). These three cases provide unique insights: for aminoacyl-tRNA synthetases, the trees are substantially different from those obtained under gradualist models; we estimate that 99% of cephalopod morphological changes coincided with speciation events; and Indo-European dispersal is estimated to have started around 6000 BCE, corroborating the recently proposed hybrid explanation. Our open-source code is available under a General Public License.