The species censorship problem: A general solution

The longevities of species constituting a statistical population have an underlying distribution whose form and parametric values reflect probabilities of origination and extinction through time. In the case that a part of the population is extant, the form of distribution and its parameters cannot be estimated directly from the longevity data without bias. Longevities of extant censored species are truncated and thus do not statistically represent the underlying distribution. The remaining uncensored species do not represent the true relative abundances of longevities. These biases can be defined from the probability densities for species longevitys and intervalr between successive originations of species. For realistic densities ofs andr, species with an intermediate longevity are preferentially censored. This simple, general result arises because the probability of censoring a species increases with its longevity, whereas the probability of censoring a given longevity varies with its relative abundance.