A general expression for the likelihood of a set of phenotypic observations on a randomly sampled pedigree, suitable for a wide variety of genetic models, has been previously modified to allow for independent ascertainments via probands. In this paper, further allowance is made for the fact that a pedigree usually contains some individuals who, whatever their phentoype, could never be probands, and we derive the limiting form of the likelihood appropriate for single ascertainment. The case when the sampling frame is ill-defined is discussed, and suggestions made for how to proceed in such a case.
