Branching patterns in phylogenies cannot distinguish diversity-dependent diversification from time-dependent diversification

One of the primary goals of macroevolutionary biology has been to explain general trends in long-term diversity patterns, including whether such patterns correspond to an up-scaling of processes occurring at lower scales. Reconstructed phylogenies often show decelerated lineage accumulation over time. This pattern has often been interpreted as the result of diversity-dependent diversification, where the accumulation of species causes diversification to decrease through niche filling. However, other processes can also produce such a slowdown, including time-dependence without diversity-dependence. To test whether phylogenetic branching patterns can be used to distinguish these two mechanisms, we formulated a time-dependent, but diversity-independent model that matches the expected diversity through time of a diversity-dependent model. We simulated phylogenies under each model and studied how well likelihood methods could recover the true diversification mode. Standard model selection cri...