When assessing distribution range shifts, precise information is required on distribution limits, densities in occupied regions, unoccupied gaps, and changes in these measures over time. The local convex hull method recently developed for home range delineation to provide these measures was compared with that of the widely applied parametric kernel density estimation and with the commonly used tile method. The assessment used location records from 14 years of aerial surveys on four mammalian herbivores selected because of their distinct distribution patterns. Impala showed an almost continuous distribution with few gaps, wildebeest a wide distribution with regional concentrations, waterbuck a linear distribution along rivers, and sable antelope a widespread but patchy distribution. The kernel method tended to extend ranges beyond observed records, obscuring gaps within distributions. With parametric kernel approaches, bandwidth obtained via Least Squares Cross Validation techniques was not optimal when the local abundance was widely disparate, as was the case for wildebeest. The LoCoH method most effectively revealed meaningful gaps. The LoCoH method is advantageous for precisely mapping the distributions of conspicuous species for which the absence of records indicates true gaps in occurrence.