Estimating gene regulatory networks over biological lineages is central to a deeper understanding of how cells evolve during development and differentiation. However, one challenge in estimating such evolving networks is that their host cells not only contiguously evolve, but also branch over time. For example, a stem cell evolves into two more specialized daughter cells at each division, forming a tree of networks. Another example is in a laboratory setting: a biologist may apply several different drugs individually to malignant cancer cells to analyze the effects of each drug on the cells, the cells treated by one drug may not be intrinsically similar to those treated by another, but rather to the malignant cancer cells they were derived from.