Diversification rates are estimated from phylogenies, typically without fossils, except in paleontological studies. By nature, rate estimations depend heavily on the time data provided in phylogenies, which are divergence times and (when used) fossil ages. Among these temporal data, fossil ages are by far the most precisely known (divergence times are inferences calibrated with fossils). We propose a method to compute the likelihood of a phylogenetic tree with fossils in which the only known time information is the fossil ages. Testing our approach on simulated data shows that the maximum likelihood rate estimates from the phylogenetic tree shape and the fossil dates are almost as accurate as the ones obtained by taking into account all the data, including the divergence times. Moreover they are substantially more accurate than the estimates obtained only from the exact divergence times (without taking into account the fossil record).
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