Global species counts are a key measure of biodiversity and associated metrics of conservation. It is both scientifically and practically important to know how many species exist, how many undescribed species remain, and where they are found. We modify a model for the number of undescribed species using species description data and incorporating taxonomic information. We assume a Poisson distribution for the number of species described in an interval and use maximum likelihood to estimate parameter values of an unknown intensity function. To test the model's performance, we performed a simulation study comparing our method to a previous model under conditions qualitatively similar to those related to mammal species description over the last two centuries. Because our model more accurately estimates the total number of species, we predict that 5% of mammals remain undescribed. We applied our model to determine the biogeographic realms which hold these undescribed species.