Figure 3. Extinction probabilities are independent of the tree and diversification-rate shifts on observed lineages. Let's try to imagine the birth-death process that produced this observed tree. At time t1 we observe a speciation event resulting in node N. The speciation event produces a left and right daughter lineage. To compute the probability of observing this speciation event, we need to compute the probability of a speciation event at time t1 and the probability that both daughter lineages survive. Clearly, the survival probabilities (i.e., 1 – extinction probability) of both daughter lineages must be equivalent because both daughter lineages start in the blue rate category. At time t1 we do not know the fate of the daughter lineages (e.g., if diversification-rate shifts will occur on either lineage); thus, if we were to simulate a process for both daughter lineages, they would both have the same probability of ultimate extinction.