Second-order approximations of ascertainment probabilities

A second-order correction is derived for the usual first-order order approximation to the probability of ascertaining a pedigree. Both the first- and second-order approximations are compared to the exact ascertainment probability for selected examples of monogenic and polygenic traits. The second-order approximation is shown to be accurate within 10% when the individual ascertainment probability is less than 0.2, for most cases examined. In all cases, the first- and second-order approximations provide upper and lower bounds, respectively, for the exact ascertainment probability.