Understanding the rules of macroevolution remains an important topic of biological research. Phylogenetic trees serve as an estimated macroevolutionary relationship structure, usually obtained directly from molecular data. In this work, we first reanalyse such tree structures and report scaling laws which have not been explained yet by branching models with biological interpretation. We propose a one-parameter family of branching models, in which branching probability depends on the age of the species, and investigate it analytically and computationally, exploring the transitions among different behaviors. We identify a member of the family producing scaling laws similar to the empirically observed ones.