The reconstructed evolutionary process with the fossil record

► We give a model of the reconstructed process from extant taxa and the fossil record. ► We show that it is a nonhomogeneous birth-and-death process. ► Its rates are expressed from time and speciation, extinction and fossil find rates. ► We give a formula for the likelihood of a realization of this reconstructed process. ► Simulations show that fossils improve speciation and extinction rate estimates.