We develop a new tree-free phylodynamic method to estimate the reproduction number (R0) of a pathogen from large numbers of sequences of a pathogen. It is based on the convergence of the cherry-to-tip ratio (CTR) to a constant depending on R0 in supercritical branching trees. It is a tree-free method because tree reconstruction is not required: the number of cherries and the CTR is estimated directly from the sequences using the new computational method Cherries Without Tree (CWT). With simulations, we compare CWT to other methods currently in use. We use the new inference method to estimate R0 from simulated sequences and discuss its accuracy. We explore the potential bias arising from sub-sampling.