Figure 1.

Examples of four different types of probability densities and associated hyperparameters commonly used as priors on the ages of calibrated nodes when provided a minimum age estimate. The ages of the N = 10 tips (a₁,a₂,…,a₁₀) are known and indicated with black circles. The internal nodes are labeled N + 1,…,2N − 1 in postorder sequence. For the majority of empirical data sets, it is not possible to place a reliable age constraint on most internal nodes (white circles: a₁₁,a₁₃,a₁₄,a₁₆,a₁₈,a₁₉) and a general prior on branching times is assumed for uncalibrated internal nodes (e.g., birth–death process or uniformly distributed node times). Geological data can provide information that can be used to calibrate certain nodes (gray circles: a₁₂,a₁₅,a₁₇). Typically, a node is calibrated by placing a minimum age obtained from the oldest known descendant fossil taxon (gray arrows). Provided that the phylogenetic placement of the fossil is correct, the age of the calibrated node is assigned a prior distribution. This example shows four different prior densities for the age of calibrated node number 17 (separate priors can be specified for nodes 12 and 15 in the same manner). The gray dotted line indicates the minimum age constraint placed on the age of node 17 by the fossil descendant (gray arrow). Commonly used parametric distributions are offset by the minimum age provided by the fossil and each requires that hyperparameter values (in parentheses) be specified prior to analysis.