Darwin's panoramic view of biology encompassed two metaphors: the phylogenetic tree, pointing to relatively linear (and divergent) complexity, and the tangled bank, pointing to reticulated (and convergent) complexity. The emergence of phylogenetic systematics half a century ago made it possible to investigate linear complexity in biology. Assumption 0, first proposed in 1986, is not needed for cases of simple evolutionary patterns, but must be invoked when there are complex evolutionary patterns whose hallmark is reticulated relationships. A corollary of Assumption 0, the duplication convention, was proposed in 1990, permitting standard phylogenetic systematic ontology to be used in discovering reticulated evolutionary histories. In 2004, a new algorithm, phylogenetic analysis for comparing trees (PACT), was developed specifically for use in analyses invoking Assumption 0. PACT can help discern complex evolutionary explanations for historical biogeographical, coevolutionary, phylogenetic, and tokogenetic processes.