Biodiversity on Earth is shaped by abiotic perturbations and rapid diversifications. At the same time, there are arguments that biodiversity is bounded and regulated via biotic interactions. Evaluating the role and relative strength of diversity regulation is crucial for interpreting the ongoing biodiversity changes. We have analyzed Phanerozoic fossil record using public databases and new approaches for identifying the causal dependence of origination and extinction rates on environmental variables and standing diversity. While the effect of environmental factors on origination and extinction rates is variable and taxon specific, the diversity dependence of the rates is almost universal across the studied taxa. Origination rates are dependent on instantaneous diversity levels, while extinction rates reveal delayed diversity dependence. Although precise mechanisms of diversity dependence may be complex and difficult to recover, global regulation of diversity via negative diversity dependence of lineage diversification seems to be a common feature of the biosphere, with profound consequences for understanding current biodiversity crisis.