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We describe the speciation process with the FBD model conditioning on sampling at least one extant individual (equation ( 2 ) in Gavryushkina et al. 2014 ). This model assumes a constant rate birth–death process with birth rate $$\lambda$$ and death rate $$\mu$$ where fossils are sampled through time according to a Poisson process with a constant sampling rate $$\psi$$ and extant species are sampled at present with probability $$\rho$$ . The process starts at some time $$t_{\rm or}$$ in the past–-the time of origin, where time is measured as a distance from the present. This process produces species trees with sampled two-degree nodes which we call sampled ancestors (following Gavryushkina et al. 2013 ; 2014 ). Such nodes represent fossil samples and lie directly on branches in the tree. They are direct ancestors to at least one of the other fossils or extant taxa that has been sampled.

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