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High-throughput sequencing projects generate genome-scale sequence data for species-level phylogenies^{, –}. However, state-of-the-art Bayesian methods for inferring timetrees are computationally limited to small datasets and cannot exploit the growing number of available genomes. In the case of mammals, molecular-clock analyses of limited datasets have produced conflicting estimates of clade ages with large uncertainties^,, and thus the timescale of placental mammal evolution remains contentious^{, , –}. Here we develop a Bayesian molecular-clock dating approach to estimate a timetree of 4,705 mammal species integrating information from 72 mammal genomes. We show that increasingly larger phylogenomic datasets produce diversification time estimates with progressively smaller uncertainties, facilitating precise tests of macroevolutionary hypotheses. For example, we confidently reject an explosive model …