A linear-time algorithm to sample the dual-birth model

The ability to sample models of tree evolution is essential in the analysis and interpretation of phylogenetic trees. The dual-birth model is an extension of the traditional birth-only model and allows for sampling trees of varying degrees of balance. However, for a tree with n leaves, the tree sampling algorithm proposed in the original paper is O(n log n). I propose an algorithm to sample trees under the dual-birth model in O(n), and I provide a fast C++ implementation of the proposed algorithm.