Abstract Aim Tests for faunal relaxation in reserves, particularly for mammals, have relied on comparisons of current species richness with estimates of species richness derived from historical range maps. However, any range map reflects the extent of occurrence of species and not necessarily the area of occupancy. Thus, estimates of historical species richness might be prone to error introduced by ‘false positives’, that is, a species might be considered to have been present in locations where it actually was not. The effect of such ‘false positives’ could bias statistical tests of faunal relaxation to type I error, and result in estimates of the extent of faunal relaxation in reserves greater than was actually the case. We evaluated the potential for errors in historical range maps to generate inflated estimates of historical species richness of mammals at sites that are reserves today. Location Canadian national parks in the Canadian portion of the Alleghenian--Illinoian mammal province in south-eastern Canada (the maritime region and parts of southern Québec, Ontario and Manitoba). Methods The effect of varying levels of error in range maps on estimates of historical species richness was tested using geographical information systems (GIS)-based statistical sampling of simulated historical ranges. Species’ areas of occupancy were simulated to be only 25%, 75% and 95% of published historical species ranges. For each reserve, estimates of historical species richness from these simulated species ranges were then compared with similar, previously published estimates of richness based on published historical species ranges. Results Previous estimates of historical species richness for reserves were inversely and linearly related to the degree of inaccuracy of species ranges. If species ranges were, on average, 5% smaller than the accepted ranges, then estimates of historical species richness agreed with previous estimates in c. 90% of cases. However, if historical ranges were, on average, 25% smaller than those used in previous analyses, then previous historical estimates of species richness may be overestimates in c. 40% of cases. Main conclusions Estimates of the extent of faunal relaxation in reserves that use historical range maps to quantify past species richness appear to be sensitive to even small errors in the degree to which range maps may overestimate ‘area of occupancy’.